We revive the study of the symmetric three-term recurrence equations. Our main result shows that these equations have a natural symplectic structure, that is, every symmetric three-term recurrence equation is a special discrete symplectic system. The assumptions on the coefficients in this paper are weaker and more natural than those in the current literature. In addition, our result implies th...

The symmetric multistep methods developed by Quinlan and Tremaine (1990) are shown to suffer from resonances and instabilities at special stepsizes when used to integrate nonlinear equations. This property of symmetric multistep methods was missed in previous studies that considered only the linear stability of the methods. The resonances and instabilities are worse for high-order methods than ...

Interteaching is a new method of classroom instruction that is based on behavioral principles but offers more flexibility than other behaviorally based methods. We examined the effectiveness of interteaching relative to a traditional form of classroom instruction-the lecture. In Study 1, participants in a graduate course in special education took short quizzes after alternating conditions of in...

We present a family of rank symmetric diamond-colored distributive lattices that are naturally related to the Fibonacci sequence and certain its generalizations. These re-interpret unify descriptions some un- or differently-colored found variously in literature. demonstrate our Fibonaccian realize (often reducible) representations special linear Lie algebras, with weight basis vectors realized ...

An imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al. (1950) gave a way of passing from a given two person game to a symmetric game whose symmetric Nash equilibria are in oneto-one correspondence with the Nash equilibria of the ...

We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated symmetric function in noncommuting variables for which we give a deletion-contraction formula. In the case of graphs this symmetric function in noncommuting variab...

The formation of a perfect vertebrate body plan poses many questions that thrill developmental biologists. Special attention has been given to the symmetric segmental patterning that allows the formation of the vertebrae and skeletal muscles. These segmented structures derive from bilaterally symmetric units called somites, which are formed under the control of a segmentation clock. At the same...

Symmetry breaking of solitons in a class of one-dimensional parity-time (PT) symmetric complex potentials with cubic nonlinearity is reported. In generic PT-symmetric potentials, such symmetry breaking is forbidden. However, in a special class of PT-symmetric potentials V(x)=g(2)(x)+αg(x)+ig'(x), where g(x) is a real and even function and α a real constant, symmetry breaking of solitons can occ...