Under favorable soil conditions such as existence of easily destructible organic compounds, balanced heat and moisture, adequate ventilation and abundant nutrients, organic materials are mineralized. Once mineralizing occurs, mineral elements like P, S, Ca, Mg, K and other cations are released. A related study was conducted to determine the effect of seven organic fertilizers (Leaf Mold (LM), R...

For $$p \in (1,N)$$ and $$\Omega \subseteq {\mathbb {R}}^N$$ open, the Beppo-Levi space $${\mathcal {D}}^{1,p}_0(\Omega )$$ is completion of $$C_c^{\infty }(\Omega with respect to norm $$\left[ \int _{\Omega }|\nabla u|^p dx \right] ^ \frac{1}{p}.$$ Using p-capacity, we define a then identify Banach function {H}}(\Omega set all g in $$L^1_{loc}(\Omega that admits following Hardy–Sobolev ty...

The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts w...

We obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. Also weconsider relations Kadec-Klee property and shur property with this objects.These theorems are extend of papers mohebi and Narayana.

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...