pp interactions at 303GeVc: Separation of diffractive and nondiffractive components of the multiplicity distribution

We have studied the properties of the inclusive pp → pX reation at $\text{303}\text{GeV}\text{c}$. Protons of momentum $\text{1.4}\text{GeV}\text{c}$ or less are measured and identified by their ionization. We investigate the multiplicity distribution associated with those events having a small four-momentum transfer to the target proton. Under the assumption that this selection enhances or isolates the diffractive component of the interaction, we discuss the properties of the diffractive and nondiffractive components.     

Waring's problem for the ring of polynomials

We investigate the question of which polynomials are not representable as the sum of “few” powers of polynomials. In particular for Waring's problem over the ring of polynomials we show that there exist polynomials which are not the sum of fewer than $\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$nth powers of polynomials.     

A numerical method for determining nonlinear normal modes

This paper examines a new approach for determining the nonlinear normal modes of undamped non-gyroscopic multiple degree-of-freedom systems. Unlike algebraic solutions that generally assume a solution in the form of a polynomial expansion, this method makes only the assumption of repetitive motion in numerically determining the mode shapes. The advantage of this approach is that the accuracy obtained in the mode shape identification is a function only of the accuracy of the numerical integration used and not of the number of terms in the power series expansion. The drawbacks are that invariance of the modal manifolds cannot be proven and mode bifurcations can be easily overlooked.     

Search for the rare decays K(L)→π0π0μ+μ- and K(L)→π0π0X0→π0π0μ+μ-

The KTeV E799 experiment has conducted a search for the rare decays, K(L)→π(0)π(0)μ(+)μ(-) and K(L)→π(0)π(0)X(0)→π(0)π(0)μ(+)μ(-), where the X(0) is a possible new neutral boson that was reported by the HyperCP experiment with a mass of (214.3 ± 0.5) MeV/c(2). We find no evidence for either decay. We obtain upper limits of Br(K(L)→π(0)π(0)X(0)→π(0)π(0)μ(+)μ(-)) < 1.0 × 10(-10) and Br(K(L)→π(0)π(0)μ(+)μ(-)) < 9.2 × 10(-11) at the 90% confidence level. This result rules out the pseudoscalar X(0) as an explanation of the HyperCP result under the scenario that the dsX(0) coupling is completely real.     

Particle coupling to the octupole state in 89Sr from 88Sr(p,p')88Sr analog resonances and 88Sr(d,p)89Sr

A study has been made of the six most pronounced isobaric analog resonances in the ⁸⁸Sr(p, p')⁸⁸Sr (3^?) excitation function at E_p = 7.65, 7.80, 7.92, 8.78, 9.75, and 9.90 MeV. They are believed to have a simple structure in the parent nucleus ⁸⁹Sr consisting of the lowlying positive-parity, single-neutron spectrum of ⁸⁹Sr weakly coupled to the collective 3^? state in ⁸⁸Sr. A high-resolution ⁸⁸Sr(d, p)⁸⁹Sr experiment was performed to locate small 2f and 3p admixed fragments in ⁸⁹Sr which would allow these analog resonances their entrance widths. In addition, on-resonance ⁸⁸Sr(p, p')⁸⁸Sr (3^?) angular distributions were measured in order to determine the partial waves involved in the exit channel. Results are compared to a particlephonon coupling model, and overall selectivity, strengths, and angular distributions of the (p, p') analog resonances are consistent with the above interpretation.     

On k-sequential and other numbered graphs

The concept of a k-sequential graph is presented as follows. A graph G with ∣V(G)∪ E(G)∣=t is called k-sequential if there is a bijection$\text{?: V(G)∪E(G) → {k,k+1,…,t+k?1}}$ such that for each edge$\text{e}\text{?}\text{=xy}$in E(G) one has$\text{?(}\text{e}\text{?}\text{) = ∣?(x)??(y)∣}$. A graph that is 1-sequential is called simply sequential, and, in particular the author has conjectured that all trees are simply sequential. In this paper an introductory study of k-sequential graphs is made. Further, several variations on the problems of gracefully or sequentially numbering the elements of a graph are discussed.