Large Cross-free sets in Steiner triple systems

A {\em cross-free} set of size $m$ in a Steiner triple system $(V,{\cal{B}})$ is three pairwise disjoint $m$-element subsets $X_1,X_2,X_3\subset V$ such that no $B\in {\cal{B}}$ intersects all the three $X_i$-s. We conjecture that for every admissible $n$ there is an STS$(n)$ with a cross-free set of size $\lfloor{n-3\over 3}\rfloor$ which if true, is best possible. We prove this conjecture for the case $n=18k+3$, constructing an STS$(18k+3)$ containing a cross-free set of size $6k$. We note that some of the $3$-bichromatic STSs, constructed by Colbourn, Dinitz and Rosa, have cross-free sets of size close to $6k$ (but cannot have size exactly $6k$). The constructed STS$(18k+3)$ shows that equality is possible for $n=18k+3$ in the following result: in every $3$-coloring of the blocks of any Steiner triple system STS$(n)$ there is a monochromatic connected component of size at least $\lceil{2n\over 3}\rceil+1$ (we conjecture that equality holds for every admissible $n$). The analogue problem can be asked for $r$-colorings as well, if r-1 \equiv 1,3 \mbox{ (mod 6)} and $r-1$ is a prime power, we show that the answer is the same as in case of complete graphs: in every $r$-coloring of the blocks of any STS$(n)$, there is a monochromatic connected component with at least ${n\over r-1}$ points, and this is sharp for infinitely many $n$.Comment: Journal of Combinatorial Designs, 201

Preliminary Investigation of Over-all Performance of Experimental Turbojet Engine for Guided Missiles

A preliminary investigation of the over-all performance of a simply constructed, short-life, turbojet engine was conducted. The unit was operated at a pressure altitude of 15,000 feet for ram-pressure ratios of 1.2 t o 1.8. The corrected engine speed was varied from the minimum for good combustion to about 17,000 rpm, which is approximately 75 percent of rated speed. The performance is given by generalized parameters that permit the calculation of performance at any altitude. The corrected net thrust of the turbojet engine increased with ram-pressure ratio for a given corrected engine speed above 14,500 rpm and reached a maximum of 425 pounds at a ram-pressure ratio of 1.8 and a corrected engine speed of 16,650 rpm, The corrected thrust specific fuel consumption decreased with flight speed for corrected engine speeds higher than 13,600 rpm, The minimum corrected thrust specific fuel consumption of 1.48 was obtained at a ram-pressure ratio of 1,8 and a corrected engine speed of 15,000 rpm. For all ram-pressure ratios, choking occurred in the engine for corrected engine speeds greater than 14,500 rpm

Experiential avoidance as a mechanism of change across cognitive-behavioral therapy in a sample of participants with heterogeneous anxiety disorders

Despite the substantial evidence that supports the efficacy of cognitive-behavioral therapy for the treatment of anxiety and related disorders, our understanding of mechanisms of change throughout treatment remains limited. The goal of the current study was to examine changes in experiential avoidance across treatment in a sample of participants (N = 179) with heterogeneous anxiety disorders receiving various cognitive-behavioral therapy protocols. Univariate latent growth curve models were conducted to examine change in experiential avoidance across treatment, followed by parallel process latent growth curve models to examine the relationship between change in experiential avoidance and change in anxiety symptoms. Finally, bivariate latent difference score models were conducted to examine the temporal precedence of change in experiential avoidance and change in anxiety. Results indicated that there were significant reductions in experiential avoidance across cognitive-behavioral treatment, and that change in experiential avoidance was significantly associated with change in anxiety. Results from the latent difference score models indicated that change in experiential avoidance preceded and predicted subsequent changes in anxiety, whereas change in anxiety did not precede and predict subsequent changes in experiential avoidance. Taken together, these results provide additional support for reductions in experiential avoidance as a transdiagnostic mechanism in cognitive-behavioral therapy.First author draf

Voting, the Symmetric Group, and Representation Theory

We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied QSn-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and some basic ideas from representation theory (e.g., Schur\u27s Lemma), this allows us to recast and extend some well-known results in the field of voting theory

Compression Theorems for Periodic Tilings and Consequences

We consider a weighted square-and-domino tiling model obtained by assigning real number weights to the cells and boundaries of an n-board. An important special case apparently arises when these weights form periodic sequences. When the weights of an nm-tiling form sequences having period m, it is shown that such a tiling may be regarded as a meta-tiling of length n whose weights have period 1 except for the first cell (i.e., are constant). We term such a contraction of the period in going from the longer to the shorter tiling as period compression . It turns out that period compression allows one to provide combinatorial interpretations for certain identities involving continued fractions as well as for several identities involving Fibonacci and Lucas numbers (and their generalizations)

Photoelectron spectroscopy and theoretical studies of [Com(pyrene)n]− (m=1,2 and n=1,2) complexes

Anion photoelectron spectroscopic experiments and density functional theory based calculations have been used to investigate the structural, electronic, and magnetic properties of neutral and anionic [Com(pyrene)n] (m,n=1–2) complexes. The calculated electron affinities and vertical transition energies of Com(pyrene)n are in good agreement with the measured values. Our results provide clear evidence for dimerization of Co atoms and formation of sandwich structures in these complexes. While the calculated spin magnetic moments of neutral Co2(pyrene)n complexes suggest a preference for ferromagnetic coupling between Co atoms, the spin magnetic moment of Co atom in Co(pyrene) and Co(pyrene)2 complexes was reduced to 1μB

The Negs and Regs of Continued Fractions

There are two main aims of this thesis. The first is to further develop and demonstrate applications of the combinatorial interpretation of continued fractions introduced in [Benjamin and Quinn, 2003]. The second is to investigate the theory of negative continued fractions, a relatively unresearched topic. That is, discuss the ways in which they are similar to and different from the regular class, describe how to convert between the two forms, and show that the central theorems concerning regular continued fractions also apply to the negative ones