On graphs with a large chromatic number containing no small odd cycles

In this paper, we present the lower bounds for the number of vertices in a graph with a large chromatic number containing no small odd cycles

A study on the radiation hardness of lead tungstate crystals

This report presents recent progress of a study on the radiation damage in lead tungstate (PbWO_4) crystals. The dose rate dependence of radiation damage in PbWO_4 has been observed, confirming our early prediction based upon a kinetic model of color centers. An optimization of the oxygen compensation through post-growth thermal annealing, carried out in Shanghai Institute of Ceramics, has led to PbWO_4 crystals with significantly improved radiation hardness. A comparison between front versus uniform irradiations revealed that the later caused a factor of 2 to 6 times more severe damage. A measurement of a preliminary batch of lanthanum doped PbWO_4 crystals indicates that the La doping seems not a determine factor for PbWO_4 radiation hardness improvement. Finally, a TEM/EDS analysis confirmed our previous conjecture that the radiation damage in PbWO_4 crystals is caused by oxygen vacancies

A study of the optical and radiation damage properties of lead tungstate crystals

A study has been made of the optical and radiation damage properties of undoped and niobium doped lead tungstate crystals. Data were obtained on the optical absorbance, the intensity and decay time of the scintillation light output, and the radioluminescence and photoluminescence emission spectra. Radiation damage was studied in several undoped and niobium doped samples using ^(60)Co gamma ray irradiation. The change in optical absorption and observed scintillation light output was measured as a function of dose up to total cumulative doses on the order of 800 krad. The radiation induced phosphorescence and thermoluminescence was also measured, as well as recovery from damage by optical bleaching and thermal annealing. An investigation was also made to determine trace element impurities in several samples

A study on the radiation hardness of lead tungstate crystals

This report presents recent progress of a study on the radiation damage in lead tungstate (PbWO_4) crystals. The dose rate dependence of radiation damage in PbWO_4 has been observed. An optimization of the oxygen compensation through post-growth thermal annealing has led to PbWO_4 samples with significantly improved radiation hardness. Front irradiation is found to cause a factor of 2 to 6 times less severe damage than uniform irradiation. Lanthanum doping was found not to be a determining factor for PbWO_4 radiation hardness improvement. Finally, a TEM/EDS analysis revealed that the radiation damage in PbWO_4 crystals is caused by oxygen vacancies

A study on the radiation hardness of lead tungstate crystals

This report presents recent progress of a study on the radiation damage in lead tungstate (PbWO_4) crystals. The dose rate dependence of radiation damage in PbWO_4 has been observed, confirming our early prediction based upon a kinetic model of color centers. An optimization of the oxygen compensation through post-growth thermal annealing, carried out in Shanghai Institute of Ceramics, has led to PbWO_4 crystals with significantly improved radiation hardness. A comparison between front versus uniform irradiations revealed that the later caused a factor of 2 to 6 times more severe damage. A measurement of a preliminary batch of lanthanum doped PbWO_4 crystals indicates that the La doping seems not a determine factor for PbWO_4 radiation hardness improvement. Finally, a TEM/EDS analysis confirmed our previous conjecture that the radiation damage in PbWO_4 crystals is caused by oxygen vacancies

On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

A study of the optical and radiation damage properties of lead tungstate crystals

A study has been made of the optical and radiation damage properties of undoped and niobium doped lead tungstate crystals. Data were obtained on the optical absorbance, the intensity and decay time of the scintillation light output, and the radioluminescence and photoluminescence emission spectra. Radiation damage was studied in several undoped and niobium doped samples using ^(60)Co gamma ray irradiation. The change in optical absorption and observed scintillation light output was measured as a function of dose up to total cumulative doses on the order of 800 krad. The radiation induced phosphorescence and thermoluminescence was also measured, as well as recovery from damage by optical bleaching and thermal annealing. An investigation was also made to determine trace element impurities in several samples

A study of the optical and radiation damage properties of lead tungstate crystals

A study has been made of the optical and radiation damage properties of undoped and niobium doped lead tungstate crystals. Data were obtained on the optical absorbance, the intensity and decay time of the scintillation light output, and the radioluminescence and photoluminescence emission spectra. Radiation damage was studied in several undoped and niobium doped samples using ^(60)Co gamma ray irradiation. The change in optical absorption and observed scintillation light output was measured as a function of dose up to total cumulative doses on the order of 800 krad. The radiation induced phosphorescence and thermoluminescence was also measured, as well as recovery from damage by optical bleaching and thermal annealing. An investigation was also made to determine trace element impurities in several samples

Open problems on graph coloring for special graph classes.

For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c:V→{1,2,…}c:V→{1,2,…} such that c(u)≠c(v)c(u)≠c(v) for every edge uv∈Euv∈E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring