强∑~*空间是D空间

研究了强∑^＊空间和D空间的关系，证明了强∑^＊空间是D空间，改进了R．Z．Buzyakova等的结果．

Visualization of uncertainty associated with spatial prediction of continuous variables using HSI color model:a case study of prediction of pH for topsoil in peri-urban Beijing,China

Hue-Saturation-Intensity （HSI） color model, a psychologically appealing color model, was employed to visualize uncertainty represented by relative prediction error based on the case of spatial prediction of pH of topsoil in the peri-urban Beijing. A two-dimensional legend was designed to accompany the visualization-vertical axis （hues） for visualizing the predicted values and horizontal axis （whiteness） for visualizing the prediction error. Moreover, different ways of visualizing uncertainty were briefly reviewed in this paper. This case study indicated that visualization of both predictions and prediction uncertainty offered a possibility to enhance visual exploration of the data uncertainty and to compare different prediction methods or predictions of totally different variables. The whitish region of the visualization map can be simply interpreted as unsatisfactory prediction results, where may need additional samples or more suitable prediction models for a better prediction results.

Positioning planning of high-intensity-focused ultrasound surgery platform using Bezier curve

A positioning volume ellipsoid method is proposed to represent tumor volume in the workspace of a high-intensity-focused ultrasound (HIFU) surgery platform during the platform's positioning motion. To this simplified tumor model, a nearest neighbor search method is used to determine intermediate configuration and goal configuration, which the treatment head and ultrasound focus must pass in their localization to target volume. Based on the decided configurations, the continuity condition of combined Bezier curve in Euclidean space and De Casteljau algorithm on Lie group SO(3) are integrated to construct a combined Bezier positioning path of C2 continuity at junctional configuration, and an illustration of different positioning path planning is analyzed based on a liver tumor case.

Coastal Erosion Along the West Coast of the Taiwan Strait and It’s Influencing Factors

Based on the field surveys and repeated cross-profile observations combined with the comparison of many years’ topog-raphic maps,this study shows the spatial variability and varying patterns of coastal erosion along the west coast of the Taiwan Strait.Regional differentiation in the Meso-Cenozoic coastal tectonics determined the irregular coastline and geological background for large-scale coastal erosion distribution.The intensity of coastal erosion on the west side of the Taiwan Strait is mild in the northern region,severe in the central region and modest in the southern region.The beaches along the coast are mainly backed by dunes,sea-walls or cliffs.The dunes and beaches show periodic erosion and recovery along the coast adjacent to river mouths,while persistent retreat of frontal dunes and beaches tends to occur in other areas.The beach erosion occurs mainly in front of seawalls.Due to the low strength of the unconsolidated sediment the soft cliffs suffer the severest coastline recession.Sea level rise and river sediment discharge reduction are main causes of coastal erosion.Storm surge is common in the studied area and plays an important role in the progress of coastal erosion.Human activities including coastal constructions and sand mining also tend to interfere strongly with the balance of sediment budget in some coastal cells.

State Space-Time and Four States of Universe

All things in the universe possess a state and characteristics of state, resultantly in presence of space-time, which is perceived by human beings. An outlook of space-time is shaped in human by perceiving the existence and change of objects. The state space is all state characteristics exhibited in objects whilst the state time refers to the duration of an object＇s state. The time is a spatial property and not an independent dimension. The state space-time is a unity of internal and external space-time. The internal space-time is stemmed from the overall internal forces and internal energies and is a covert space-time. The external space-time refers to a space-time manifested by the external characteristics and movement of an object and is an overt space-time. In physics, there are four kinds of forces and four state space-times： bonding force and three-dimensional space-time; strong interaction of exchangeable n meson and two-dimensional space-time; quark confinement and one-dimensional space-time; and weak interaction and zero-dimensional space-time. The universe is constituted by dissimilar state space-times. Newton space-time is a three-dimensional state space-time; Einstein＇s theory of relativity is a two-dimensional state space-time. Newton and Einstein were different observers. Temporal and spatial perception of human is dependent upon human＇s intemal energy and quality. Through Qigong exercises, the human is able to enter the three-dimensional, two-dimensional, one-dimensional and zero-dimensional space-times. The relativity theory of human body will solve the time problems at the interplanetary voyage of astronauts.

K-very Smooth Banach Spaces

We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions.

Selective transmission and channel estimation in massive MIMO systems

Massive MIMO systems have got extraordinary spectral efficiency using a large number of base station antennas,but it is in the challenge of pilot contamination using the aligned pilots.To address this issue,a selective transmission is proposed using time-shifted pilots with cell grouping,where the strong interfering users in downlink transmission cells are temporally stopped during the pilots transmission in uplink cells.Based on the spatial characteristics of physical channel models,the strong interfering users are selected to minimize the inter-cell interference and the cell grouping is designed to have less temporally stopped users within a smaller area.Furthermore,a Kalman estimator is proposed to reduce the unexpected effect of residual interferences in channel estimation,which exploits both the spatial-time correlation of channels and the share of the interference information.The numerical results show that our scheme significantly improves the channel estimation accuracy and the data rates.

A MULTI-CRC SELECTIVE HARQ SCHEME FOR MIMO SYSTEMS

A multi-Cyclic Redundancy Check (CRC) selective Hybrid Automatic-Repeat-reQuest (HARQ) scheme for improving the throughput efficiency of Multiple Input Multiple Output (MIMO) systems is proposed in this paper. According to different feedback information from the receiver, the proposed HARQ scheme employs two strategies, referred to as retransmission frame selection and space diversity. These two strategies decrease the successive frame errors upon retransmission. Theoretic analysis and computer simulation results show that this HARQ scheme achieves higher throughput than the existing HARQ schemes even in poor conditions of low Signal-to-Noise Ratio (SNR).

Design and implementation of square Helmholtz coil for uniform magnetic field generation

In order to calibrate electrical instruments and generate a constant magnetic field, a novel design method for square Helmholtz coil is proposed. According to the superposition principle in electromagnetics, the theory of the square Helmholtz coil is established, and the design method is verified by Matlab calculation. Compared with conventional circular Helmholtz coil, the novel square one is with a larger uniform region. Simulation work is conducted in Maxwell, and the distribution of the magnetic field is obtained. The results demonstrate the validation of the applied calculation method of the proposed Helmholtz model. The space utilization rate η is used to make a comparison between the square and circular coils for the uniform region. The square Helmholtz coil is fabricated, the length of a single square coil is 1.5 m, and the amplitude of the magnetic field is controlled by the current. The GSM-19 T proton magnetometer is used to measure the amplitude of the magnetic field generated by the square Helmholtz coil. Experimental results indicate that a wide-range variable uniform magnetic field from 0 to 120 μT is generated in the center of Helmholtz coils.

Edge Enhancement for Remote Sensing Image Using Norm Algorithm in L_2 Vector Space

The Householder transformation-norm structure function in L2 vector space of linear algebra is introduced, and the edge enhancement for remote sensing images is realized. The experiment result is compared with traditional Laplacian and Sobel edge enhancements and it shows that the effect of the new method is better than that of the traditional algorithms.

On the Smallest Base of the Stone Space

In this paper,first we define the concept of strong open set for topological space. Then we prove: 1 ) a distributive lattice L possesses the smallest set of generating elements if and only if the Stone space (L) of L possesses a smallest base constructed by strong open sets; 2) a Bollean lattice B possesses the smallest set of generating elements if and only if B is a finite Boolean lattice.

Damage Pattern Recognition of Spatially Distributed Slope Damages and Rainfall Using Optimal GIS Mesh Dimensions

Damage assessment for slopes using geographical information system(GIS) has been actively carried out by researchers working on several government organizations and research institutes in Korea. In this study, 596 slope damages were examined to identify the types of damage associated with dip angles, dip directions, and heavy rainfall resulting from typhoons in South Korea. Heavy rainfall of 100 mm to 300 mm resulted in 80% at the investigated slope damages. A GIS database was developed for highways, rainfall, soil or rock geometry, and types of damage. A grid of rainfall intensity was generated from the records of maximum daily rainfall. Contours for slope damages and heavy rainfall using optimal GIS mesh dimensions were generated to visualize damage patterns and show substantially strong correlation of rainfall with slope damages. The combination of remote sensing with the GIS pattern recognition process described in this work are being expanded for a new generation of emergency response and rapid decision support systems.

Site-Dependent TERS Study of a Porphyrin Molecule on Ag(100) at 7 K

Single-molecule tip-enhanced Raman spectroscopy(TERS)has emerged as an important technique for structural analysis at sub-molecular scale.Here in this work,we report a TERS study of an isolated free-base porphyrin molecule adsorbed on the Ag(100)surface at cryogenic temperature(~7 K).Site-dependent TERS spectra reveal distinct local vibrational information for the chemical constituents within a single molecule.Moreover,distinct spatial features among different Raman peaks can be resolved from the TERS mapping images.These images are found to associate with related vibrational modes,enabling to resolve the mode associated with N-H bonds at the sub-nanometer level.This study will provide deep insights into the symmetry of adsorption configurations and local vibrational information within a single molecule.

Study on Potential Strong Earthquake Risks Around the Mabian Area,Southern Sichuan

Based on seismic data from the regional network for the last 34 years, we analyzed the present fault behavior of major fault zones around the Mabian area, southern Sichuan, and identified the risky fault-segments for potential future. The method of analysis is a combination of activity background of historical strong earthquakes mainly show ~ （ 1 ） The spatial distribution of b-values strong and large earthquakes in the spatial distribution of b-values with and current seismicity. Our results indicates significant heterogeneity in the studied area, which reflects the spatial difference of cumulative stress levels along various fault zones and segments. （2） Three anomalously low b-value areas with different dimensions were identified along the Mabian-Yanjin fault zone. These anomalies can be asperities under relatively high cumulated stress levels. Two asperities are located in the north of Mabian county, in Lidian town in western Muchuan county, and near Yanjin at the south end of the fault zone. These two areas represent potential large earthquake seismogenic sites around the Mabian area in the near future. Besides them, the third relatively smaller asperity is identified at southern Suijiang, as another potential strong- earthquake source. （3） An asperity along the southwestern segment of the Longquanshan fault zone indicates the site of potential moderate-to-strong earthquakes. （4） The asperity along the segment between Huangmu town in Hanyuan county and Longchi town in Emeishan city on Jinkouhe-Meigu fault has potential for a moderate-strong earthquake.

Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces

In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given. Some examples are illustrated.

Statistical Analysis of Influencing Factors of Temporal and Spatial Variation Patterns of Decadal Accumulative Heavy Rainfall in China

Daily precipitation analyses for 659 Chinese meteorological stations from 1951 to 2010 show that the rapid urbanization may have triggered the significant increase of heavy rainfall in China. During the last decades, HRAs （Heavy Rainfall Amounts）, HRDs （Heavy Rainfall Days） and HRI （Heavy Rainfall Intensity） in China have increased. Impressively, the upward trends are not randomly observed among stations, but of robust consistency with quite large regional scale over large widely and significantly. Compared to the 1950s, the HRA, HRD, and HRI increased by 68.71%, 60.15% and 11.52% during the 2000s. The significant increase of accumulative heavy rainfall appears firstly in the southeastern coasts in the early period, and then gradually expands to the central, southwest, north and northeast China. Rapid urbanization is very likely the main cause of large-scale heavy rainfall increase in China. The urbanization indicators including the industrial production output （GDP2）, UP （Urban Population） and annual average HDs （Haze Days） are in good agreement with the heavy rainfall variations, and these indicators can statistically explain the variance of HRA, HRD and HRI by 61.54%, 58.48% and 65.54%, respectively. Meanwhile, the explained variance by leading climate indices including WPSH （Western Pacific Subtropical High）, ENSO （El Nino-Southern Oscillation）, AMO （Atlantic Multi-decadal Oscillation） and AAO （Antarctic Oscillation） are respectively 24.30%, 26.23% and 21.92%, being only about 1/3 of the urbanization-related variance. Panel data analysis of county-level total population and annual average visibility days less than 10 km also show that these two indicators have significant correlation with decadal HRA, HRD ＆ HRI and the spatial correlation coefficient increases gradually with time. These consistent temporal and spatial features strongly suggest that rapid urbanization most likely triggered the steady increase of heavy rainfall over China during the recent decades.

Spatial Variation of the Characteristics of Urban Heat Island Effect in Hong Kong

Recent studies by the Hong Kong Observatory show that the urban centre of Hong Kong has considerable Urban Heat Island （UHI） effect that arises from the different thermal properties between urban and the surrounding rural areas. The studies have also shown that the urban-rural temperature difference or UHI intensity in the urban centre of Hong Kong can be greater than 10℃. However, the characteristics of UHI in Hong Kong would not be unique were it not for its complex topography and the significant spatial variation in the degree of urbanization within the territory. Making use of the extensive spatial coverage of the automatic weather stations operated by the Observatory, this study attempts to document the spatial variation of the characteristics of UHI effect in Hong Kong in summer and winter through cases studies. Cases in summer and winter with meteorological conditions typical for high UHI effect （that is, clear sky, light wind and stable atmospheric condition） are selected for the study. The characteristics of UHI effect in terms of the daytime warming rates, nocturnal cooling rates and diurnal temperature ranges at the selected automatic weather stations are analysed. The territory of Hong Kong is then classified into different categories according to the identified characteristics with a view to portraying the spatial morphology of UHI effect in Hong Kong.

Influence of Collective Boulder Array on the Surrounding Time-averaged and Turbulent Flow Fields

Arrays of large immobile boulders,which are often encountered in steep mountain streams,affect the timing and magnitude of sediment transport events through their interactions with the approach flow.Despite their importance in the quantification of the bedload rate,the collective influence of a boulder array on the approach timeaveraged and turbulent flow field has to date been overlooked.The overarching objective is,thus,to assess the collective effects of a boulder array on the time-averaged and turbulent flow fields surrounding an individual boulder within the array,placing particular emphasis on highlighting the bed shear stress spatial variability.The objective of this study is pursued by resolving and comparing the timeaveraged and turbulent flow fields developing around a boulder,with and without an array of isolated boulders being present.The results show that the effects of an individual boulder on the time-averaged streamwise velocity and turbulence intensity were limited to the boulder's immediate vicinity in the streamwise(x/d c < 2-3) and vertical(z/d c < 1) directions.Outside of the boulder's immediate vicinity,the time-averaged streamwise velocity was found to be globally decelerated.This global deceleration was attributed to the form drag generated collectively by the boulder array.More importantly,the boulder array reduced the applied shear stress exerted on theindividual boulders found within the array,by absorbing a portion of the total applied shear.Furthermore,the array was found to have a "homogenizing" effect on the near-bed turbulence thus significantly reducing the turbulence intensity in the near-bed region.The findings of this study suggest that the collective boulder array bears a portion of the total applied bed shear stress as form drag,hence reducing the available bed shear stress for transporting incoming mobile sediment.Thus,the effects of the boulder array should not be ignored in sediment transport predictions.These effects are encapsulated in this study by Equation(6).

Iterative Approximation of Fixed Points for Uniformly Continuous and Strongly Pseudocontractive Mappings in Smooth Banach Spaces

With an inequality and some analysis techniques,iterative approximation of fixed points for uniformly continuous and strongly pseudocontractive mappings in smooth Banach spaces is studied,and the recent corresponding results of Chidume are improved.

Analysis on b-value Abnormality of the Minxian-Zhangxian,Gansu M_S6.6 Earthquake

In this paper,based on Gansu Digital Seismic Network data since 1990,we calculated b-value and ⊿ b-value of the neighborhood area before the 2013 Minxian-Zhangxian M_S6. 6,earthquake. The results show that the earthquake occurred at the margin of the significantly lower b-value area in southeast of Gansu and before the earthquake the neighborhood area had an obviously abnormal ⊿ b-value. From the earthquake and the spatial distribution of low b-value, the region still has the possibility of generating dangerous strong earthquakes.