Kernels by monochromatic paths in digraphs with covering number 2

We call the digraph D an k-colored digraph if the arcs of D are colored with k colors. A subdigraph H of D is called monochromatic if all of its arcs are colored alike. A set N⊆V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u,v∈N, there is no monochromatic directed path between them, and (ii) for every vertex x∈(V(D)?N), there is a vertex y∈N such that there is an xy-monochromatic directed path. In this paper, we prove that if D is an k-colored digraph that can be partitioned into two vertex-disjoint transitive tournaments such that every directed cycle of length 3,4 or 5 is monochromatic, then D has a kernel by monochromatic paths. This result gives a positive answer (for this family of digraphs) of the following question, which has motivated many results in monochromatic kernel theory: Is there a natural numberlsuch that if a digraphDisk-colored so that every directed cycle of length at mostlis monochromatic, thenDhas a kernel by monochromatic paths?     

Effects of hyperthermia on bioenergetic status and phosphorus T1S in human melanoma xenografts monitored by 31P-MRS.

Conventional hyperthermia enhances tumor response to radiotherapy through thermal cell inactivation and vascular shut-down, whereas mild hyperthermia potentiates the effect of radiotherapy by improving tumor oxygenation. The work reported here was aimed at investigating whether 31P-magnetic resonance spectroscopy (31P-MRS) measurements of tumor bioenergetic status; i.e., the (PCr + NTPbeta)/Pi resonance ratio, and/or the spin lattice relaxation times, T1s, of the Pi and NTPbeta resonances can be used to distinguish between the effects of conventional and mild hyperthermia. BEX-t human melanoma xenografts were treated at 43.0 degrees C for 15 or 60 min, and bioenergetic status and T1s were measured as function-of-time after treatment. Hyperthermia-induced effects on tumor blood flow was measured by using the 86Rb uptake method. The morphology of the capillary network in treated and untreated tumors was studied by histologic examination. Tumors treated for 15 min showed increased blood flow and dilated capillaries, whereas tumors treated for 60 min showed decreased blood flow and capillary occlusions; i.e., 43.0 degrees C for 15 min was a treatment consistent with mild hyperthermia and 43.0 degrees C for 60 min was consistent with conventional hyperthermia treatment of BEX-t tumors. Bioenergetic status increased after treatment at 43.0 degrees C for 15 min, and decreased after treatment at 43.0 degrees C for 60 min, similar to the blood flow. Likewise, the T1 of the Pi resonance increased after treatment at 43.0 degrees C for 15 min, and decreased after treatment at 43.0 degrees C for 60 min. The T1 of the NTPbeta resonance showed a similar change as the T1 of the Pi resonance, but less pronounced. Consequently, 31P-MRS measurements of tumor bioenergetic status and the T1 of the Pi resonance may perhaps be utilized to distinguish between vascular effects of mild and conventional hyperthermia.     

Greenhouse gas abatement — toward Pareto-optimal decisions under uncertainty

This paper examines the economic logic of integrated assessment — balancing the costs against the benefits of greenhouse gas abatement. Stylized facts are employed in a multiregion computable general equilibrium model with a public good. The percentage shares of global emissions are determined outside the model — based upon some form of international agreement — and emission rights are tradeable between regions. The analysis is confined to Pareto-optimal (cooperative) solutions. We focus on the sensitivity of initial decisions to low-probability, high-consequence scenarios associated with cumulative emissions. For simplicity, there are only two regions, two tradeable goods, two time periods, and two states-of-world. With the particular form of public good model adopted here (production rather than utility function impacts), it turns out that a Pareto-optimal hedging strategy is indepedent of the emission shares allocated to each region. Equity issues may be separated from those of economic efficiency. Similar results extend to cases in which there are additional regions, tradeable goods, time periods, and states-of-world.Presented at the Conference on the Economics of Global Environmental Change, Birmingham University, May 9–11, 1994. This research was funded by the Electric Power Research Institute (EPRI). The views presented here are solely those of the individual authors, and do not necessarily represent the views of EPRI or its members.     

QCD exotics

I review first some theoretical motivations for violation of Lorentz and/or CPT Invariance. Although the latter symmetries may be violated in a quantum gravity setting, nevertheless there are situations in which these violations are due to a given classical background geometry that may characterised early epochs of our Universe, and in fact be responsible for the observed dominance of matter over antimatter in the Universe. In this way I estimate some of the coefficients of the Standard Model Extension (SME), which is a framework for a field theoretic study of such a breakdown of fundamental symmetries. Then I describe briefly some tests of these symmetries, giving emphasis in low-energy antiproton physics and electric dipole moment measurements, of interest to this conference. I also mention the rôle of entangled states of neutral mesons in providing independent measurements of T(ime reversal) and CP Violation, thus providing independent tests of CPT symmetry, as well as novel (“smoking-gun” type) tests of decoherence-induced CPT violation, which may characterise some models of quantum gravity.     

Comment on the Chou-Yang model for elastic scattering

The Chou-Yang model forpp elastic scattering, modified to include the effect of coupled inelastic channels, is used to fit recent data in the region of the dip, i.e., 1.0≦|t|≦2.0 (GeV/c)² for incident momenta ranging from 35 to 250 GeV/c. Good quantitative agreement is found for an inelastic coupling which is predominantly real, as compared to the mostly imaginary elastic coupling. Implications for dips at highert, which are predicted by the model but as yet not observed experimentally, are discussed.     

Quantum dynamics of the dissociation of H2 on Cu(100): dependence of the site-reactivity on initial rovibrational state

We perform six-dimensional (6D) quantum wavepacket calculations for H2 dissociatively adsorbing on Cu(100) from a variety of rovibrational initial states. The calculations are performed on a new potential energy surface (PES), the construction of which is also detailed. Reaction probabilities are in good agreement with experimental findings. Using a new flux analysis method, we calculate the reaction probability density as a function of surface site and collision energy, for a variety of initial states. This approach is used to study the effects of rotation and vibration on reaction at specific surface sites. The results are explained in terms of characteristics of the PES and intrinsically dynamic effects. An important observation is that, even at low collision energies, reaction does not necessarily proceed predominantly in the region of the minimum potential barrier, but can occur almost exclusively at a site with a higher barrier. This suggests that experimental control of initial conditions could be used to selectively induce reaction at particular surface sites. Our predictions for site-reactivity could be tested using contemporary experimental methods: The calculations predict that, for reacting molecules, there will be a dependence of the quadrupole alignment of j on the incident vibrational state, v. This is a direct result of PES topography in the vicinity of the preferred reaction sites of v = 0 and v = 1 molecules. Invoking detailed balance, evidence for this difference in preferred reaction site of v = 0 and 1 molecules could be obtained through associative desorption experiments.     

Synthesis of sulfur-bridged piperazinediones by reaction of 3,6-dibromo-1,4-dimethyl-2,5-piperazinedione with geminal dithiols

The reaction of several geminal dithiols with 3,6-dibromo-1,4-dimethyl-2,5-piperazinedione gave in good yields piperazinedione derivatives substituted at the 3,6-position with a geminal dithiol-bridging group. These sulfur-bridged piperazinediones formally represent derivatives of the 2,4-dithia-6,8-diaza-7,9-dioxobicyclo[3.2.2]nonane ring system. Attempts to transform these sulfur-bridged piperazinediones to 3,6-epidithiopiperazinediones by removal of the bridging group common to the sulfur functionality were unsuccessful. Studies also are reported of addition of thioacetic acid to 3,6-dimethylene-2,5-piperazinedione to give 3,6-diacetylthio-3,6-dimethyl-2,5-piperazinedione. Conversion of the 3,6-diacetylthio derivative to the epithiopiperazinedione ring system yielded a mixture of epimono- and epidithiopiperazinediones.     

Nuclear size dependence of inclusive particle production

The inclusive production of π⁺, π^?, K⁺, K^?, p and $\text{p}$ for protons incident on carbon and tungsten targets was studied at the Internal Target Area of the Fermilab. We assume an A^α dependence for the inclusive cross sections and report here on the variation of α with incident momentum, transverse momentum and particle species.     

Synthesis of des-n-tetramethyltriostin a from C-terminal Z-d-serine tetra-and octadepsipeptide intermediates

Des-N-tetramethyltriostin A (1), a known DNA-intercalation agent, has been synthesized from tetra- and octapeptide intermediates that have Z-d-serine at the C-terminal position. The procedure thus allows the fragment coupling and cyclization reactions leading to the synthesis of the title compound to occur without racemization at the C-terminal amino acid. Esterification of Boc-Val-OH with the p-bromophenacyl ester of Z-d-serine provided didepsipeptide Z-d-Ser(Boc-Val)-OBpa (4). Stepwise addition of the requisite amino acids provided tetradepsipeptide Z-d-Ser[Boc-Ala-Cys(Acm)-Val]-OBpa (6). Fragment coupling of the respective C- and N-deprotected tetradepsipeptides 7 and 8, derived from 6, furnished linear octadepsipeptide 9, which upon cyclization and disulfide formation gave the bicyclic octadepsipeptide 11, a known synthetic precursor to 1. The degree of racemization incurred in the alanine and valine residues of selected depsipeptides was measured and the results compared with those obtained in previous studies. It was concluded that alanine, perhaps because of sequence effects, undergoes a degree of racemization (4–10%) during hydrolysis of tetradepsipeptide 6 and octadepsipeptide 9.