motivated by the terminal wiener index‎, ‎we define the ashwini index $mathcal{a}$ of trees as‎ begin{eqnarray*}‎ % ‎nonumber to remove numbering (before each equation)‎ ‎mathcal{a}(t) &=& sumlimits_{1leq i‎&+& deg_{_{t}}(n(v_{j}))],‎ ‎end{eqnarray*}‎ ‎where $d_{t}(v_{i}‎, ‎v_{j})$ is the distance between the vertices $v_{i}‎, ‎v_{j} in v(t)$‎, ‎is equal to the length of the shortest path start...

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A family of non-Hermitian but ${\cal PT}-$symmetric $2J$ by toy-model tridiagonal-matrix Hamiltonians $H^{(2J)}=H^{(2J)}(t)$ with $J=K+M=1,2,\ldots$ and $t<J^2$ is studied, for which a real $2K$ tridiagonal-submatrix component $C(t)$ the Hamiltonian assumed coupled to its other two complex Hermitian $M$ components $A(t)$ $B(t)$. By construction, (i) all submatrices get decoupled at $t=t_M=M\,(2...

During B and T cell development, the RAG1/RAG2 protein complex cleaves DNA at conserved recombination signal sequences (RSS) to initiate V(D)J recombination. RAG1/2 has also been shown to catalyze transpositional strand transfer of RSS-containing substrates into target DNA to form branched DNA intermediates. We show that RAG1/2 can resolve these intermediates by two pathways. RAG1/2 catalyzes h...

We study the nonequilibrium dynamics of a homogeneous quantum Ising ring after quench, in which transverse field $g$ suddenly changes from zero to nonzero value. The long-timescale reduced single spin and two nearest-neighbor spins, involves evaluation expectation values odd operators that break fermion parity, is exactly obtained for finite-size but large rings through use recently developed P...

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

B. Liu, J. Meyer-ter-Vehn, K-U. Bamberg, W. J. Ma, J. Liu, X. T. He, X. Q. Yan, and H. Ruhl Institute for Computational and Plasma Physics, Ludwig-Maximilian-Universitaet, 80333 Muenchen, Germany Key Laboratory of HEDP of the Ministry of Education, CAPT, and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China Institute of Applied Physics and Computat...

let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$&apos;s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$&apos;s are complex slowlyvarying functions.under the assumption that th...