The Depth Distribution of Constacyclic Codes Over the Ring F_(p)+vF_(p)+v^(2)F_(p)

In this paper,we studied the depth spectrum and the depth distribution of constacyclic codes over the non-chain ring R=F_(p)+vF_(p)+v^(2)F_(p),where v^(3)=v.By decomposing the linear codes C over R into the linear codes over the finite field F_(p),three corresponding constacyclic codes C_(1),C_(2),C_(3) over F_(p)were obtained.Furthermore,considering the depth spectrum of constacyclic codes over the finite filed F_(p),and the relationship between constacyclic codes C_(1),C_(2),C_(3) and C,the depth spectrum and the depth distribution of constacyclic codes over R were discussed.

Variability of water supply affected shoot biomass and root depth distribution of four temperate grassland species in monocultures and mixtures

Aims Research on the effects of extreme rainfall events on ecosystem function has primarily focussed on drought or flooding events,which usually include changes to mean or total rainfall,annually or over a season.However,less is known about the effects of increased rainfall variability without change to mean or total amounts.We investigated the effects of increased variation of water supply on shoot and root biomass as well as the distribution of root biomass of four grassland plant species,grown in monoculture and mixture communities.Methods Perennial ryegrass(Lolium perenne L.,shallow-rooting grass),chicory(Cichorium intybus L.,deep-rooting forb),white clover(Trifolium repens L.,shallow-rooting legume)and red clover(Trifolium pratense L.,deep-rooting legume)were established in mesocosms.Four plants of the same species were grown in monoculture communities and one of each species grown in four-species communities.Water supply was manipulated such that;compared with a baseline level with low variation in water supply,there was a treatment with medium variation(±40%)and another with high variation(±80%).Shoot and root biomass were measured,and vertical root distribution models fitted.Important Findings Compared with the low variation treatment,shoot biomass was significantly reduced under high variation for white clover,red clover and four-species communities.Under all conditions,four-species communities produced more shoot and root biomass than predicted by species performance in monoculture(overyielding).Under increased water variation,chicory monocultures allocated a higher proportion of root biomass to deeper soil layers while the total root biomass of white clover monocultures was significantly reduced.These results indicate that increased variability of water supply can negatively affect the shoot and root biomass production of single and multi-species grasslands.There is a need for further investigation of water variation effects on the functioning of multi-species grassland systems at field scale.

Estimating distribution of water uptake with depth of winter wheat by hydrogen and oxygen stable isotopes under different irrigation depths

Crop root system plays an important role in the water cycle of the soil-plant-atmosphere continuum. In this study, com- bined isotope techniques, root length density and root cell activity analysis were used to investigate the root water uptake mechanisms of winter wheat （Triticum aesfivum L.） under different irrigation depths in the North China Plain. Both direct inference approach and multisource linear mixing model were applied to estimate the distribution of water uptake with depth in six growing stages. Results showed that winter wheat under land surface irrigation treatment （Ts） mainly absorbed water from 10-20 cm soil layers in the wintering and green stages （66.9 and 72.0%, respectively）; 0-20 cm （57.0%） in the jointing stage; 0-40 （15.3%） and 80-180 cm （58.1%） in the heading stage; 60-80 （13.2%） and 180-220 cm （35.5%） in the filling stage; and 0-40 （46.8%） and 80-100 cm （31.0%） in the ripening stage. Winter wheat under whole soil layers irrigation treatment （Tw） absorbed more water from deep soil layer than Ts in heading, filling and ripening stages. Moreover, root cell activity and root length density of winter wheat under TW were significantly greater than that of Ts in the three stages. We concluded that distribution of water uptake with depth was affected by the availability of water sources, the root length density and root cell activity. Implementation of the whole soil layers irrigation method can affect root system distribution and thereby increase water use from deeper soil and enhance water use efficiency.

Spatial distribution of snow depth based on geographically weighted regression kriging in the Bayanbulak Basin of the Tianshan Mountains, China

Snow depth is a general input variable in many models of agriculture,hydrology,climate and ecology.This study makes use of observational data of snow depth and explanatory variables to compare the accuracy and effect of geographically weighted regression kriging(GWRK)and regression kriging(RK)in a spatial interpolation of regional snow depth.The auxiliary variables are analyzed using correlation coefficients and the variance inflation factor(VIF).Three variables,Height,topographic ruggedness index(TRI),and land surface temperature(LST),are used as explanatory variables to establish a regression model for snow depth.The estimated spatial distribution of snow depth in the Bayanbulak Basin of the Tianshan Mountains in China with a spatial resolution of 1 km is obtained.The results indicate that 1)the result of GWRK's accuracy is slightly higher than that of RK(R^2=0.55 vs.R^2=0.50,RMSE(root mean square error)=0.102 m vs.RMSE=0.077 m);2)for the subareas,GWRK and RK exhibit similar estimation results of snow depth.Areas in the Bayanbulak Basin with a snow depth greater than 0.15m are mainly distributed in an elevation range of 2632.00–3269.00 m and the snow in this area comprises 45.00–46.00% of the total amount of snow in this basin.However,the GWRK resulted in more detailed information on snow depth distribution than the RK.The final conclusion is that GWRK is better suited for estimating regional snow depth distribution.

Permeability in Flysch-Distribution Decrease with Depth and Grout Curtains Under Dams

A considerable number of in situ permeability tests in flysch are processed to a depth of 120m with a good spatial distribution. The distribution of permeability values for the different litho-types of this formation, their comparison and their decrease with depth is discussed. The depth where a permeability of 3 to 5×10-7m/sec can be retained (the limit of a reasonable grouting under a high dam) may be twofold if the geological history of the formation could not contain a compressional tectonic process. This depth may reach 100m in some cases. The differences in the mean values of permeability among the various litho-types are minor, while the presence of siltstones, always present although with varied participation, dramatically controls the global permeability.

Numerical method for wave height distribution within the artificial harbor with water depth of steep variation

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Study on System of Faults in the Gulf of Mexico and Adjacent Region based on Gravity Data

In the Gulf of Mexico and adjacent landmasses,faults are very complex,and their distribution is closely related to plate tectonics,ocean-land boundary,and former structure.The plane position of the faults can be identified by the maximum characteristic of the vertical derivative of the normalized vertical derivative of the total horizontal derivative(NVDR-THDR)of the Bouguer gravity anomaly.The apparent depth of the faults is inverted by the Bouguer gravity anomaly curvature property.Based on tectonic evolutionary processes and the plane distribution and apparent depth characteristics of the faults,a complete fault system for the Gulf of Mexico and adjacent areas has been established,including 102 faults.The apparent depths of 33 first-class faults are 16-20 km and for 69 second-class faults are 12-16 km.The F_(1-2)and F_(1-3)subduction fault zones are two caused by the subduction of the Cocos Plate into the old Yucatan and Chorti landmasses;F_(1-11)and F_(1-12)fault zones extend westward to the coast of Guatemala and do not extend into the continent;F_(1-17)and F_(1-20)faults,which control the boundary of the oceanic crust,do not extend southward into the continent.The fault system,which radiates in a"fan-shaped"structure as a whole,unfolds to the northeast.Faults of different nature and sizes are distributed in the Cocos Plate subduction zone,Continental,Gulf of Mexico,Yucatan old landmass and Caribbean Plate in NW,NNW,NS,NE and NEE directions.In the Gulf of Mexico region,the fault system is a comprehensive reflection of former tectonic movements,such as plate movement,drift of old landmasses and expansion of oceanic crusts.The first-class faults control the plate and ocean-continental boundaries.The second-class faults are subordinate to the first-class faults or related to the distribution of different sedimentary layers.

DISTRIBUTION OF WAVE INDUCED EXCESS MOMENTUM FLUXES OVER DEPTH AND APPLICATION TO THREE DIMENSIONAL NUMERICAL MODELING OF WAVE CURRENT INTERACTIONS

Using the linear wave theory, the distributions of the wave induced excess momentum fluxes over depth at the arbitrary wave angle and their asymptotic forms for deep and shallow water are developed. Results indicate that the distribution of the wave induced excess momentum fluxes over depth is non uniform and the contributions of the component below the wave trough to the total momentum fluxes become considerable in shallow water. On the basis of the Navier Stokes equations, the simplified three dimensional mathematical model is established by taking a phase average over a wavelength. It is found that there are the terms of the wave induced excess momentum fluxes varying over depth in the model, which illustrates the situation of wave current interactions and the vertical structure of current velocity are changed because of different wave induced excess momentum fluxes at various vertical location. The finite difference method is employed to solve the simplified model. Performances of the two dimensional vertically integrated equations are evaluated against available numerical and experimental results including the cases of wave set up on a plane beach, longshore current due to an oblique wave, wave induced nearshore circulation in a semi enclosed seas, and wave current interactions. All cases yield satisfactory agreements. The three dimensional mathematical model is applied to the numerical simulation of wave current interactions, and it performs well in predicting the vertical velocity structure and the plane flow field.

Most root-derived carbon inputs do not contribute to long-term global soil carbon storage

Plant root-derived carbon(C)inputs(I_(root))are the primary source of C in mineral bulk soil.However,a fraction of I_(root)may lose quickly(I_(loss),e.g.,via rhizosphere microbial respiration,leaching and fauna feeding)without contributing to long-term bulk soil C storage,yet this loss has never been quantified,particularly on a global scale.In this study we integrated three observational global data sets including soil radiocarbon content,allocation of photo synthetically assimilated C,and root biomass distribution in 2,034 soil profiles to quantify I_(root)and its contribution to the bulk soil C pool.We show that global average I_(root)in the 0-200 cm soil profile is 3.5 Mg ha^(-1)yr^(-1),~80%of which(i.e.,I_(loss))is lost rather than co ntributing to long-term bulk soil C storage.I_(root)decreases exponentially with soil depth,and the top 20 cm soil contains>60%of total I_(root).Actual C input contributing to long-term bulk soil storage(i.e.,I_(root)-I_(loss))shows a similar depth distribution to I_(root).We also map I_(loss)and its depth distribution across the globe.Our results demonstrate the global significance of direct C losses which limit the contribution of I_(root)to bulk soil C storage;and provide spatially explicit data to facilitate reliable soil C predictions via separating direct C losses from total root-derived C inputs.

An empirical approach to predict regional organic carbon in deep soils

Deep soil organic carbon(SOC)plays an important role in carbon cycling.Precisely predicting deep SOC at the regional scale is crucial for the accurate assessment of carbon sequestration potential in soils but has been challenging for a century.Herein,we developed a depth distribution function-based empirical approach to predict SOC in deep soils at the regional scale.We validated this approach with a dataset from four regions of the world and examined the application of this approach in China’s Loess Plateau.We found that among the reported depth distribution functions describing vertical patterns of SOC,the negative exponential function performed best in fitting SOC along the soil profile in various regions.Moreover,the parameters(i.e.,Ceand k)of the negative exponential function were linearly correlated to surface SOC(0–20 cm)and the changing rates of SOC within the topsoil(0–40 cm).Based on the above relationships,the empirical equations for predicting the negative exponential parameters are established.The validation results from site-specific and regional dataset showed that combining the negative exponential function and such empirical equations can precisely predict SOC concentration in soils down to 500 cm depth.Our study provides a simple,rapid and accurate method for predicting deep soil SOC at the regional scale,which could simplify the assessment of deep soil SOC in various regions.