We give a description of invariants and attractors the critical subcritical Galton–Watson tree measures under operation Horton pruning (cutting leaves with subsequent series reduction). Under regularity condition, class invariant consists binary one-parameter family trees offspring distribution {qk} that has power tail qk∼Ck−(1+1/q0), where q0∈(1/2,1). Each measure non-empty domain attraction c...

The t region of mouse chromosome 17 exhibits recombination suppression with wild-type chromatin. However, the region has resisted classical genetic dissection because of a lack of defined variants. Mutations induced by N-ethyl-N-nitrosourea (ENU) at the Brachyury (T), quaking (qk), and tufted (tf) loci of the mouse tw5 haplotype have now allowed the analysis of crossovers between two complete t...

Using e+e− → γ +X as an example, we show that the conventional factorization theorem in perturbative quantum chromodynamics breaks down for isolated photon cross sections in a well defined part of phase space. Implications and physical consequences are discussed. 12.38.Bx, 13.65.+i, 12.38.Qk Typeset using REVTEX

We give the matrix characterizations from Nakano vector-valued sequence space (X,p) and Fr (X,p) into the sequence spaces Er , ∞, ∞(q), bs, and cs, where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk > 1 for all k∈N and r ≥ 0. 2000 Mathematics Subject Classification. 46A45.

Let (Xi)i∈N be a sequence of independent and identically distributed random variables with values in the set N0 of non-negative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X1, . . . , Xn} of the first n values. We obtain necessary and sufficient conditions in terms of ...

Quaking protein isoforms arise from a single Quaking gene and bind the same RNA motif to regulate splicing, translation, decay, and localization of a large set of RNAs. However, the mechanisms by which Quaking expression is controlled to ensure that appropriate amounts of each isoform are available for such disparate gene expression processes are unknown. Here we explore how levels of two isofo...