Space S3 Research Articles

Effect of Spacing and Ratooning on Growth and Yield of Okra (Abelmoschus esculentus L. Moench) Var. Lal Bhendi No. 533

The experiment was laid down in Factorial Randomized Block Design (FRBD) with nine treatment combinations and four replications during year 2023. The experiment consists of two factors, factor A: Spacings (S1- 60 cm x 30 cm, S2- 90 cm x 30 cm and S3- 120 cm x 30 cm) and factor B: Stages of ratooning (R1- Ratooning at 90 DAS, R2- Ratooning at 105 DAS and R3- No ratooning). Among the three spacings, 120 cm x 30 cm (S3) revealed higher values for growth parameters such as number of leaves (33.96), nodes (17.25), branches (1.42), yield parameters like number of fruits (24.37), yield per plant (304.31 g). The highest yield per hectare (15.07 t/ha) was obtained under closer spacing S1 - 60 cm x 30 cm. Among various ratooning treatments, number of fruits (25.33), yield per plant (315.98 g) and total yield (12.51 t/ha) was significantly higher in control (R3-No ratooning), the number of fruits (22.93), yield per plant (277.54 g) and total yield (10.99 t/ha) was greater in R1 than R2. Among ratooning treatment, R1 was better than R2 in terms of growth and yield characters. In interaction, spacing of 120 cm x 30 cm without ratooning (S3R3) was found better with respect to growth and yield of okra, whereas overall yield per hectare (16.53 t/ha) was greater in (S1R3) spacing 60 cm x 30 cm without ratooning. The data recorded in present investigation revealed that spacing and ratooning influenced the growth and yield parameters of okra. Thus, considering the yield of okra, spacing of 60 cm x 30 cm without ratooning found to be beneficial for Konkan agro-climatic conditions.

Minimally extended current algebras of toroidal conformal field theories

It is well-known that families of two-dimensional toroidal conformal field theories possess a dense subset of rational toroidal conformal field theories, which makes such families an interesting testing ground about rationality of conformal field theories in families in general. Rational toroidal conformal field theories possess an extended chiral and anti-chiral algebra known as W-algebras. Their partition functions decompose into a finite sum of products of holomorphic and anti-holomorphic characters of these W-algebras. Instead of considering these characters, we decompose the partition functions into products of characters of minimal extensions of û1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\hat{\\mathfrak{u}}(1) $$\\end{document} current algebras, which already appear for rational conformal field theories with target space S1. We present an explicit construction that determines such decompositions. While these decompositions are not unique, they are universal in the sense that any rational toroidal conformal field theory with a target space torus of arbitrary dimension admits such decompositions. We illustrate these decompositions with a few representative examples of rational toroidal conformal field theories with two- and three-dimensional target space tori.

Enhancing biomass and seed production in Kalmegh [Andrographis paniculata (Burm. F.) Wall ex. Nees] through optimal plant spacing and nutrients under the Western Himalayan region of India

The field experiment was conducted during the winter (kharif) seasons of 2021-22 and 2022-23 at CSIR-Central Institute of Medicinal and Aromatic Plants Research Centre Purara, Bageshwar, Uttarakhand. The study's objective was to investigate the most effective combinations of plant spacing configurations and NPK levels to enhance biomass and seed yield of kalmegh [Andrographis paniculata (Burm. F.) Wall ex. Nees] under the Western Himalayan region of Uttarakhand. The experiment consisted of nine treatments, comprising three different plant spacing (60x30 cm, 60 x45 cm, 60x60 cm) and three NPK levels (40:30:20, 80:60:30, 120:90:40), arranged in factorial randomised block design. The results indicated that treatment T3 (120:90:40 NPK) and spacing S3 (60x60 cm) consistently demonstrated superior performance, resulting in the highest plant height, number of branches, LAI, total dry matter weight, dry seed weight, and leaf stem ratio. Treatment T2 (80:60:30 NPK) and spacing S2 (60x 45 cm) displayed intermediate results, while treatment T1 (40:30:20 NPK) and spacing S1 (60 x 30 cm) exhibited relatively lower values for most parameters.

On the stability of the dimensions of spline spaces with highest order of smoothness over T-meshes

This paper studies the stability of the dimension of the spline space Sd(T) of bi-degree (d,d) with highest order of smoothness over a T-mesh T. By decomposing the T-connected component of T into a diagonalizable component and a non-diagonalizable component, we prove that the stability of the dimension of the spline space Sd(T) depends only on the stability of the rank of a matrix M̃ corresponding to the multi-vertices of the non-diagonalizable component. The matrix M̃ has a much smaller size than the conformality matrix associated with the T-connected component, and thus the stability is much easier to verify. As an application, we reprove the stability of the dimension of the spline space S3(T) over a T-mesh which is generated by subdividing a collection of 2 × 2 submeshes of a tensor product mesh under cross subdivision.

Performance of Row Spacing on the Yield of Sesame Varieties

The experiment was carried out during kharif-I season of 2020 in the experimental field of Regional Agricultural Research Station (RARS), Bangladesh Agricultural Research Institute (BARI), Cumilla to evaluate the optimum plant spacing of sesame varieties. There were four plants spacing S1 (30 ××5 cm2), S2 (30×× 10 cm2), S3 (40 ××5 cm2) and S4 (40×× 10 cm2) and two sesame varieties of V1 (BARI Til 3) and V2 (BARI Til 4) were included in the experiment. The experiment was conducted using a split-plot design with three replications. The highest seed yield (1646 kg ha-1) was found from BARI Til 4 but the highest number of capsule plant-1 and number of branches plant-1 were obtained from BARI Til-3. The maximum seed yield (1913 kg ha-1) was achieved in the interaction of S4V2 (40 ××10 cm2 and BARI Til 4) that was identical to S2V2 (30 x 10 cm2 and BARI Til 4).
 Bangladesh Agron. J. 2023, 26(1): 28-31

Swirling of Horizontal Skyrmions into Hopfions in Bulk Cubic Helimagnets

Magnetic hopfions are three-dimensional topological solitons embedded into a homogeneously magnetized background. The internal structure of hopfions is distinguished by the linked preimages—closed loops with a single orientation of the magnetization on the target space S2—and is thus characterized by the integer Hopf index QH. Alternatively, hopfions can be visualized as a result of the swirling of two-dimensional bimerons around the direction of an applied magnetic field. Since the bimeron consists of a circular core and an anti-skyrmion crescent, two hopfion varieties can be achieved with either bimeron constituent facing the hopfion interior. In bulk cubic helimagnets, however, the applied magnetic field leads to a spontaneous collapse of hopfions, i.e., the eigen-energy of hopfions has the minimum for zero hopfion radius R. Anti-hopfions with QH=−1, in this case, pass through the intermediate toron state with two-point defects. Here, we demonstrate that the competing cubic and exchange anisotropies inherent in cubic non-centrosymmetric magnets (e.g., in the Mott insulator Cu2OSeO3) as a third level of the hierarchy of energy scales following the exchange and Dzyaloshinskii–Moriya interactions, may shift the energy minimum into the region of finite hopfion radii.

Effect of Date of Planting and Spacing on Growth and Yield of Sprouting Broccoli (B. oleraceae (L.) var. italica Plenck) cv. Green Magic

The field experiment was conducted during autumn-winter (October to December) seasons of 2017–18 and 2018–19 at Horticultural Farm of Uttar Banga Krishi Viswavidyalaya, Pundibari, Cooch Behar, West Bengal, India. Treatments comprised of four planting dates viz., D1: 21st October, D2: 28th October, D3: 7th November, D4: 14th November and four spacing viz., S1: 30×45 cm2, S2: 45×45 cm2, S3: 60×45 cm2 and S4: 60×60 cm2 were assessed in factorial randomized block design with three replications. The broccoli transplanted on 21st October (D1) reported significantly maximum head weight (464.95 g) and projected yield (11.46 t ha-1) which was statistically at par with 2nd date of planting D2 i.e 28th October (423.91 g and 11.03 t ha-1 respectively) over the other dates of planting, while the wider spacing S4 i.e. 60×60 cm2 showed significantly maximum head weight (400.74 g) over other spacing’s and closer spacing S1 i.e 30×45 cm2 had recorded significantly highest yield (13.48 kg plot-1 and 14.98 t ha-1). Interaction between date of planting and spacing was significant in respect of head yield per hectare. Maximum projected head yield (17.19 t ha-1) was obtained in D1S1: 21st October and 30×45 cm2 combination. After adopting the planting dates from October 21st (D1) to October 28th (D2) and closer spacing of 30×45 cm2 (S1) was found more gainful in terms of yield and other growth parameters also.

Full higher-dimensional analysis of moduli oscillation and radiation in expanding universe

We investigate effects of the radiation and the moduli oscillation around the stabilized values on the evolution of a 6-dimensional spacetime compactified on S2. In order to see the transition from the 5-dimensional space to the 3-dimensional one, we develop a procedure to pursue the spacetime evolution with appropriate approximations, which is valid until the spacetime behaves like 4-dimensional. In the case that the moduli stabilization process cannot be described in the context of the 4-dimensional effective theory, it takes quite a long time for the moduli oscillation to dominate the total energy density, in contrast to the conventional result obtained by the 4-dimensional effective theory approach. We also found that even if the moduli are set at the stabilized values, they start to oscillate due to the pressure in the extra space S2 in some cases.

Effect of Different Spacing and Varieties on Growth, Quality and Yield in Onion (Allium cepa L.)

The present experiment was conducted at the field of Horticulture Research Farm, Babasaheb Bhimrao Ambedkar University, Lucknow (Uttar Pradesh) during rabi season of 2019-2020. The experiment was laid out in factorial randomized block design (FRBCD) and treatments comprised of three varieties i.e. V1 (Agrifound Light Red), V2 (NHRDF-Red), V3 (NHRDF-2) and three planting spacing S1 (20×7.5cm), S2 (20×10cm) and S3 (20×15 cm). The parameters were observed viz. plant height (cm), number of leaves /plants, neck thickness (cm), bulb diameter (cm), Number of scales, bulb length (cm). TSS (ᵒbrix), ascorbic acid (mg/100gm ), total sugar (%), reducing sugar (%), non- reducing sugar (%), acidity (%) yield per plot (kg) and yield per hectare (q).The results of this study revealed that the combination application of variety (Agrifound Light Red ( V1) with spacing 20X 15 cm ( S3) was best under Lucknow conditions and lowest values were noted in of variety Agrifound Light Red ( V1) with spacing 20X 7.5 cm (S1).

Effect of Different Spacing and Nitrogen Levels on of Beetroot cv. Detroit Dark Red Quality Parameters under Telangana State Conditions

The aim of this paper was to establish the effect of different spacing and nitrogen levels on quality parameters of beetroot cv. Detroit Dark Red under Telangana state conditions. It was carried out during rabi season of 2020-21 at SKLTSHU, College of Horticulture, Rajendranagar, Hyderabad, India. The experiment was laid out in Factorial Randomized Block Design with sixteen treatments replicated thrice. Treatment consisted of four levels of spacing S1 (45cm ×15cm), S2 (30cm×15cm), S3 (30cm×10cm) and S4 (15cm ×15cm) and four levels of nitrogen N1 (70 Kg ha-1), N2 (87.5 Kg ha-1), N3 (105 Kg ha-1) and N4 (122.5 Kg ha-1). The effects of the spacing and nitrogen levels was observed for quality characters. Highest total soluble solids (TSS) (9.93 oBrix), reducing sugars (1.64%), total sugars (7.31%) and chlorophyll content 45.50 (SPAD value) were recorded in wider spacing S1- 45 cm x 15 cm and highest ascorbic acid content (10.09 mg 100g-1) was recorded in closer spacing S4-15 cm x 15 cm, whereas pH and titrable acidity were found to be non-significant. Highest pH (6.20), reducing sugars (1.52%), total sugars (7.29%), ascorbic acid content (10.06 mg 100g-1) were recorded in nitrogen level N1-70 Kg N ha-1, whereas highest TSS (9.79 oBrix), chlorophyll content 45.70 (SPAD value) were observed in nitrogen level N4-122.5 Kg N ha-1. The interaction effect on quality parameters was found to be non-significant.

Influence of Varieties and Spacings on Growth, Yield Attributes and Productivity of Pigeonpea

Background: The field experiment was conducted to evaluate pigeon pea varieties viz., AL 882 and Pusa Arhar 16 under different spacing in Amritsar region” during kharif season 2019-2020 at Students’ Research Farm, Department of Agriculture, Khalsa College, Amritsar. Methods: The experiment was laid out in Randomized Block Design (factorial), replicated thrice. There were six treatments of spacing S1 (30 × 12.5), S2 (40 × 12.5), S3 (50 × 12.5), S4 (30 × 25), S5 (40 × 25), S6 (50 × 25cm) and two varieties V1 (Pusa Arhar 16) and V2 (AL 882). All the cultural practices were performed to get maximum productivity of pigeonpea from each plot. Result: The results revealed that cv. AL 882 performed better under spacing 30 × 12.5 cm for growth parameters such as plant height and LAI whereas dry matter accumulation, crop growth rate and number of primary and secondary branches were significantly higher in spacing 50 × 25 cm. Among yield attributes, cv. AL 882 showed significantly higher number of pods per plant, pod length (cm), number of seeds per plant and 100 seed weight (g) under spacing 50 × 25 cm than cv. Pusa Arhar 16. However, seed yield was maximum in wider spacing (50 × 25 cm) and narrow spacing (30 × 12.5 cm) with cv. AL 882 and Pusa Arhar 16, respectively. However, both varieties produced highest stover and biological yield under narrow spacing 30 × 12.5 cm.

Growth and Quality Responses to Plant Spacing in Potato (Solanum tuberosum L.) Varieties

The present investigation was conducted during winter season of 2020 at Experimental Farm of Vegetable Sciences, DAV University, Jalandhar to study the growth and quality responses to plant spacing in potato (Solanum tuberosum L.) varieties. Experimental material consisted of four varieties (Kufri Pukhraj, Kufri Jyoti, Kufri Badshah, Kufri Chandramukhi) sown at three spacings (70 cm × 20 cm, 60 cm × 20 cm, 50 cm × 20 cm) and laid in Factorial Randomized Block design with three replications. Observations on number of leaves per plant at 30 DAS, number of leaves per plant at 60 DAS, number of leaves per plant at 90 DAS, Plant height (cm) at 30 Days After Sowing (DAS), Plant height (cm) at 60 DAS, Plant height (cm) at 90 DAS, average tuber weight (g), number of tuber plant, marketable tuber yield per plot (kg), unmarketable tuber yield per plot (kg),tuber yield per plot (kg), TSS, ascorbic acid (mg/100g), starch content (%) and dry matter content (%) were recorded. Analysis of Variance (ANOVA) revealed significant effect of spacing, varieties and their interaction for all the characters under study. It was observed that plants sown at spacing S1 (70 cm × 20 cm) resulted in superior performance for most of the traits studied. Among cultivars, desirable results were observed in V1 (Kufri Pukhraj). Considering the interaction of varieties and spacing it was concluded that Kufri Pukhraj sown at a spacing of 70 cm × 20 cm can result in superior performance with respect to growth, yield, and quality parameters of potato.

Effect of Plant spacing and cultivar on quality attributes in sprouting broccoli

The effects of plant spacing on broccoli (Brassica oleracea L. var. italica Plenck) commercial characteristics are well determined such as yield, growth and quality parameter. However, it is not completely clear how the broccoli plant respond to changes in quality traits as a result of different plant densities. According to recent field tests, wider spacing contributes towards larger and heavier heads while, yield per hectare can be increased by close spacing. Hence, it is necessary to optimize proper plant spacing for obtaining higher yield with better quality. The study evaluated effects of the plant spacing S1 (60×45 cm), S2 (45×45 cm) and S3 (45×30 cm) on ascorbic acid, total soluble solid, total sugar, reducing sugar and non-reducing sugar contents of sprouting broccoli (Brassica oleracea L var. italica Plenck). cvs. Palam Samridhi (V1), Palam Vichitra (V2) and Palam Kanchan (V3). The cv. Palam Kanchan had the highest ascorbic acid (78.64 mg/100 g), ‘Palam Vichitra’ had the highest total soluble solids (11.21%), total (4.084%) and reducing sugar (5.62%) content was highest in ‘Palam Samridhi’. Plant spacing of 60×45 cm had the highest total soluble solids (11.15%), total sugar (4.058%) and reducing sugar (5.02%), maximum ascorbic acid (78.35 mg/100 g) content for spacing 45×30 cm. The interaction effect of variety and spacings affected all but non-reducing sugar content, maximum ascorbic acid content was recorded for the interaction of the Palam Kanchan (V3) and S3 (45×30 cm) was found (82.28 mg/100 g) while maximum total soluble solids (11.38%), total sugar (4.38%), reducing sugar (6.73%) and non-reducing sugar (0.8%) content was recorded for the treatment combination V3 S1. This study aimed to determine the effect of plant spacing on the quality parameter of sprouting broccolis. Increasing the area per plant resulted in a shortening of the time to the beginning of head formation, technical maturity; harvest and increased content of various quality attributes such as ascorbic acid, total sugar and reducing sugar content in spear than close planting.

Influence of spacing and pruning on growth, yield and economics of off-season long melon (Cucumis melo)

Long melon [Cucumis melo var. utilissimus (Roxb.) Duthie & Fuller] cultivation in open field condition in northern India is hampered due to extremes of the temperature from September to January. Therefore, the present study was carried out to explore possibility for off-season production of long melon under protected conditions at Center for Protected Cultivation Technology (CPCT), ICAR-IARI, New Delhi in 2016–17 and 2017–18. Seedlings were transplanted as per five different spacing and branch pruning methods. The combination of closer spacing with maximum branch node pruning method under polyhouse structure was found better for off-season long melon production. Flowering appeared earlier by 4.02 days, first fruit picking by 5 days, additional number of pickings (5 times) and harvesting period extended by 60 days in polyhouse compared to insect proof net-house structure. The closer spacing S1 (50 cm × 20 cm) exhibited maximum weight of fruits, fruit yield, gross income as well as net-income and B: C ratio. Among pruning methods, complete branch pruning method P1 (single stem cultivation or branch less cultivation) contributed positively significant effect on all parameters of long melon. The combination of polyhouse structure with closer spacing (50 cm × 20 cm) and optimum branch pruning (after one node cutting) gave highest yield and net income per unit area for off-season cultivation of long melon.

Effect of Different Spacing and Weed Management Practices on Weeds, Crop Growth and Productivity of Pigeon Pea Variety Pusa Arhar-16

Background: To study effect of various spacing and weed management practices on weed control, growth parameter, yield and yield attributes of pigeon pea variety Pusa Arhar-16, field experiments were conducted at Student’s Research Farm, Khalsa College Amritsar, Punjab, India during kharif season of 2019-20.Methods: The experiment was laid out in Split plot design with three replications. The treatments comprised of four different spacing i.e. S1 (30×10 cm), S2 (30×15 cm), S3 (40×15 cm) and S4 (50×25 cm) which were considered as main plot treatments and three weed management practices W1 (weedy check), W2 (pendimethalin @ 1.5 kg a.i. ha-1 at 1DAS) and W3 (rice straw mulch) as sub-plot treatments.Result: It was found that maximum plant height (218.2 cm) and highest leaf area index (2.104) was recorded in treatment S1 (30×10 cm) whereas treatment S4 (50×25 cm) was superior in rest of growth parameters viz. maximum crop growth rate (0.85 gram per plant per day), number of primary branches (18.2 per plant) and number of secondary branches (13.8 per plant). Among yield and yield attributes, spacing S1 (30×10 cm) showed maximum grain yield (16.29 q ha-1) and stover yield (49.29 q ha-1) whereas, maximum number of pods per plant (154.6), pod length (4.83 cm), number of seeds per pod (3.90) and 100-seed weight (7.14 grams) were recorded in spacing S4 (50×25 cm). The weed management treatments showed non-significant effect on growth and yield parameters due to weed suppressing ability of the crop. which might be due to weed suppressing ability of the crop. It may be concluded that pigeon pea cultivar Pusa Arhar-16 performed better in narrower spacing of 30×10 cm due to its dwarf nature and it also showed good smothering effect on the weeds due to its smothering effect.

Maximal equivariant compactification of the Urysohn spaces and other metric structures

We study isometric G-spaces and the question of when their maximal equivariant compactification is the Gromov compactification (meaning that it coincides with the compactification generated by the distance functions to points). Answering questions of Pestov, we show that this is the case for the Urysohn sphere and related spaces, but not for the unit sphere of the Gurarij space.We show that the maximal equivariant compactification of a separably categorical metric structure M under the action of its automorphism group can be identified with the space S1(M) of 1-types over M, and is in particular metrizable. This provides a unified understanding of the previous and other examples. In particular, the maximal equivariant compactifications of the spheres of the Gurarij space and of the Lp spaces are metrizable.We also prove a uniform version of Effros' Theorem for isometric actions of Roelcke precompact Polish groups.

Performance of Canola (Brassica napus L.) at Different Age of Seedling under System of Mustard Intensification

Background: Rapeseed (Brassica napus L.) also known as ‘rape’ is bright yellow flowering member of family Brassicaceae, cultivated for its oil rich seed. It is third most important oilseed crop after soybean and oil palm. Despite an important oilseeds crop there is little advancement in suitable crop management strategies for improving crop productivity. The SRI has set of principles such as use of young seedlings, one seedling per hill, square planting, mechanical weeding, addition of organic matter. Recently the SRI is being successfully experimented in other crops such as wheat, maize, soybean, blackgram, kidney bean, potato in the name of System of Crop Intensification. Methods: This research experiment was carried out at the Student’s Research Farm, Khalsa College, Amritsar during the rabi season of 2018-19. The Split plot design with three replications was carried under age of seedling in main plot treatments A1 [20 day seedling], A2 [30 day seedling] and A3 [40 day seedling] and four intra row spacing treatments in sub plots S1 [15cm], S2 [30 cm], S3 [45 cm] and S4 [60 cm]. Result: Seed yield decreased progressively with increase in age of seedling. Wider spacing between plants (45 cm) observed high number of siliquae per plant than closer spacing (15 cm). Seed yield was significantly highest when crop was transplanted with 45 cm intra row spacing. The percent increase in seed yield in different SMI (System of Mustard Intensification) spacing treatments over closer spacing S1 (15 cm) were 21.62, 6.36, 4.89, per cent in S3, S4 and S2 respectively.

Wilson-\u2019t Hooft lines as transfer matrices

We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional mathcal{N} = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space S1 × ϵ ℝ2 × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.

Performance of White Maize under Different Spacing and Integrated Fertilizer Management

An experiment was conducted during December, 2017 to May, 2018 at the Agronomy field of Sher-e-Bangla Agricultural University, Dhaka to evaluate the performance of white maize variety under different spacing and integrated fertilizer management. The experiment comprised two different factors; (1) two plant spacing viz. S1 (60 cm × 20 cm) and S2 (40 cm × 20 cm) and (2) four levels of integrated fertilizer application viz. T1: All chemical fertilizer (recommended dose), T2: maize straw compost +½ of recommended dose,T3: cowdung+½ of recommended dose and T4: vermicompost +½ of recommended dose. The experiment was set up in split plot design with three replications. Results revealed that both the individual and the interaction treatments had effect on different growth and yield parameters of white maize. In respect of the spacing effect, the wider spacing S1 showed higher plant height, number of leaves plant-1, cob length, cob circumference, number of grains cob-1, shelling percentage, 100 grains weight and harvest index where S2 showed higher grain yield. The integrated fertilizer had significant effect on different growth and yield parameters of white maize. In respect of the integrated fertilizer effect, the highest values in plant height, number of leaves plant-1, leaf area index and crop growth rate, cob length, cob circumference, number of grains cob-1, shelling percentage, 100 grains weight, grain yield, stover yield and biological yield were highest with T3 whereas, the lowest corresponding values were recorded from T2. Among the interaction treatments, higher seed yield was obtained with the interaction treatment S2T3 (10.01 t ha-1) while S1T2 showed significantly the lowest seed yield (5.27 t ha-1). The highest seed yield was mostly attributed to the number of grains per cob (328-433) and 100 seed weights (29.67-33.33 g).

C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion

Smooth orientation planning is beneficial for the working performance and service life of industrial robots, keeping robots from violent impacts and shocks caused by discontinuous orientation planning. Nevertheless, the popular used quaternion interpolations can hardly guarantee C2 continuity for multiorientation interpolation. Aiming at the problem, an efficient quaternion interpolation methodology based on logarithmic quaternion was proposed. Quaternions of more than two key orientations were expressed in the exponential forms of quaternion. These four-dimensional quaternions in space S3, when logarithms were taken for them, could be converted to three-dimensional points in space R3 so that B-spline interpolation could be applied freely to interpolate. The core formulas that B-spline interpolated points were mapped to quaternion were founded since B-spline interpolated point vectors were decomposed to the product of unitized forms and exponents were taken for them. The proposed methodology made B-spline curve applicable to quaternion interpolation through dimension reduction and the high-order continuity of the B-spline curve remained when B-spline interpolated points were mapped to quaternions. The function for reversely finding control points of B-spline curve with zero curvature at endpoints was derived, which helped interpolation curve become smoother and sleeker. The validity and rationality of the principle were verified by the study case. For comparison, the study case was also analyzed by the popular quaternion interpolations, Spherical Linear Interpolation (SLERP) and Spherical and Quadrangle (SQUAD). The comparison results demonstrated the proposed methodology had higher smoothness than SLERP and SQUAD and thus would provide better protection for robot end-effector from violent impacts led by unreasonable multiorientation interpolation. It should be noted that the proposed methodology can be extended to multiorientation quaternion interpolation with higher continuity than the second order.