Guanine-rich oligonucleotides and short telomeric DNA sequences can self-associate into G-quartet stabilized complexes. We discovered that this self-association can occur in sequencing reactions and that higher-order structures stimulate DNA polymerase to synthesize extended DNA strands. Base analogues were used to identify Hoogsteen base pairings as stabilizing forces in these stimulatory DNA ...

The floral quartet model of floral organ specification poses that different tetramers of MIKC-type MADS-domain transcription factors control gene expression and hence the identity of floral organs during development. Here, we provide a brief history of the floral quartet model and review several lines of recent evidence that support the model. We also describe how the model has been used in con...

Homeotic MADS box genes encoding transcription factors specify the identity of floral organs by interacting in a combinatorial way. The 'floral quartet model', published several years ago, pulled together several lines of evidence suggesting that floral homeotic proteins bind as tetramers to two separated DNA sequence elements termed 'CArG boxes' by looping the intervening DNA. However, experim...

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This article concerns the existence and multiplicity of positive solutions for the singular Sturm-Liouville boundary value problem (p(t)u′(t))′ + h(t)f(t, u(t)) = 0, 0 < t <∞, au(0)− b lim t→0+ p(t)u′(t) = 0, c lim t→∞ u(t) + d lim t→∞ p(t)u′(t) = 0. We use fixed point index theory to establish our main results based on a priori estimates derived by utilizing spectral properties of associated l...

Let ε > 0 and consider ε2u′′(t; ε) + u′(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε)ds+ f(t; ε), t ≥ 0, u(0; ε) = u0(ε), u ′(0; ε) = u1(ε), and w′(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t), t ≥ 0, w(0) = w0, in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear operator for t ≥ 0. With some conv...

We now define random walks on weighted graphs. We will let A denote the adjacency matrix of a weighted graph. We will also the graph to have self-loops, which will correspond to diagonal entries in A. Thus, the only restriction on A is that is be symmetric and non-negative. When our random walk is at a vertex u, it will go to node v with probability proportional to au,v: mu,v def = au,v ∑ w au,w .

Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of S-asymptotically !-periodic mild solutions for a class of linear and semilinear fractional order differential equations of the form D +1 t u(t) + D t u(t)−Au(t) = f(t, u(t)), t > 0, 0 < ≤ ≤ 1, ≥ 0.

g e y w o r d s N o n a n t o n o m o u s equation, Wave equation, Uniform attractor, Exponential attractor, a-contraction, Squeezing property. 1 . I N T R O D U C T I O N In this note, we s tudy the long t ime behavior of a general wave equat ion of the form Pu" + Qu' + Au + F (t, u) = h (t) , (1.1) in a Hilbert space H, where A, P , and Q are linear positive self-adjoint operators. This class...

We study nonnegative solutions u(x, t) of the nonlinear parabolic inequalities au ≤ ut −∆u ≤ u in various subsets of R×R, where λ > n+2 n and a ∈ (0, 1) are constants. We show that changing the value of a in the open interval (0, 1) can dramatically affect the blow-up of these solutions.