Inclusion Matrices and Chains

Given integers $t$, $k$, and $v$ such that $0\leq t\leq k\leq v$, let $W_{tk}(v)$ be the inclusion matrix of $t$-subsets vs. $k$-subsets of a $v$-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset $2^{[v]}$ into symmetric skipless chains is given. Based on this decomposition, we construct an inclusion matrix, denoted by $W_{\bar{t}k}(v)$, which is row-equivalent to $W_{tk}(v)$. Its Smith normal form is determined. As applications, Wilson's diagonal form of $W_{tk}(v)$ is obtained as well as a new proof of the well known theorem on the necessary and sufficient conditions for existence of integral solutions of the system $W_{tk}\bf{x}=\bf{b}$ due to Wilson. Finally we present anotherinclusion matrix with similar properties to those of $W_{\bar{t}k}(v)$ which is in some way equivalent to $W_{tk}(v)$.Comment: Accepted for publication in Journal of Combinatorial Theory, Series

Alleviation of cold stress in vegetable crops

Low temperature is a major environmental factor that limits crop productivity of plants. Cold stress is a serious threat to the sustainability of crop yields. Low temperature has a huge impact on the survival and geographical distribution of plants. It negatively affects cellular components and metabolism, and temperature extremes impose stresses of variable severity that depend on the intensity and duration of the stress. Low temperature (less than minimum) leads to chlorosis, necrosis, membrane damage, changes in cytoplasm viscosity, and changes in enzyme activities leading to death of plant. Cold stress disrupts the integrity of intracellular organelles, leading to the loss of compartmentalization. It also causes reduction and impairing of photosynthesis, protein assembly and general metabolic processes. Moreover, cold stress during anthesis induces flower dropping, sterility of pollen, pollen tube distortion, ovule abortion and reduced fruit set, which leads to declined growth and lower yield. A number of approaches are being used to mitigate the deleterious effects of cold stress which threatens the successful vegetable crop production, application of plant growth regulators (salicylic acid, abscisic acid, jasmonic acid, Gibberellin and brassinosteroids) and unitization of genetics tools and plant breeding is one of the strategies to alleviate the low temperature stress in vegetable crops. Plant growth regulators play a greater role in improving the cold stress tolerance. In this paper, the effects of cold stress on vegetable growth, productivity and physiological activities were discussed, and some effective techniques for the mitigation of cold stress that help sustainable vegetable production under fluctuating climate is presented

Nutritional and Bread-Making Quality of Wheat as Influenced by Mineral Fertilization in a Compost-Amended Regosol soil

This experiment was conducted to assess the effect of different levels of nitrogen (N), phosphorus (P) and potassium (K) fertilization on growth, grain yield, nutritional and bread-making quality of wheat in a compost-amended regosol soil. Wheat cultivar Minaminokaori was grown in containers containing a mixture of regosol and aerobic compost (2:1 v/v). This study comprised a non-fertilized control (F1) and six levels of NPK fertilizers: F2 (80 kg N + 40 kg P2O5 +40 kg K2O ha-1), F3 (110 kg N + 60 kg P2O5 + 55 kg K2O ha-1), F4 (140 kg N + 80 kg P2O5 + 70 kg K2O ha-1), F5 (170 kg N + 100 kg P2O5 + 85 kg K2O ha-1), F6 (200 kg N + 120 kg P2O5 + 100 kg K2O ha-1) and F7 (230 kg N + 140 kg P2O5 + 115 K2O kg ha-1). A significant improvement in agronomic performance, grain nutritional and bread-making quality of wheat was observed with the F6 treatment, it increased the grain yield (151.6%), crude protein (65.3%), water-soluble pentosan (40.5%), and dry gluten (4-fold) compared to the control. The F6 treatment also increased grain total N, P, K, Mg, Ca, Zn and inorganic phosphorus contents by 65.2, 33.6, 8.9, 19.7, 165.9, 26.1 and 80.0%, respectively, compared to control. However, it slightly increased grain phytate P content. The results from this study suggest that agronomic performance, grain yield, nutritional and bread-making quality of wheat can be improved with an appropriate dose of NPK in a compost-amended regosol soil

Outage probability based on telecommunication range for multi-hop HALE UAVs

Cooperative relaying increases telecommunication range, improves the connectivity, and increases the reliability of data transmission; however, the transmitted power does not change. This paper analyzes the extended telecommunication range of a multi-hop cascaded network comprising N–cooperative relaying high-altitude long endurance (HALE) unmanned aerial vehicles (UAVs) under ambient conditions. A notable ambient condition is rain, which causes signals to scatter in different directions; hence, one should model the communication channel for HALE UAV as a Rayleigh channel. This paper proposes a statistical model that is based on the effect of the telecommunication range on the outage probability in an N-Rayleigh fading channel. The simulation results show that as the telecommunication range increases, the outage probability (Poutage) also increases, whereas when both the telecommunication range and the number of relays increase, Poutage decreases. An issue that has been highlighted in this paper is that, by increasing number of relays from N=1 to N=5 the telecommunication range increases and Poutage about 40% decreases. Moreover, in rainy conditions and with a fixed number of relays, when both the intensity of rainfall and telecommunication range increases, Poutage increases. For example by increasing rate of rain (Rr) from 1mm/h to 100 mm/h, Poutage increases around 30% in 100 Km with two relays