Vector spaces as unions of proper subspaces

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.Comment: 8 pages, LaTex; to appear in "Linear Algebra and its Applications

Maximal partial spreads and the modular n-queen problem III

AbstractMaximal partial spreads in PG(3,q)q=pk,p odd prime and q⩾7, are constructed for any integer n in the interval (q2+1)/2+6⩽n⩽(5q2+4q−1)/8 in the case q+1≡0,±2,±4,±6,±10,12(mod24). In all these cases, maximal partial spreads of the size (q2+1)/2+n have also been constructed for some small values of the integer n. These values depend on q and are mainly n=3 and n=4. Combining these results with previous results of the author and with that of others we can conclude that there exist maximal partial spreads in PG(3,q),q=pk where p is an odd prime and q⩾7, of size n for any integer n in the interval (q2+1)/2+6⩽n⩽q2−q+2

A Comparison of the Effects of Simulation Training and Non-Simulation Training On Self-Efficacy in Providing Women\u27s Health Care

The Veterans Administration (VA) recognizes that proficiency in the core concepts of primary care women\u27s health is required to provide comprehensive primary care for women. A potentially superior form of training that has been recently used for care providers is simulation. The examination of the relationship between simulation training through the Mini-Residency Course and increased self-efficacy among Women\u27s Health Primary Care Providers (WH-PCP) is important, as the Mini-Residency Course is designed specifically to fill knowledge gaps and enhance the participant\u27s knowledge and skill. A single post-test only, two group design was used for this study. The experimental group included those who completed simulation training on how to provide effective, essential healthcare to women veterans. The simulation-based training occurred July, 2012. The study gathered survey data designed to determine the level of self-efficacy of practitioners from a sample who had participated in the Mini-Residency program (Part I, or Parts I and II) and compared the levels of self-efficacy to a sample of practitioners who did not participate in simulations. Limited by a low response rate, the study sample included 23 practitioners. A self-efficacy survey was constructed using Bandura\u27s self-efficacy theory. The self-efficacy score for this analysis used the mean of six discrete skill items. The reliability of this self-efficacy scale was examined using Cronbach\u27s alpha. Results indicated reliability at a = .71. The results failed to demonstrate any statistically significant differences between groups. However, it was noted that a significant result ( p = .10 level) was evident in the differences in mean self-efficacy scores based on standardized patient experience, which suggests the need for future research using a larger sample size

On perfect 1-mathcalEmathcal E-error-correcting codes

We generalize the concept of perfect Lee-error-correcting codes, and present constructions of this new class of perfect codes that are called perfect 1-$mathcal{E}$-error-correcting codes. We also show that in some cases such codes contain quite a few perfect 1-error-correcting $q$-ary Hamming codes as subsets

Some necessary conditions for vector space partitions

Some new necessary conditions for the existence of vector space partitions are derived. They are applied to the problem of finding the maximum number of spaces of dimension t in a vector space partition of V(2t,q) that contains m_d spaces of dimension d, where t/2<d<t, and also spaces of other dimensions. It is also discussed how this problem is related to maximal partial t-spreads in V(2t,q). We also give a lower bound for the number of spaces in a vector space partition and verify that this bound is tight.Comment: 19 pages; corrected typos and rewritten introductio

Perfect 1-error-correcting Lipschitz weight codes

Let $pi$ be a Lipschitz prime and $p=pipi^star$. Perfect 1-error-correcting codes in $H(mathbb{Z})_pi^n$ are constructed for every prime number $pequiv1(bmod;4)$. This completes a result of the authors in an earlier work, emph{Perfect Mannheim, Lipschitz and Hurwitz weight codes}, (Mathematical Communications, Vol 19, No 2, pp. 253 -- 276 (2014)), where a construction is given in the case $pequiv3,(bmod;4)$

Resistance exercise timing and metabolic risk factors in type 2 diabetics

"July 2014."Dissertation Advisor: Dr. Jill A. Kanaley.Includes vita.Abnormally elevated postprandial glucose and triacylglycerol (TAG) concentrations are risk factors for cardiovascular disease in patients with type-2 diabetes. The most effective time to exercise to lower postprandial glucose and TAG concentrations is unknown. Thus, the aim of this study was to determine what time is more effective, either pre- or post-dinner resistance exercise (RE), at improving postprandial risk factors in patients with type-2 diabetes. Methods: Thirteen obese patients with type 2 diabetes completed three trials in a random order in which they consumed a standardized dinner meal with 1) no RE (NoRE), 2) pre-dinner RE (RE?��M), and 3) post-dinner RE beginning 45 min after dinner (M?��RE). During each trial blood samples were taken to measure glucose, TAG, acetaminophen (gastric emptying), endocrine responses, and mathematical modeling was used to assess beta-cell function. Indirect calorimetry was used to measure energy expenditure and substrate oxidation. A continuous glucose monitor was used to assess nocturnal and morning glycemic control the next day. A fasting blood sample was taken the following morning and the quantitative insulin sensitivity check index (QUICKI) was used to estimate whole body insulin sensitivity and the homeostatic model assessment of insulin resistance (HOMA-IR) was used as an estimate of hepatic insulin resistance. Results: The postprandial glucose iAUC was reduced (P < 0.05) by ?�18% and 30% during the RE?��M and M?��RE trials, respectfully, compared to NoRE, with no difference between RE trials. The postprandial total TAG iAUC was ?�92% lower (P < 0.05) during M?��RE compared to NoRE and RE?��M, an effect due to lower VLDL-1 TAG concentrations. RE?��M and M?��RE reduced the insulin iAUC by 35% and 48%, respectfully, compared to NoRE (P < 0.05), but via different mechanisms as RE?��M enhanced insulin clearance, whereas M?��RE reduced pancreatic insulin secretion and enhanced insulin clearance. The postprandial GLP-1Includes bibliographical references (pages 84-95)