MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.

Effects of Winter Planting Milk Vetch on Yield and PartialProductivity of Nitrogen Fertilizer of Machine-transplantedDouble-cropping Rice under Straw Returning to the Field

From 2017 to 2018,the effects of winter planting of milk vetch on yield and partial productivity of nitrogen fertilizer of machine-transplanted double-cropping rice under straw returning were studied in Ningxiang city,Hunan Province.The results showed that the dry matter accumulation,effective panicle,yield and partial productivity of nitrogen fertilizer in the stem,leaf,panicle and aboveground parts of early and late rice treated with winter planting milk vetch and straw returning were signi ficantly higher than those treated with straw returning only.Among them,the effective panicles of early and late rice increased by 2.58%,3.18%(2017)and 5.22%,6.32%(2018),respectively.Yield increased by 11.85%,10.07%(2017)and 12.42%,10.92%(2018),annual partial productivity of nitrogen fertilizer increased by 10.90%(2017)and 11.66%(2018),respectively.In conclusion,winter planting milk vetch under straw returning is beneficial to increase dry matter accumulation,rice yield and partial productivity of nitrogen fertilizer in mechanized double cropping rice.

Almost sure central limit theory for products of sums of partial sums

Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

Varied previous crops on improving oilseed flax productivity in semiarid Loess Plateau in China

To investigate the effects of crop rotation on oilseed flax growth and yield,three season experiments were carried out in semi-arid area of Dingxi,Gansu from 2017 to 2019.The designed 6 rotational systems were FFF(flax-flaxflax),PFF(potato-flax-flax),WPF(wheat-potato-flax),FPF(flax-potato-flax),PWF(potato-wheat-flax)and FWF(flax-wheat-flax).Flax growth and yield investigation results showed that crop rotation increased leaf area duration,dry matter accumulation,seed nitrogen accumulation,water and nitrogen used efficiency,compared with continuous cropping of flax.Flaxseed yields in rotation systems were 22.23%–44.11%greater than those of continuous cropping system.Those in wheat and potato stubbles had higher tiller number(21.43%and 29.46%),more branches(14.24%and 6.97%),effective capsules(26.35%and 28.79%),higher water use efficiency(40.26%and 33.5%),higher nitrogen partial factor productivity(33.85%and 31.46%)and dry matter(41.98%and 25.47%)than those in oilseed flax stubble.It concluded that crop rotation system was an effective measure for oilseed flax productivity in semi-arid area by improving yield components and promoting biomass.

Tentative tariff rate for partial import and export products adjusted

The tentative tariff rate for partial import and export products was adjusted since November 1^(st) of 2006.Total 58 imported commodities will be imposed lower tentative

Effects of deep vertical rotary tillage on the grain yield and resource use efficiency of winter wheat in the Huang-Huai-Hai Plain of China

Tillage represents an important practice that is used to dynamically regulate soil properties,and affects the grain production process and resource use efficiency of crops.The objectives of this 3-year field study carried out in the Huang-Huai-Hai(HHH) Plain of China were to compare the effects of a new deep vertical rotary tillage (DVRT) with the conventional shallow rotary tillage (CT) on soil properties,winter wheat (Triticum aestivum L.) grain yield and water and nitrogen use efficiency at different productivity levels,and to identify a comprehensive management that optimizes both grain yield and resource use efficiency in the HHH Plain.A split-plot design was adopted in field experiments in the winter wheat growing seasons of 2016–2017 (S1),2017–2018 (S2) and 2018–2019 (S3),with DVRT (conducted once in June 2016) and CT performed in the main plots.Subplots were treated with one of four targeted productivity level treatments (SH,the super high productivity level;HH,the high productivity and high efficiency productivity level;FP,the farmer productivity level;ISP,the inherent soil productivity level).The results showed that the soil bulk density was reduced and the soil water content at the anthesis stage was increased in all three years,which were due to the significant effects of DVRT.Compared with CT,grain yields,partial factor productivity of nitrogen (PFP_(N)),and water use efficiency (WUE) under DVRT were increased by 22.0,14.5 and 19.0%.Path analysis and direct correlation decomposition uncovered that grain yield variation of winter wheat was mostly contributed by the spike numbers per area under different tillage modes.General line model analysis revealed that tillage mode played a significant role on grain yield,PFP_(N) and WUE not only as a single factor,but also along with other factors(year and productivity level) in interaction manners.In addition,PFP_(N) and WUE were the highest in HH under DVRT in all three growth seasons.These results provided a theoretical basis and technical support for coordinating the high yield with high resource use efficiency of winter wheat in the resource-restricted region in the HHH Plain of China.

Optimization of water and nitrogen management for surge-root irrigated apple trees in the Loess Plateau of China

The Loess Plateau is one of the main regions for growing apple trees in China, but a shortage of water resources and low utilization of nitrogen have restricted its agricultural development. A 2-year field experiment was conducted which included three levels of soil water content(SWC), 90–75%, 75–60%, and 60–45% of field capacity, and five levels of nitrogen application(N(app)), 0.7, 0.6, 0.5, 0.4 and 0.3 kg/plant. The treatments were arranged in a strip-plot design with complete randomized blocks with three replications. For both years, the water and N(app) had significant(P<0.05) effects on leaf area index(LAI), yield, water use efficiency(WUE) and nitrogen partial factor productivity(NPFP) while the interaction effect of water and N(app) on yield, WUE and NPFP was significant(P<0.05) in 2018, and not in 2017. For the same SWC level, WUE first increased, then decreased as N(app) increased, while NPFP tended to decrease, but the trend of LAI with different N(app) was closely related to SWC. At the same N(app), the LAI increased as SWC increased, while the WUE and NPFP first increased, then decreased, but the yield showed different trends as the SWC increased. The dualistic and quadric regression equations of water and N(app) indicate that the yield, WUE and NPFP cannot reach the maximum at the same time. Considering the coupling effects of water and N(app) on yield, WUE and NPFP in 2017 and 2018, the SWC level shall be controlled in 75–60% of field capacity and the N(app) is 0.45 kg/plant, which can be as the suitable strategy of water and N(app) management for the maximum comprehensive benefits of yield, WUE and NPFP for apple trees in the Loess Plateau and other regions with similar environments.

Statistical analysis of nitrogen use efficiency in Northeast China using multiple linear regression and Random Forest

Understanding the spatial-temporal dynamics of crop nitrogen(N)use efficiency(NUE)and the relationship with explanatory environmental variables can support land-use management and policymaking.Nevertheless,the application of statistical models for evaluating the explanatory variables of space-time variation in crop NUE is still under-researched.In this study,stepwise multiple linear regression(SMLR)and Random Forest(RF)were used to evaluate the spatial and temporal variation of NUE indicators(i.e.,partial factor productivity of N(PFPN);partial nutrient balance of N(PNBN))at county scale in Northeast China(Heilongjiang,Liaoning and Jilin provinces)from 1990 to 2015.Explanatory variables included agricultural management practices,topography,climate,economy,soil and crop types.Results revealed that the PFPN was higher in the northern parts and lower in the center of the Northeast China and PNBN increased from southern to northern parts during the 1990–2015 period.The NUE indicators decreased with time in most counties during the study period.The model efficiency coefficients of the SMLR and RF models were 0.44 and 0.84 for PFPN,and 0.67 and 0.89 for PNBN,respectively.The RF model had higher relative importance of soil and climatic covariates and lower relative importance of crop covariates compared to the SMLR model.The planting area index of vegetables and beans,soil clay content,saturated water content,enhanced vegetation index in November&December,soil bulk density,and annual minimum temperature were the main explanatory variables for both NUE indicators.This is the first study to show the quantitative relative importance of explanatory variables for NUE at a county level in Northeast China using RF and SMLR.This novel study gives reference measurements to improve crop NUE which is one of the most effective means of managing N for sustainable development,ensuring food security,alleviating environmental degradation and increasing farmer’s profitability.

Economically Optimal Rates and Nutrients Use Efficiency Indices of Maize to the Application of Different Rates of Nutrients in Central Rift Valley of Ethiopia

The use of balanced fertilizers in adequate amount is very important to increase crop productivity and production in Ethiopia. The study was executed to quantify maize (Zea mays L.) grain yield response to different rates of nitrogen (N), phosphorus (P), potassium (K) and sulfur (S) under balanced fertilization of other nutrients. On farm trials were conducted at seven sites on 8 farmers’ fields in Negele Arsi districts, west Arsi zone of Oromia region for three consecutive cropping seasons (2014-2016). Six rates of N, P, S and eight rates of K treatments established separately for each nutrient were laid out in randomized complete block (RCB) design with three replicates per farm. Nutrient response function modelling showed that 184, 20 and 80 kg•ha−1 were the agronomic optimum rate for N, P, and K, respectively. Mean agronomic efficiency (AE) of N, P and K were recorded at the lower rates of these nutrients, application of 46, 10 and 20 kg•ha−1 N, P and K resulted in 19.1, 61.0, and 24 kg additional grain yield•kg−1 N, P and K, respectively. Also, the mean partial factor productivity (PFP) of N, P and K were 77.6, 370 and 158 kg additional grain•kg−1 applied N, P and K respectively. Economically optimal rate (EOR) of N, P and K were 48 - 114 kg•ha−1 N with CP 8 - 3.5, 12 - 20 kg•ha−1 P with CP 18 - 4.5 and 32 - 53 kg•ha−1 K with CP 8-4, from these rates net returns of US$487.23 - 143.30, US$698.16 - 498.3 and US$359.31 - 193.63 could be obtained respectively. To conclude, application of 84, 12 and 40 kg•ha−1 N, P and K could be recommended for the production of maize.

Genotypic variations in nitrogen use efficiency of rice cultivars at various levels of nitrogen under subtropical environment

Insufficient N supply is an important constraint to productivity of lowland rice. Studies on N nutrition of rice cultivars with different durations representing the north western part of Indo-Gangetic Plains are scanty. A field experiment was conducted during kharif seasons of 2006 and 2007 at PAU, Ludhiana to assess the differences in grain yield and N utilization of three popular rice cultivars at varying N doses. Significant differences among genotypes were observed in grain yield, N uptake, N use efficiency and N utilization efficiency. The cultivar PAU-201 was found to be superior among all the tested genotypes. Total N uptake and grain N uptake was highest in cultivar PAU-201 followed by cultivars PR-115 and PR-113. On an average, the response to applied N for grain yield was observed upto 90 kg N ha1. Grain yield increased significantly up to 90 kg N hal in cultivars PR-115 and PAU-201 and up to 120 kg N ha1 in PR-113. Apparent recovery efficiency （ARE） and Partial factor productivity （PFPN） of N was significantly reduced at higher level of N （150 kg N hal）. It was concluded that N uptake is predominant factor in grain yield formation and cultivars differ in NUE suggesting that it may be possible to develop cultivars that are efficient at low nutrient level or are capable of using N more efficiently when applied as fertilizer.

Energy consumption hierarchical analysis based on interpretative structural model for ethylene production

Interpretative structural model(ISM) can transform a multivariate problem into several sub-variable problems to analyze a complex industrial structure in a more efficient way by building a multi-level hierarchical structure model. To build an ISM of a production system, the partial correlation coefficient method is proposed to obtain the adjacency matrix, which can be transformed to ISM. According to estimation of correlation coefficient, the result can give actual variable correlations and eliminate effects of intermediate variables. Furthermore, this paper proposes an effective approach using ISM to analyze the main factors and basic mechanisms that affect the energy consumption in an ethylene production system. The case study shows that the proposed energy consumption analysis method is valid and efficient in improvement of energy efficiency in ethylene production.

An Improved Result in Almost Sure Central Limit Theory for Products of Partial Sums with Stable Distribution

Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.

On the Semiprimitivity and Semiprimality Problems for Partial Smash Products

In this paper we discuss about the semiprimitivity and the semiprimality of partial smash products. Let H be a semisimple Hopf algebra over a field k and let A be a left partial H-module algebra. We study the H-prime and the H-Jacobson radicals of A and their relations with the prime and the Jacobson radicals of A#H, respectively. In particular, we prove that if A is H-semiprimitive, then A^fH is semiprimitive provided that all irreducible representations of A are finite-dimensional, or A is an affine PI-algebra over k and k is a perfect field, or A is locally finite. Moreover, we prove that A=#=H is semiprime provided that A is an H-semiprime PI-algebra, generalizing to the setting of partial actions the known results for global actions of Hopf algebras.

Optimizing Nitrogen Use Efficiency for No-Till Corn Production by Improving Root Growth and Capturing NO_(3)-N in Subsoil

Subsoil acidity restricts root growth and reduces crop yields in many parts of the world. More than half of the fertilizer nitrogen(N) applied in crop production is currently lost to the environment. This study aimed to investigate the effect of gypsum application on the efficiency of N fertilizer in no-till corn(Zea mays L.) production in southern Brazil. A field experiment examined the effects of surface-applied gypsum(0, 5, 10, and 15 Mg ha^(-1)) and top-dressed ammonium nitrate(NH_4NO_3)(60, 120, and 180 kg N ha^(-1)) on corn root length, N uptake, and grain yield. A greenhouse experiment was conducted using undisturbed soil columns collected from the field experiment site to evaluate NO_3-N leaching, N uptake, and root length with surface-applied gypsum(0 and 10 Mg ha^(-1)) and top-dressed NH_4NO_3(0 and 180 kg N ha^(-1)). Amelioration of subsoil acidity due to gypsum application increased corn root growth,N uptake, grain yield, and N use efficiency. Applying gypsum to the soil surface increased corn grain yield by 19%–38% and partial factor productivity of N(PFPN) by 27%–38%, depending on the N application rate. Results of the undisturbed soil column greenhouse experiment showed that improvement of N use efficiency by gypsum application was due to the higher N uptake from NO_3-N in the subsoil as a result of increased corn root length. Our results suggest that ameliorating subsoil acidity with gypsum in a no-till corn system could increase N use efficiency, improve grain yield, and reduce environmental risks due to NO_3-N leaching.

Yield-scaled nitrous oxide emissions from nitrogen-fertilized croplands in China: A meta-analysis of contrasting mitigation scenarios

Nitrogen(N) losses in cropland resulting from the application of synthetic fertilizers decrease crop productivity and exacerbate environmental pollution.Mitigation measures, such as reduction in N fertilizer application rates, can have unintentional adverse effects on crop yield. We conducted a meta-analysis of soil N_(2)O emissions from agricultural fields across China under contrasting mitigation scenarios as a novel approach to identify the most effective strategy for the mitigation of emissions of N_(2)O derived from N fertilizer use in China. Current standard agricultural practice was used as a baseline scenario(BS), and 12 potential mitigation scenarios(S1–S12) were derived from the available literature and comprised single and combinations of management scenarios that accounted for crop yield. Mitigation scenarios S6(nitrification inhibitor 3,4-dimethylpyrazole phosphate) and S11(20% reduction in N application rate plus nitrification inhibitor dicyandiamide) in maize, rice, and wheat crops led to an average 56.0% reduction in N_(2)O emissions at the national level, whereas scenario S4(nitrification inhibitor dicyandiamide) led to yield optimization, with a 14.0% increase for maize and 8.0% increase for rice as compared to the BS. Implementation of these most effective mitigation scenarios(S4, S6, and S11) might help China, as a signatory to the 2015 United Nations Framework Convention on Climate Change(Paris Agreement), to achieve a 30% reduction in N_(2)O emissions by 2030.

New method for high performance multiply-accumulator design

This study presents a new method of 4-pipelined high-performance split multiply-accumulator (MAC) architecture, which is capable of supporting multiple precisions developed for media processors. To speed up the design further, a novel partial product compression circuit based on interleaved adders and a modified hybrid partial product reduction tree (PPRT) scheme are proposed. The MAC can perform 1-way 32-bit, 4-way 16-bit signed/unsigned multiply or multiply-accumulate operations and 2-way parallel multiply add (PMADD) operations at a high frequency of 1.25 GHz under worst-case conditions and 1.67 GHz under typical-case conditions, respectively. Compared with the MAC in 32-bit microprocessor without interlocked piped stages (MIPS), the proposed design shows a great advantage in speed. Moreover, an improvement of up to 32% in throughput is achieved. The MAC design has been fabricated with Taiwan Semiconductor Manufacturing Company (TSMC) 90-nm CMOS standard cell technology and has passed a functional test.

Comparing Operational Efficiency of Mobile Operators in Brazil, Russia, India and China

Using partial factor productivity and data envelopment analysis approaches, this study measures and compares the operational efficiency of the 10 dominant mobile operators in Brazil, Russia, India and China （BRIC） between 2002 and 2006. The results of data envelopment analysis indicate that the two leading Brazilian mobile operators, Vivo and TIM, are fully efficient throughout the entire period of study, however, Indian mobile operators are the least efficient among BRIC operators. Interestingly, the findings of this study verify that full operational efficiency can be achieved by operators with large revenues, such as China Unicorn, and by other, y with medium and small revenues, such as Hvo, TIM and Oi. Partial faetor productivity demonstrates that 3 of the 4 Brazilian mobile operators, Vivo, TIM and Oi, have remarkable productivity ratios, and that the state-owned operator, China Unicom, has the highest revenue per capital expenditure among BRIC operators. In contrast, Indian mobile operators ＇productivity ratios are generally low compared to other BRIC mobile carriers.