It has been proved that algebraic polynomials P are dense in the space Lp(R, dμ), p∈ (0,∞), iff the measure μ is representable as dμ = wp dν with a finite non-negative Borel measure ν and an upper semi-continuous function w : R → R+ : = [0,∞) such that P is a dense subset of the space C0 w : = {f ∈ C(R) : w(x)f(x) → 0 as |x| → ∞} equipped with the seminorm ‖f‖w := supx∈R w(x)|f(x)|. The similar...

low phosphorous (p) availability in soils limits production of soybean [glycine max (l.) merr.] around the world. this study was conducted to determine whether exogenous expression of the rice (oryza sativa l.) phosphates transporter gene ospt2 would increase inorganic phosphates (pi) acquisition and improve yield in transgenic soybean. cotyledonary-node explants of the soybean were inoculated ...

We study angles of multipliers repelling cycles for hyperbolic rational maps in $\mathbb {C}(z)$. For a fixed $K \gg 1$, we show that nearly every interval length $2\pi /K$ $(-\pi ,\pi ]$ contains multiplier angle with the property abs

in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

In this short note we provide an example of a semi-linear group G which does not admit a semi-linear affine embedding; in other words, there is no semi-linear isomorphism between topological groups f : G → G′ ⊆ Mm, such that the group topology on G′ coincides with the subspace topology induced by Mm. Let M be an o-minimal structure. By “definable” we mean “definable in M” possibly with paramete...