Path coverings of the vertices of a tree

Consider a collection of disjoint paths in graph G such that every vertex is on one of these paths. The size of the smallest such collection is denoted i(G). A procedure for forming such collections is established. Restricting attention to trees, the range of values for the sizes of the collections obtained is examined, and a constructive characterization of trees T for which one always obtains a collection of size i(T) is presented.     

Counterexamples to randić's conjecture on distance degree sequences for trees

As counterexamples to a conjecture of Randi?, pairs of nonisomorphic trees with the same collections of distance degree sequences are presented.     

On graphs containing a given graph as center

We examine the problem of embedding a graph H as the center of a supergraph G, and we consider what properties one can restrict G to have. Letting A(H) denote the smallest difference ∣V(G)∣ - ∣V(H)∣ over graphs G having center isomorphic to H it is demonstrated that A(H) ≤ 4 for all H, and for 0 ≤ i ≤ 4 we characterize the class of trees T with A(T) = i. for n ≥ 2 and any graph H, we demonstrate a graph G with point and edge connectivity equal to n, with chromatic number X(G) = n + X(H), and whose center is isomorphic to H. Finally, if ∣V(H)∣ ≥ 9 and k ≥ ∣V(H)∣ + 1, then for n sufficiently large (with n even when k is odd) we can construct a k-regular graph on n vertices whose center is isomorphic to H.     

A limit on the lepton-family number violating process π → μe

A FNAL E799 Collaboration has carried out a search for the lepton-family number violating decay π⁰ → μ^±e using π⁰'s produced from K_L → π⁰π⁰π⁰ decays in flight. No events were observed. Assuming that lepton-family number violation is charge independent, the 90% confidence level upper limit on

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was determined to be 8.6 × 10⁻⁹.     

Calculation of the magnetization and total energy of vanadium as a function of lattice parameter

Self-consistent spin-polarized APW calculations have been performed to determine the energy band structure of metallic vanadium in an assumed ferromagnetic b.c.c. structure as a function of lattice parameter. The statistical exchange (‘Xα’) and muffin-tin approximations were used. At each lattice parameter for which a calculation was performed, the Xα cohesive energy, the pressure, and the magnetization were calculated. The calculated cohesive energy and pressure agree fairly well with experiment. The calculations also correctly predict the absence of a magnetic moment for vanadium at its equilibrium lattice constant. However, a nonmagnetic-to-magnetic transition is found to occur abruptly at a lattice constant which is about a factor of 1·25 larger than the equilibrium value, and which is in good qualitative agreement with the appearance of a local magnetic moment in certain vanadium alloys.     

Sequence effects on the forced translocation of heteropolymers through a small channel

By using a recently developed Monte Carlo algorithm and an exact numerical method, we calculate the translocation probability and the average translocation time for charged heterogeneous polymers driven through a nanopore by an external electric field. The heteropolymer chains are composed of two types of monomers (A and B) which differ only in terms of their electric charge. We present an exhaustive study of chains composed of eight monomers by calculating the average translocation time associated with the 256 possible arrangements for various ratios of the monomer charges (lambda(A)lambda(B)) and electric field intensities E. We find that each sequence leads to a unique value of the translocation probability and time. We also show that the distribution of translocation times is strongly dependent on the two forces felt by the monomers ( approximately lambda(A)E and approximately lambda(B)E). Finally, we present results that highlight the effect of having repetitive patterns by studying the translocation times of various block copolymer structures for a very long chain composed of N=2(18) monomers (all with the same number of A and B monomers).     

Advantages of deuterium-labelled mixed triacylglycerol in studies of intraluminal fat digestion

The (13)C-mixed triacylglcerol (MTG, 1,3-distearyl, 2-[1-(13)C]octanoyl glycerol) breath test is a non-invasive measure of intraluminal fat digestion. Recovery of (13)C in breath CO(2) is incomplete (<50%) owing to sequestration of (13)C into organic molecules via the tricarboxylic acid (TCA) cycle. In addition lack of knowledge of CO(2) production rate (VCO(2)) during the test leads to errors in the calculated percentage dose recovered (PDR). (2)H sequestration into organic molecules is low ( approximately 4%) and is not influenced by factors that affect VCO(2) such as food intake or physical activity. After oxidation of (2)H-labelled macromolecules, the label appears in body water, which can be sampled non-invasively in urine or saliva. After an overnight fast, two healthy adults consumed [(2)H]MTG (1,3-distearyl, 2-[(2)H(15)]octanoyl glycerol) and [(13)C]MTG (1,3 distearyl, 2-[1-(13)C]octanoyl glycerol) simultaneously. Total body water (TBW) was measured by (18)O dilution and also estimated from height and weight. Urine and saliva were sampled at baseline and for 10 h after consumption of the test meal. The abundance of (2)HOH and H(2) (18)O in urine and saliva was measured by continuous-flow isotope-ratio mass spectrometry. Cumulative PDR of (2)H and (18)O was calculated from the plateau enrichment, which was reached by 6 h in both saliva and urine. Recovery of (2)H calculated using measured TBW was compared with that using an estimated value of TBW. Mean recovery of (2)H in saliva was 99.3% and in urine was 96.4%. Errors introduced by estimating TBW were <5%. [(2)H]MTG could provide a simpler, more robust, indirect test of intraluminal fat digestion compared with the (13)C-breath test. Further studies are required in pancreatic insufficient patients.     

Insight into the local structure of barium indate oxide-ion conductors: an X-ray total scattering study

In this paper we presented the X-ray PDF investigation of orthorhombic Ba(2)In(2)O(5) and cubic Ba(2)In(1.7)P(0.3)O(5.3) and Ba(2)In(1.7)S(0.3)O(5.45) samples. Pure Ba(2)In(2)O(5) was found to be properly described-at the local scale-by the orthorhombic average structure. Ba(2)In(1.7)P(0.3)O(5.3) and Ba(2)In(1.7)S(0.3)O(5.45) cannot be described, at the local scale, by a cubic symmetry. The PDFs of these two samples clearly showed a distorted atom arrangement in the short-range which can be described again with the orthorhombic symmetry found in pure barium indate.     

A polar corundum oxide displaying weak ferromagnetism at room temperature

Combining long-range magnetic order with polarity in the same structure is a prerequisite for the design of (magnetoelectric) multiferroic materials. There are now several demonstrated strategies to achieve this goal, but retaining magnetic order above room temperature remains a difficult target. Iron oxides in the +3 oxidation state have high magnetic ordering temperatures due to the size of the coupled moments. Here we prepare and characterize ScFeO(3) (SFO), which under pressure and in strain-stabilized thin films adopts a polar variant of the corundum structure, one of the archetypal binary oxide structures. Polar corundum ScFeO(3) has a weak ferromagnetic ground state below 356 K-this is in contrast to the purely antiferromagnetic ground state adopted by the well-studied ferroelectric BiFeO(3).