This study was conducted to determine the yield response factor (Ky) of sugar beet to deficit irrigation at different growth stages. A field experiment was conducted in Sharekord Agricultural Research Station over two growing crop seasons (1996 -1997) using a randomized complete block design with three replications. Plots were assigned to five levels of deficit irrigation treatments: E0 (Full Irrigation), E1 (85%), E2 (70%), E3 (55%) and E4 (30%) of actual evapotranspiration of sugar beet plant at three growth stages T1: leaf growth stage, T2: tuber growth stage and T3: sugar accumulation growth stage. Reference crop evapotranspiration and potential evapotranspiration of sugar beet was determined by drainage lysimeter using neutron meter. After maturity, root yield, yield components and yield response factor were measured. Results showed that yield was highest (49.500 t/ha) in E0 (Full irrigation) and lowest (24.6 t/ha) in E4T2. Actual evapotranspiration of sugar beet was 884mm. The values of yield response factor (ky) were 0.34- 1.38 at the first stage, 0.34- 1.33 at the second stage and 0.34- 1.39 at the third stage and the lowest evapotranspiration (625 mm) was obtained in E4T2.

This study was conducted to determine the yield response factor potato (ky) to deficit irrigation at different growth stages in a randomized complete block design with five treatment, E0 (Full Irrigation), E1 (85%), E2 (70%), E3 (55%) and E4 (30%) of actual evapotranspiration plant potato in three growth stages T1: seed and vegetative establishment, T2: the full development and T3: get the plant growing season in three years. the sharekord. Evapotranspiration potential of the potato crop was lysimeter drainage water balance method used to estimate the neutron meter. After harvest, yield and yield components were determined and potato yield response coefficient was calculated. The results of data analysis showed that deficit irrigation effects on potato yield is significant at the 5% .Maximum potato yield in full irrigation equal to 43416 kg up to 22150 kg in the lowest 70 percent evapotranspiration treatment- plant evapotranspiration in the third stage of plant growth. evapotranspiration potential of the potato in the region with 944 mm and 542 mm minimum was E4T3 treatment. Coefficient responses yield of potato (Ky) with respect to the treatment of low irrigation for the first stage of growth between 0.65 to 1.18 and the second stage of growth between 0.82 and 1, and in the third stage of growth between 0.7 to 1.17 and the maximum growth season with 1.11 respectively.

In order to adapt to water scarcity, various strategies can be proposed and implemented including; the adoption of appropriate policies for optimizing water use through the determination of optimal production functions. Water scarcity and a decreasing in the quality of water and soil resources in the country are among the main causes of production decline. Hence, this study was conducted to determine the sensitivity coefficients of plant and optimum water-salinity-yield function for turnip in Kashmar. A factorial experiment was conducted in a completely randomized design with three replications including two factors salinity and irrigation water. Four levels of irrigation water salinity were, drinking water: S1 = 0. 7, S2 = 4, S3 = 8 and S4 = 12 dS/m3, and three levels of irrigation water, including: full irrigation (100% water requirement) = W1, W2= 75 % W1 and W3 = 50% W1, applied to a sandy-loam soil texture. Functional data were fitted to different forms of production functions (linear, logarithmic, quadratic and exponential), and after sensitivity analysis, the optimum production function of turnip was determined. Then the water use efficiency and the sensitivity coefficients of the plant were determined. The results of the sensitivity analysis indicated that the quadratic production function for turnips as the optimal production function is recommended. The study of maximum error (ME) showed that the most error is related to simple logarithmic and linear functions. The Control treatment (W1S1) and W2S1 treatment (75% water requirement) were the highest yield with 6. 66 and 7. 24 kg/m3, respectively, but the water productivity decreased with increasing water stress and salinity. The average amount of crop yield response factor (Ky) was estimated at the rate of 1. 73 in the salinity and water stress combination. Also, the sensitivity coefficient (Ks) decreased with increasing salinity and water stress and the lowest value of (Ks) belonged to W3S4 treatment at the rate of 0. 5. The same product curves demonstrate that with an increasing amount of irrigation water, higher saline irrigation water can be used for turnip, which the yield does not change.

Deficit Irrigarion in water scarcity is the most important strategy to maintain crop water productivity. Therefore, cultivating drought-resistant crops such as quinoa can increase physical productivity on farm. To evaluate the yield and growth of quinoa in water shortage conditions, information about yield response factor is required. In this study, Quinoa cultivar Titicaca was cultivated in two cropping years of 2020 and 2021. To evaluate different levels of irrigation, four irrigation treatments were applied based on measuring soil moisture in different periods of plant growth, including: full irrigation, 30% Allowable Depletion, 50% Allowable Depletion and 70% Allowable Depletion. Based on the results in the two years, the initial growth period was 20 days, the development period was 30 days, the middle period was 28 days and the final period was 12 days. The most sensitive growth period in quinoa plant was determined as the middle period with a yield response factor of 0. 88. On average, with a consumption of 2563 cubic meters of water, the maximum productivity will be about 1. 85 kg per cubic meter. In general, the results show that this plant has a high resistance to deficit irrigation and therefore this plant can be grown in areas with water shortage and good performance can be expected in water stress conditions.

In order to investigate the possibility of quinoa producing in Garmsar, Iran, a factorial experiment conducted in randomized complete block design with three replications in 2018-2019 growing season at Garmsar Agricultural Research Station. The factors were planting date at three levels (March 6th, April 1st and April 6th) and the three genotypes of quinoa (Q26, Q29 and Titicaca). Results showed that the effect of planting date was significant for all studied traits except the harvest index. Also, all studied traits were significantly different in all genotypes. Titicaca planted on March 6th had the highest yield (2276 kg.ha-1).The grain yield and yield components decreased with the delaying the planting date. Compared to early plantings, Latest date, April 6th, led to reduction of all traits, especially grain yield (about 50%). The results of simple phenotypic correlation between the studied traits showed that grain yield per hectare had the highest correlation with plant yield (0.877) and then with leaf area index (0.832), panicle weight (0.815) and number of branches per plant (0.745) that was significant at the 1% probability level.

To increase the agricultural profit, an experiment was conducted at the Scientific Agricultural Research Center (SARC) at Salamiyah, Syria. The experiment aimed to estimate the optimum irrigation level that maximizes productivity as well as the black cumin's quality local quality standards under experimental conditions. The irrigation treatments were 25, 50, 75 and 100% of the Potential Evapotranspiration (ETP) based on Class-A pan evaporation. The treatments were denoted as B, C, D and E, respectively. The no-irrigation treatment (A) was considered as control. Irrigation water was applied by a drip system. The A-E treatments were designed and implemented using complete randomized block design (CRBD) with four replications. The actual Evapotranspiration (ETa) was calculated after calibration of soil using SPAW software. Furthermore, crop yield, Irrigation Water Use Efficiency (IWUE), yield response factor (ky) and some parameters (period of growth stage, date of flowering…etc.) were studied during 2018-2019 successive growth seasons. Results showed that irrigation could be scheduled using some equations and Class-A pan evaporation. Moreover, the vegetative growth parameters flourished virtually and significantly by comparing higher and lower irrigation levels. However, Irrigation Water Use Efficiency (IWUE) values increased by reducing the applied irrigation water. Treatment B recorded the highest IWUE value (2.4 kg ha-1 mm-1), but key values remained less than 1.0, indicating that the plant tolerates drought. Furthermore, treatment C scored the top-seed (130.6%) concerning the profit/total costs ratio. Finally, based on the results, we recommend that irrigation should not be more than 75% and not less than 25% of the ETP.

We prove that for a separable Hilbert space H with an orthonormal basis {ei}¥i=1, the equality ||.||=||S¥i=1 si (.) eiÄei|| holds for all unitarily invariant norms on B(H) and Ky Fan's dominance theorem remains valid on B(H).

Background and Aim: Due to the importance of determining the behavior of plants in water shortage conditions, it is necessary to determine the coefficients of plant sensitivity to water at different stages of plant growth. Water shortage in the Sistan plain is a serious and important issue, so that the lack of water supply to the Helmand border river, which is the only source of water supply in the region, leads to the destruction of agriculture. The low possibility of increasing new water resources and the need to increase agricultural production from limited water resources in this region requires the use of appropriate scientific and technical methods to increase the productivity of agricultural water consumption. Also, changing the pattern of cultivation and replacement of high-income crops in recent years in arid areas has received much attention from farmers. The purpose of this study is to investigate the effects of water stress on the behavior of garlic in dehydrated conditions to calibrate the production function of this plant to obtain yield response coefficients in conditions of water shortage. Method: In this study, garlic plant was implemented in the form of a randomized complete block design with three replications in 1398 and 1399 in Sistan and Baluchistan province. Treatments were applied based on stress levels compared to control 30, 35, 40, 45, 50, 60 and 70% of water requirement. This station is located 20 km southeast of Zabol city at latitude 61 degrees and 41 minutes and latitude 30 degrees and 54 minutes in Sistan region. The altitude of the station is 483 meters above sea level, the average annual rainfall is 55 mm and the annual evaporation rate is 4500 to 5000 mm. This region has a very dry climate with very hot summers and mild winters. The area of the experimental plot was equal to 750 square meters was selected for planting garlic of Chinese cultivar before planting the bed was reinforced with animal manure and after growing based on soil fertilizer test, 300 kg of potassium phosphate, 200 kg of triple phosphate and 100 kg. One kilogram of urea was added to the soil. Then plow and disc and finally leveled. On the 24th of October, grooves were planted with a shovel at a distance of 20 cm and a depth of 5 cm to plant garlic of Chinese cultivar, and garlic tubers were planted at a distance of 8 cm on the rows. Then, based on the obtained information, the two functions of Tafteh and Raes production were investigated and yield response factors were determined during the growing period. Results: Comparing the two methods used the highest yield of garlic in the study was 8240 kg / ha, for the production of which 833 mm of water was used. The data of the first year were used to calibrate the yield response factors of garlic and after calibrating the two production functions of Raes and Tafteh, the values of the yield response factors of garlic were presented. This coefficient was different in the range of 0. 5 to 1. 2 in different periods of garlic plant growth, the change curve was presented. Evaluation of Rice method in the second year with root mean square error of 1302 kg / ha and normalized value was about 23%. Conclusion: In the method of Tafteh the mean root mean square error was 485 kg / ha and the normalized value was about 11%. Therefore, the method of Tafteh is recommended in determining the yield of garlic under water stress conditions.

Due to limited water resources and the problem of water distribution in irrigation and drainage networks and non-compliance of plant irrigation needs with existing irrigation periods, a water stress is introduced to the plants systematically. Therefore, in this study, two production functions of Raes (2004) and Tafteh et al. (2013) were evaluated for corn using the yield response factor suggested by Tafteh et al. (2014a). For this purpose, two varieties of corn 500 and 302 were harvested in two years of cultivation with irrigation treatments of 100, 75 and 50% of water requirement and their yield values were evaluated using the proposed functions. The results showed that both production functions in determining corn yield of 500 and 320 together with the amount of root mean square error is about 591 kg / ha, the normal root mean square error is about 8% and the mean bias error is about 25 kg / ha. The agreement index was about 0. 94 and the efficiency factor index of the model was about 0. 81. These statistical results showed that the proposed functions are highly effective in determining the yield of both varieties. A separate study of these two varieties also showed that the 302 cultivar has lower yield and in water shortage conditions, its sensitivity to the plant, especially in the middle period of growth, is higher than the 500 cultivar. Therefore, cultivar 500 has a higher yield than cultivar 302 and in water shortage conditions, its sensitivity coefficients are less and it shows more resistance to water stress. Yield response factor of cultivar 302 in the initial, middle and final stages of growth were determined to be 0. 5, 1. 4 and 0. 8, respectively Which is different from the suggested values. . Therefore, it is necessary to evaluate the proposed cultivars in water stress conditions using production functions.

In order to investigate the effect of water stress at different growing stages of soybean, an experiment was conducted in Mazandaran in a complete random block design with seven treatments and three replications. The treatments were consisted of: TR0 (no water stress), TR1 (water stress at vegetative stage), TR2 (water stress at flowering stage), TR3 (water stress at grin filling stage), TR4 (water stress at vegetative and flowering stage), TR5 (water stress at vegetative and grin filling stage) and TR6 (water stress at flowering and grin filling stage). The soil moisture was measured during the experiment by a gravimetric method, and hence, crop actual evapotranspiration was calculated by water balance method. The low rainfall amount did not disturb the treatments. After maturity, grin yield was measured, with yield response factor (Ky) being calculated for each growth stage and according to FAO method. The results indicated that the highest (5100 kg. ha-1) and lowest (2590 kg. ha-1) yield were obtained in TR0 and TR6 treatments, respectively. The largest seasonal evapotranspiration (367mm) and the lowest (225mm) were belonged to TR1 and TR6, respectively. The yield response factor (Ky) was 0.87 for the total growth period and this factor at vegetative, flowering and grin filling stages were 0.148, 0.8 and 1, respectively.