Related papers: Enumerations of 1-rotational Steiner systems

In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of order $v$, where $v=3^k$, and $3$-rank $v-k$. We develop an…

Let $\mathcal{R}$ be a unital ring with involution. The notions of 1MP-inverse and MP1-inverse are extended from $M_{m,n}(\mathbb{C)}$, the set of all $m\times n $ matrices over $\mathbb{C}$, to the set $\mathcal{R}% ^{\dagger}$ of all…

We are concerned with the invariants of Steiner chains consisting of four circles. In particular, we compute the invariant moments of curvatures in Steiner 4-chains and give two applications of the obtained formulas. Specifically, we…

Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…

We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems…

We report on the orbital architectures of Kepler systems having multiple planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting…

The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute…

We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is will known that Steiner quadruple systems of order v, or SQS(v), exist if and only if v = 2, 4 mod 6. Universal cycles, introduced by…

We enumerate the number of complex irreducible representations of each degree of general unitary groups of degree 4 over principal ideal rings of length 2.

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary…

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped…

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…

Considering spin-orbit coupling, the tetragonal crystal-field, and all relevant superexchange processes including quantum interference, we derive expressions for the energy levels of the vanadium ions in tetragonal Sr2VO4. The used…

We consider a superexchange Hamiltonian, $H=-\sum_{<i,j>}(2{\bf S}_i\cdot {\bf S}_j-\frac 12)(2{\bf T}_i\cdot {\bf T}_j-\frac 12)$, which describes systems with orbital degeneracy and strong electron-phonon coupling in the limit of large…

First order integrals of motion for Schr\"odinger equations with position dependent masses are classified. Seventeen classes of such equations with non-equivalent symmetries are specified. They include integrable, superintegrable and…

In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…

For coherent families of crystals of affine Lie algebras of type B^{(1)}_n, D^{(1)}_n, A^{(2)}_{2n} and D^{(2)}_{n+1} we describe the combinatorial R matrix using column insertion algorithms for B,C,D Young tableaux.