The Asymptotic Behavior of Solutions of Second order Difference Equations With Damping Term

  The author presents some sufficient conditions for second order difference equation with damping term of the form                                                                             ^(an ^(xn + cxn-k)) + pn^xn + qnf(xn+1-l) = 0 An example is given to illustrate the main results. 2010 AMS Subject Classification: 39A11 Keywords and Phrases: Second order, difference equation, damping term

Oscillatory Behavior of Even Order Quasilinear Delay Difference Equations

In this paper, we consider the quasilinear delay difference equation of the form and obtained sufficient conditions for the oscillation for all solutions. Example are given to illustrate the main results

Existence of Nonoscillatory Solutions of First Order Nonlinear Neutral Dierence Equations

In this paper, we discuss the existence of nonoscillatory solutions of first order nonlinear neutral difference equations of the form We use the Knaster-Tarski xed point theorem to obtain some sucient conditions for the existence of nonoscillatory solutions of above equations. Example are given to illustrate the main results

Prospects of biodrainage to mitigate problems of waterlogging and soil salinity in context of India - A review

Major parts of agricultural lands in arid and semi-arid regions of India are affected by soil salinity and waterlogging in canal command area and outside. Waterlogging is caused by a rising water table and poor drainage conditions.  Stress due to waterlogging and salinity are serious to plants in all stages from seed germination to active growth and maturity. Unmanaged affected agricultural lands turn into low productive marshlands in the long run. Physical provision of surface or sub-surface drainage structures can rescue in such a situation. Yet, high skill and investment are required in the installation and maintenance of such structures. Alternatively, biodrainage method has been evolved as an effective method recently world over. In biodrainage, plants are raised over a larger area, which can transpire and remove an enormous amount of water from the soil. Plants having adequate adaptive traits and tolerance mechanisms are desirable to mitigate waterlogging and salinity. Biodrainage is suitable in rainfed and irrigated conditions. Planting of right plant species in optimum population and geometry decides the efficiency of biodrainage. Further, combining biodrainage with the conventional drainage can improve land and water productivity. Eucalyptus is the most suitable tree species for biodrainage as it has well performed in versatile environments. It possesses appreciable tolerance to salinity, sodicity and waterlogged conditions of the soil.  Fast-growing with a straight trunk, deep rooting ability, low shading effect and high transpiration capacity are promising characteristics of this tree.  Prominent woody species like Acacia nilotica, Dalbergia sissoo, Hardwickia binata can also be grown for high profit

Assessing growth performance and agro-meteorological indices of green gram (Vigna radiata L.) varieties influenced by soil amendments and foliar application under sodic soil in Cauvery delta zone of Tamil Nadu

Green gram prefers neutral soil reactions and is sensitive to saline and alkaline soil conditions. Around 2.1 % of the country's geographical area is salt-affected, of which 3.77 million ha is sodic soil. Rehabilitation of salt-affected soil using drainage is expensive and leaching with good quality water is not feasible. To overcome this, a field experiment was conducted at Anbil Dharmalingam Agricultural College and Research Institute, Tiruchirappalli, during summer 2022 to study the effect of soil amendments and foliar nutrition under sodic soil. The experiment was laid out in a split-plot design with three replications. The treatments comprised of different varieties in main plots (M1, M2, M3, M4, M5 and M6)  and different soil amendments with foliar application in sub plots (S1, S2 and S3). The results showed that VBN (Gg) 4 + gypsum @ 50 % GR + pressmud @ 10 t ha-1 + FS of brassinosteroid 0.2 ppm (M4S1) registered higher plant height (18.31, 31.52 & 60.63 cm), DMP (907, 1932 & 2969 kg ha-1), CGR (3.02, 6.83 & 4.15 g m-2 d-1) and SPAD value (37.56, 41.62 & 30.57) at 30, 45 DAS and harvest. The same treatments increased grain and haulm yield of 997 and 2232 kg ha-1. It also increased all agro-meteorological indices viz., GDD, HTU, PTU, RTD and HUE of green gram. However, comparable results were obtained with VBN (Gg) 4 + gypsum @ 50 % GR + CSR GROMOR @ 25 kg ha-1 + FS of brassinosteroid 0.2 ppm (M4S2)

Modulational instability in PT\cal{PT}-symmetric Bragg grating structures with saturable nonlinearity

We investigate the nontrivial characteristics of modulational instability (MI) in a system of Bragg gratings with saturable nonlinearity. We also introduce an equal amount of gain and loss into the existing system which gives rise to an additional degree of freedom, thanks to the concept of $\cal PT$- symmetry. We obtain the nonlinear dispersion relation of the saturable model and discover that such dispersion relations for both the conventional and $\cal PT$- symmetric cases contradict with the conventional Kerr and saturable systems by not displaying the typical signature of loop formation in either the upper branch or lower branch of the curve drawn against the wavenumber and detuning parameter. We then employ a standard linear stability analysis in order to study the MI dynamics of the continuous waves perturbed by an infinitesimal perturbation. The main objective of this paper is twofold. We first investigate the dynamics of the MI gain spectrum at the top and bottom of the photonic bandgap followed by a comprehensive analysis carried out in the anomalous and normal dispersion regimes. As a result, this perturbed system driven by the saturable nonlinearity and gain/loss yields a variety of instability spectra, which include the conventional side bands, monotonically increasing gain, the emergence of a single spectrum in either of the Stokes wavenumber region, and so on. In particular, we observe a remarkably peculiar spectrum, which is caused predominantly by the system parameter though the perturbation wavenumber boosts the former. We also address the impact of all the physical parameters considered in the proposed model which include coupling coefficient, dispersion parameter, and saturable nonlinearity on the phenomenon of MI for different $\cal PT$- symmetric regimes ranging from unbroken to broken one in greater detail.Comment: To appear in Phys. Rev.

Partially oxidized ferrocenyl complexes for nonlinear optics

Second-order nonlinearity (p) in a series of partially oxidized bisferrocenes linked through conducting -C=N- linkages has been measured and found to vary linearly with the redox potential difference between the ferrocene moiety and the oxidant

Impact of the orientation of seed placement and depth of its sowing on germination: A review

Seed orientation and its impacts on germination and seedling establishment mainly depend on the type of germination (hypogeal (or) epigeal), seed size and shape. Higher germination per cent is noticed when seeds are sown in the horizontal position. Planting seeds in a downward position can lead to a variety of physiological, chemical and morphological changes in seedlings. Consequences are usually manifested as noticeable modifications in their development. Vigorous seeds have strong, resilient seedlings due to their well-balanced metabolism and coordinated subcellular activity, making them well-suited for tough environments. Proper plumule and radicle growth require additional hormones and energy to ensure seedling survival. Four necessary factors must be considered while deciding the sowing depth viz., soil moisture, optimum soil temperature, soil aeration and atmospheric humidity required for seed germination, emergence and seedling growth. Variations are observed in germination behaviour and seedling growth for different sowing depths. The necessary factors are very much important for efficient nursery seedlings production. This review looks at the effects of seed depth and orientation on the germination and growth of important agricultural, horticultural and silvicultural crops

Correlation of soil physico chemical properties with a yield of green gram (Vigna radiata L.) by soil amendments and foliar nutrition under sodic soil condition

In India, about 3.77 million ha of the country's geographical area is affected by sodicity. There is an urgent need to minimize further land degradation and restore the fertility of degraded soils to meet the growing demand for food. The most effective way to overcome salt stress is by applying nutrients through soil and foliar. In this context, a field experiment was conducted at Anbil Dharmalingam Agricultural College and Research Institute (ADAC & RI), Tiruchirappalli, in the summer of 2022 to study the reclamation potential of soil amendments and foliar nutrition in sodic soil. The experiment was laid out in a split-plot design with three replications. The treatment comprised of soil amendments viz., M1- Pongamia green leaf manure (GLM) @ 6.25 t ha-1, M2- Pressmud @ 10 t ha-1, M3-CSR GROMOR @ 25 kg ha-1, M4-Gypsum @ 50 % GR, M5-Gypsum @ 50 % gypsum requirement (GR) + Pongamia GLM @ 6.25 t ha-1, M6-Gypsum @ 50 % GR + Pressmud @ 10 t ha-1, M7-Gypsum @ 50 % GR + CSR GROMOR @ 25 kg ha-1 and M8- Farmers practice, in main plots and foliar nutrition viz., S1- Foliar spray (FS) of CSR GROMOR @ 3% @ 30 DAS, S2-FS of Brassinosteroid (BRs) 0.2 ppm @ 30 DAS and S3-FS of Melatonin 60 ppm @ 30 DAS in sub plots. The results showed that gypsum @ 50 % GR + Pressmud @ 10 t ha-1+ FS of Brassinosteroid 0.2 ppm @ 30 DAS(M6S2) registered significantly (P=0.05%) lowest pH (8.07), ESP (11.62%), exchangeable Na+ (2.93 c mol (p+) kg-1) with higher exchangeable Ca2+(11.23 c mol (p+) kg-1), Mg2+ (8.09 c mol (p+) kg-1) and K+(0.82 c mol (p+) kg-1). It also increased soil available nutrients (235.6, 24.57 & 309.6 kg NPK ha-1) and grain yield (1110 kg ha-1) of green gram. However, it was on par with gypsum @ 50 % GR + CSR GROMOR @ 25 kg ha-1 + FS of Brassinosteroid 0.2 ppm @ 30 DAS(M7S2). Hence it was concluded that the application of gypsum along with pressmud or CSR GROMOR combined with FS of brassinostroid had a remarkable effect in reducing soil sodicity and increasing the productivity of green gram.

Effect of ageing on in vitro true seed and in vivo drupe germination and its dormancy mechanism in teak (Tectona grandis Linn.f)

The germination percentage of teak seed is generally very poor due to its higher percentage of empty seed and poor seed viability. The viable seeds exhibit protracted germination behaviour due to their inherent seed dormancy and other physiochemical characteristics. Hence establishing a teak nursery for largescale plantation activities is a challenging task. This study was undertaken to study the effect of ageing on in vitro true seed and in vivo drupe germination and its dormancy mechanism in teak. Fresh, one-year and two-year stored drupes were used to represent different levels of ageing. Under in vivo conditions, poor drupe germination was observed in fresh drupes (3%) and germination percentage was increased when the drupes were subjected to ageing for one year (17%) or two years (32%). When true seeds separated from fresh drupes and germinated under in vitro conditions, enhanced germination (58.3%) was observed. Biochemical analysis showed that indole-3- acetic acid, indole butyric acid, abscisic acid and coumarin are not present in fresh, one year and two-year-old true seeds. The gibberellic acid was increased with an increase in ageing, but the GA3 did not influence the germination percent under in vitro conditions. Scanning electron microscope (SEM) image of fresh teak true seed showed that embryo tip was shrivelled, whereas one and two-year-old true seed embryo tip bulged; this was confirmed that one and two-year-old true seed embryos were matured and satisfied the after-ripening requirement. Nursery studies revealed that one and two-year-old drupes recorded the highest germination compared to fresh drupes.