Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by ẋi = xi ( fi (x)−φ) , i = 1, . . . ,n, where xi is the frequency, or relative abundance, of strategy i, fi is its fitness, and φ = ∑i=1 xi fi is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A, where Ai, j is the expected payoff...

in this paper, we introduce the notion of derivation on krasner hyperrings as follows: the function d : r  r isa derivation on a krasner hyperring r if for all , , ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). then, we investigate some fundamental properties of derivation on krasnerhyperings and prime krasner hyperrings. also, we introduce differential krasner hy...

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

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A relatively potent antiserum against highly purified, unactivated human factor XI antigen was raised in a rabbit. This antiserum, after concentration, neutralized 50% of the factor XI clotting activity of a standard normal plasma at an antiserum dilution of 1/900. The antiserum was used in a neutralization-inhibition assay to study the relation between factor XI clotting activity and factor XI...

X chromosome inactivation (XCI) is an essential mechanism for dosage compensation of X-linked genes in female cells. We report that subcultures from lines of female human embryonic stem cells (hESCs) exhibit variation (0-100%) for XCI markers, including XIST RNA expression and enrichment of histone H3 lysine 27 trimethylation (H3K27me3) on the inactive X chromosome (Xi). Surprisingly, regardles...

Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...