in this paper, to account for the effect of water stresses in the various growth stages under deficitirrigation, the multiplicative, seasonal and minimal approaches are integrated in the budgetmodel. to evaluate the model, the simulated yields for winter wheat (was grown in sharif abaddistrict) under various levels of water stress were compared with observed yields. the resultshowed, simulated ...

In this paper, to account for the effect of water stresses in the various growth stages under deficitirrigation, the multiplicative, seasonal and minimal approaches are integrated in the BUDGETmodel. To evaluate the model, the simulated yields for winter wheat (was grown in Sharif Abaddistrict) under various levels of water stress were compared with observed yields. The resultshowed, simulated ...

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...