Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

The Effect of Coating Patterns with Spinel-Based Investment on the Castability and Porosity of Titanium Cast into Three Phosphate-Bonded Investments

Purpose: This study evaluated the effect of pattern coating with spinel-based investment Rematitan Ultra (RU) on the castability and internal porosity of commercially pure (CP) titanium invested into phosphate-bonded investments. The apparent porosity of the investment was also measured. Materials and Methods: Square patterns (15 x 15 x 0.3 mm(3)) were either coated with RU, or not and invested into the phosphate-bonded investments: Rematitan Plus (RP), Rema Exakt (RE), Castorit Super C (CA), and RU (control group). The castings were made in an Ar-arc vacuum-pressure machine. The castability area (mm(2)) was measured by an image-analysis system (n = 10). For internal porosity, the casting (12 x 12 x 2 mm(3)) was studied by the X-ray method, and the projected porous area percentage was measured by an image-analysis system (n = 10). The apparent porosity of the investment (n = 10) was measured in accordance with the ASTM C373-88 standard. Results: Analysis of variance (One-way ANOVA) of castability was significant, and the Tukey test indicated that RU had the highest mean but the investing technique with coating increased the castability for all phosphate-bonded investments. The analysis of the internal porosity of the cast by the nonparametric test demonstrated that the RP, RE, and CA with coating and RP without coating did not differ from the control group (RU), while the CA and RE casts without coating were more porous. The one-way ANOVA of apparent porosity of the investment was significant, and the Tukey test showed that the means of RU (36.10%) and CA (37.22%) were higher than those of RP (25.91%) and RE (26.02%). Conclusion: Pattern coating with spinel-based material prior to phosphate-bonded investments can influence the castability and the internal porosity of CP Ti.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

Ni(II)-doped CsCdBrCl2: Variation of spectral and structural properties via mixed-halide coordination

A new addition to the family of single-molecule magnets is reported: an Fete cage stabilized with benzoate and pyridonate ligands. Monte Carlo methods have been used to derive exchange parameters within the cage, and hence model susceptibility behavior.

Diet, lifestyle and the risk of Type 2 Diabetes Mellitus in women

Background Previous studies have examined individual dietary and lifestyle factors in relation to type 2 diabetes, but the combined effects of these factors are largely unknown. Methods We followed 84,941 female nurses from 1980 to 1996; these women were free of diagnosed cardiovascular disease, diabetes, and cancer at base line. Information about their diet and lifestyle was updated periodically. A low-risk group was defined according to a combination of five variables: a body-mass index (the weight in kilograms divided by the square of the height in meters) of less than 25; a diet high in cereal fiber and polyunsaturated fat and low in trans fat and glycemic load (which reflects the effect of diet on the blood glucose level); engagement in moderate-to-vigorous physical activity for at least half an hour per day; no current smoking; and the consumption of an average of at least half a drink of an alcoholic beverage per day. Results During 16 years of follow-up, we documented 3300 new cases of type 2 diabetes. Overweight or obesity was the single most important predictor of diabetes. Lack of exercise, a poor diet, current smoking, and abstinence from alcohol use were all associated with a significantly increased risk of diabetes, even after adjustment for the body-mass index. As compared with the rest of the cohort, women in the low-risk group (3.4 percent of the women) had a relative risk of diabetes of 0.09 (95 percent confidence interval, 0.05 to 0.17). A total of 91 percent of the cases of diabetes in this cohort (95 percent confidence interval, 83 to 95 percent) could be attributed to habits and forms of behavior that did not conform to the low-risk pattern. Conclusions Our findings support the hypothesis that the majority of cases of type 2 diabetes could be prevented by the adoption of a healthier lifestyle.

Prediction of mortality using dobutamine echocardiography

OBJECTIVES We sought to find out whether dobutamine echocardiography (DbE) could provide independent prediction of total and cardiac mortality, incremental to clinical and angiographic variables. BACKGROUND Existing outcome studies with DbE have examined composite end points, rather than death, over a relatively short follow-up. METHODS Clinical and stress data were collected in 3,156 patients (age 63 +/- 12 years, 1,801 men) undergoing DbE. Significant stenoses (>50% diameter) were identified in 70% of 1,073 patients undergoing coronary angiography. Total and cardiac mortality were identified over nine years of follow-up (mean 3.8 +/- 1.9). Cox models were used to analyze the effect of ischemia and other variables, independent of other determinants of mortality. RESULTS The dobutamine echocardiogram was abnormal in 1,575 patients (50%). Death occurred in 716 patients (23%), 259 of whom (8%) were thought to have died from cardiac causes. Patients with normal DbE had a total mortality of 8% per year and a cardiac mortality of 1% per year over the first four years of follow-up. Ischemia and the extent of abnormal wall motion were independent predictors of cardiac death, together with age and heart failure. In sequential Cox models, the predictive power of clinical data alone (model chi-square 115) was strengthened by adding the resting left ventricular function (model chi-square 138) and the results of DbE (model chi-square 181). In the subgroup undergoing coronary angiography, the power of the model was increased to a minor degree by the addition of coronary anatomy data. CONCLUSIONS Dobutamine echocardiography is an independent predictor of death, incremental to other data. While a normal dobutamine echocardiogram predicts low risk of cardiac death ton the order of 1% per year), this risk increases with the extent of abnormal wall motion at rest and stress, (J Am Coil Cardiol 2001;37:754-60) (C) 2001 by the American College of Cardiology.

The mechanisms of combustion and continuous reactions during mechanical alloying

Some materials exhibit a combustion event during mechanical alloying, which results in the rapid transformation of reactants into products, while others show a slow transformation of reactants into products, In this paper, the continuous W + C --> WC reaction is compared to the Ti + C --> TiC combustion reaction. Rietveld refinement of X-ray diffraction patterns is used to show that these particular reactions proceed through different pathways, determined by crystallographic factors of the reactants. When a crystallographic relationship exists between the reactants and the products, such as that between W and WC, the product forms slowly over a period of time. In contrast, insertion of C into the Ti structure is associated with atomic rearrangements within the crowded lattice planes and the subsequent catastrophic failure of the reactant lattices results in combustion to form TiC. (C) 2001 Academic Press.