Construction of rational expression from tree automata using a generalization of Arden's Lemma

Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree languages. Moreover, we propose also a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton

Existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems

summary:We study the existence and uniqueness of integrable solutions to fractional Langevin equations involving two fractional orders with initial value problems. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem. Examples are provided to illustrate the main results

Maize (Zea mays L.) response to subsoil compaction and nitrogen fertilization under semi-arid irrigated conditions

The present investigation was carried out to access the optimal N dose and its impact on growth, yield and yield attributes of hybrid maize (Zea mays. L) under subsoil compaction condition. The experiment was conducted at Research Farm, Department of Soil Science, Punjab Agricultural University, Ludhiana during the summer seasons of the year 2012 and 2013. The experiment comprised three subsoil compaction treatments in main plots and three nitrogen levels in sub plots following split-plot design with three replications. Plant height, leaf area index and dry matter accumulation were negatively affected by subsoil compaction. However nitrogen fertilization mitigates the negative effect of subsoil compaction on growth of maize. Cob length was recorded lower with higher cob barrenness under higher degree of subsoil compaction. The grain yield was reduced by 13-16 per cent and biomass yield by 10-17 per cent due to subsoil compaction. The total N uptake was 14.6 and 18.2 per cent higher under C0 treatment than that in highly compacted subsoil (C2), while N2 treatment had improved the total N uptake by 18.6 and 14.9 per cent as compared to N0 treatment during the year 2012 and 2013, respectively. The results revealed that N1 fertilization level can be recommended under subsurface compacted soils as compared to N0 and N2 rates. This study further suggests the management option should be explored in addition to deep tillage to maximize yield of maize

Phenology and thermal indices of maize (Zea mays L.) influenced by subsoil compaction and nitrogen fertilization under semi-arid irrigated conditions

The magnitude of yield reduction due to soil compaction is variable and depends on the soil type, fertility status and other soil and environmental factors. The present investigation was carried out at the research farm, Department of Soil Science, Punjab Agricultural University, Ludhiana. The experiment was conducted to evaluate the effect of different levels of subsoil compaction and nitrogen fertilization on maize phenology, yield and heat use efficiency. The C2 (subsoil bulk density (Db)= >1.8 Mg m-3) treatment reduced yield by 15.5 and 24.3 % and heat use efficiency (HUE) by 15.2 and 20.9 % than that in C0 (subsoil Db=1.55-1.65 Mg m-3) treatment during the year 2012 and 2013, respectively. The tasseling and silking stage was delayed, while physiological maturity was advanced under C2 subsoil compaction treatment than that in C0 treatment. The N2 treatment improved the yield by 14.9 and 13.9 % and HUE by 15.2 and 14.3 % than that in N0 treatment during the year 2012 and 2013, respectively. Maize took more days to reach physiological maturity under N2 treatment as compared to N0 treatment. Phenothermal index (PTI) showed that crop reached different stages earlier under C1 and C2 than that of C0. The data emphasized the need to take care of soil strength and soil temperature related parameters along with weather conditions for better yield prediction using thermal time

Quantification of surface runoff in Patiala-Ki-Rao watersheds using modified NRCS model: a case study

Quantification of the surface runoff in a watershed is of vital importance for solution of many water resource problems. It can be quantified by employing large number of estimation approaches. Of these, SCS-CN approach is quite simple effective and requires less number of parameters. Thus, the objective of the study was to employ soil conservation service-curve number (SCS-CN) approach and their modifications to estimate surface runoff for Patiala-Ki-Rao watershed, district SAS, Nagar, Punjab and to choose the best model of the 8-different employed models. Soil moisture retention parameter was characterised and optimised by using the descriptive statistics and later used in the models. The mean and median valueof soil moisture retention parameter was 47.2 mm and 35.9 mm for June to September months and 35.4 to 30.8 mm for October to March months. The models were evaluated on the basis of Root Mean Square Error (RMSE), Nash- Scutcliffe Efficiency (NSE), Coefficient of Determination (R2) and Per cent Bias (PB). Of the evaluated and tested models, NRCS model (M5) performed best with the highest score of 32 and 31 by employing mean andmedian values of soil moisture retention parameter in Patiala-Ki-Rao watersheds over the other models. Further, the results of the study suggested in evaluating the performance of NRCS model (M5) in other treated micro-watersheds at Patiala-Ki-Rao, Punjab, over the control

Evaluation of the Physical Stability of Zinc Oxide Suspensions Containing Sodium Poly-(acrylate) and Sodium Dodecylsulfate.

The physical stability of zinc oxide (ZnO) aqueous suspensions has been monitored during two months by different methods of investigation. The suspensions were formulated with ZnO at a fixed concentration (5 wt%), sodium poly-(acrylate), as a viscosifier, and sodium dodecylsulfate (SDS), as a wetting agent. The rheological study shows that the suspensions exhibit a non-Newtonian, most often shear-thinning behavior and their apparent viscosity increases with polymer concentration. The rheograms of most of the ZnO suspensions do not vary during the experimental period. The viscoelastic properties of these suspensions, such as elastic or storage modulus (G′), viscous or loss modulus (G″) and phase angle (δ) were also examined. For% strains lower than 10%, all the formulations show strong elastic properties (G′ > G″, δ varies between 5 and 15°). Beyond 10% strain, the rheological behavior changes progressively from elastic to viscous (G″ > G′ for % strain >80%). Consistently, δ increases and reaches the 50–70° zone. Multiple light scattering (back-scattered intensity), measured with the Turbiscan ags, was used to characterize suspension physical stability (early detection of particle or aggregate size variations and particle/aggregate migration phenomena). Suspensions containing 0.4 and 0.6 wt% polymer remain stable and macroscopically homogeneous, without being affected by the change of particle size observed with a laser particle sizer. Sedimentation tests, pH, and ζ potential measurements versus time, also confirmed these findings