Downloads & Free Reading Options - Results

We prove the following: For any $\rho\in\left(0,1\right)$, if a finite group $G$ has an automorphism with a cycle of length at least $\rho\cdot|G|$, then the index of the solvable radical $\operatorname{Rad}(G)$ in $G$ is bounded from above in terms of $\rho$, and such a condition is strong enough to imply solvability of $G$ if and only if $\rho>\frac{1}{10}$. Furthermore, considering, for exponents $e\in\left(0,1\right)$, the condition that a finite group $G$ have an automorphism with a cycle of length at least $|G|^e$, such a condition is strong enough to imply $|\operatorname{Rad}(G)|\to\infty$ for $|G|\to\infty$ if and only if $e>\frac{1}{3}$. We also prove similar results for a larger class of bijective self-transformations of finite groups, so-called periodic affine maps.

We prove the following: For any $\rho\in\left(0,1\right)$, if a finite group $G$ has an automorphism with a cycle of length at least $\rho\cdot|G|$, then the index of the solvable radical $\operatorname{Rad}(G)$ in $G$ is bounded from above in terms of $\rho$, and such a condition is strong enough to imply solvability of $G$ if and only if $\rho>\frac{1}{10}$. Furthermore, considering, for exponents $e\in\left(0,1\right)$, the condition that a finite group $G$ have an automorphism with a cycle of length at least $|G|^e$, such a condition is strong enough to imply $|\operatorname{Rad}(G)|\to\infty$ for $|G|\to\infty$ if and only if $e>\frac{1}{3}$. We also prove similar results for a larger class of bijective self-transformations of finite groups, so-called periodic affine maps.

In this paper we investigate the dependence of umbral core brightness, as well as the mean umbral and penumbral brightness on the phase of the solar cycle and on the size of the sunspot. Albregtsen & Maltby (1978) reported an increase in umbral core brightness from the early to the late phase of solar cycle from the analysis of 13 sunspots which cover solar cycles 20 and 21. Here we revisit this topic by analysing continuum images of more than 160 sunspots observed by the MDI instrument on board the SOHO spacecraft for the period between 1998 March to 2004 March, i.e. a sizable part of solar cycle 23. The advantage of this data set is its homogeneity, with no seeing fluctuations. A careful stray light correction, which is validated using the Mercury transit of 7th May, 2003, is carried out before the umbral and penumbral intensities are determined. The influence of the Zeeman splitting of the nearby NiI spectral line on the measured 'continuum' intensity is also taken into account. We did not observe any significant variation in umbral core, mean umbral and mean penumbral intensities with solar cycle, which is in contrast to earlier findings for the umbral core intensity. We do find a strong and clear dependence of the umbral brightness on sunspot size, however. The penumbral brightness also displays a weak dependence. The brightness-radius relationship has numerous implications, some of which, such as those for the energy transport in umbrae, are pointed out.

In this paper we modify slightly Razborov's flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4-cycle-free subgraph of the n-dimensional hypercube is at most 0.6068 times the number of its edges. We also improve the upper bound on the number of edges for 6-cycle-free subgraphs of the n-dimensional hypercube from the square root of 2 - 1 to 0.3755 times the number of its edges. Additionally, we show that if the n-dimensional hypercube is considered as a poset, then the maximum vertex density of three middle layers in an induced subgraph without 4-cycles is at most 2.15121 times n choose n/2.

In this paper we modify slightly Razborov's flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4-cycle-free subgraph of the n-dimensional hypercube is at most 0.6068 times the number of its edges. We also improve the upper bound on the number of edges for 6-cycle-free subgraphs of the n-dimensional hypercube from the square root of 2 - 1 to 0.3755 times the number of its edges. Additionally, we show that if the n-dimensional hypercube is considered as a poset, then the maximum vertex density of three middle layers in an induced subgraph without 4-cycles is at most 2.15121 times n choose n/2.

In this paper we modify slightly Razborov's flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4-cycle-free subgraph of the n-dimensional hypercube is at most 0.6068 times the number of its edges. We also improve the upper bound on the number of edges for 6-cycle-free subgraphs of the n-dimensional hypercube from the square root of 2 - 1 to 0.3755 times the number of its edges. Additionally, we show that if the n-dimensional hypercube is considered as a poset, then the maximum vertex density of three middle layers in an induced subgraph without 4-cycles is at most 2.15121 times n choose n/2.

The goal of this research was to understand what factors determine whether a diatom cell can exit the mitotic cell cycle to undergo gametogenesis and subsequent auxospore formation. Using flow cytometry, I found that the centric diatom, Thalassiosira weissflogii, could be induced to undergo spermatogenesis by exposing cells maintained in continuous light to either dim light or darkness. The use of populations representing distinct cell cycle distributions indicated that cells in early G1 could be triggered to form male gametes. Whereas cells further along in their cell cycle were unresponsive to these same cues. The size distributions of numerous isolates maintained under identical conditions were examined over time to determine the relation between cell size and the ability to undergo sexual reproduction. Each isolate underwent periodic increases and decreases in mean cell size as expected for populations alternating between asexual and sexual reproduction. However, the timing of the onset of sexual reproduction, the rate of increase in mean cell size, and the size of the post-auxospores created during a sexual event varied among isolates and within a given isolate over time. This variable behavior was hypothesized to occur because the genetic composition of diatom populations varies over time. Keywords: Medicine.

This study is a content analysis of action research articles in the field of education which were published in Turkish journals and indexed by SSCI and ULAKBIM databases. Therefore, 80 articles were examined. The data was collected through a form developed by the researchers. The articles were analyzed according to the theme and code list provided on the form. The themes included the publication date, journal title, journal type, index, language, source of the articles; the number, gender, nationality, occupation, role of the authors; location, field, topic of the studies; research design, action research type and cycle of the studies; sampling level, size and method; duration, data collection and analysis method; validity and reliability method, and citation count of the studies. The data obtained was interpreted in terms of the percentage and frequency. The most remarkable results of the study are that action research is a less preferred type of research in Turkey, mostly conducted by academicians, and the teacher researchers are very few. In addition, the need to acquire more knowledge and experience on the main features of action research such as its methodology, types and cycle, and the role of the researcher can be considered as another important result derived from the study. Finally, it is hoped that the study will increase the interest in action research and contribute to the researchers.

For cycle 24, the minimum value of the 12-month moving average (12-mma) of the AA-geomagnetic index in the vicinity of sunspot minimum (AAm) appears to have occurred in September 2009, measuring about 8.4 nT and following sunspot minimum by 9 months. This is the lowest value of AAm ever recorded, falling below that of 8.9 nT, previously attributed to cycle 14, which also is the smallest maximum amplitude (RM) cycle of the modern era (RM = 64.2). Based on the method of Ohl (the preferential association between RM and AAm for an ongoing cycle), one expects cycle 24 to have RM = 55+/-17 (the +/-1 - sigma prediction interval). Instead, using a variation of Ohl's method, one based on using 2-cycle moving averages (2-cma), one expects cycle 23's 2-cma of RM to be about 115.5+/-8.7 (the +/-1 - sigma prediction interval), inferring an RM of about 62+/-35 for cycle 24. Hence, it seems clear that cycle 24 will be smaller in size than was seen in cycle 23 (RM = 120.8) and, likely, will be comparable in size to that of cycle 14. From the Waldmeier effect (the preferential association between the ascent duration (ASC) and RM for an ongoing cycle), one expects cycle 24 to be a slow-rising cycle (ASC > or equal to 48 months), having RM occurrence after December 2012, unless it turns out to be a statistical outlier.

For cycle 24, the minimum value of the 12-month moving average (12-mma) of the AA-geomagnetic index in the vicinity of sunspot minimum (AAm) appears to have occurred in September 2009, measuring about 8.4 nT and following sunspot minimum by 9 months. This is the lowest value of AAm ever recorded, falling below that of 8.9 nT, previously attributed to cycle 14, which also is the smallest maximum amplitude (RM) cycle of the modern era (RM = 64.2). Based on the method of Ohl (the preferential association between RM and AAm for an ongoing cycle), one expects cycle 24 to have RM = 55+/-17 (the +/-1 - sigma prediction interval). Instead, using a variation of Ohl's method, one based on using 2-cycle moving averages (2-cma), one expects cycle 23's 2-cma of RM to be about 115.5+/-8.7 (the +/-1 - sigma prediction interval), inferring an RM of about 62+/-35 for cycle 24. Hence, it seems clear that cycle 24 will be smaller in size than was seen in cycle 23 (RM = 120.8) and, likely, will be comparable in size to that of cycle 14. From the Waldmeier effect (the preferential association between the ascent duration (ASC) and RM for an ongoing cycle), one expects cycle 24 to be a slow-rising cycle (ASC > or equal to 48 months), having RM occurrence after December 2012, unless it turns out to be a statistical outlier.

On the basis of 12-month moving averages (12-mma) of monthly mean sunspot number (R), sunspot cycle 24 had its minimum amplitude (Rm = 1.7) in December 2008. At 12 mo past minimum, R measured 8.3, and at 18 mo past minimum, it measured 16.4. Thus far, the maximum month-to-month rate of rise in 12-mma values of monthly mean sunspot number (AR(t) max) has been 1.7, having occurred at elapsed times past minimum amplitude (t) of 14 and 15 mo. Compared to other sunspot cycles of the modern era, cycle 24?s Rm and AR(t) max (as observed so far) are the smallest on record, suggesting that it likely will be a slow-rising, long-period sunspot cycle of below average maximum amplitude (RM). Supporting this view is the now observed relative strength of cycle 24?s geomagnetic minimum amplitude as measured using the 12-mma value of the aa-geomagnetic index (aam = 8.4), which also is the smallest on record, having occurred at t equals 8 and 9 mo. From the method of Ohl (the inferred preferential association between RM and aam), one predicts RM = 55 +/- 17 (the ?1 se prediction interval) for cycle 24. Furthermore, from the Waldmeier effect (the inferred preferential association between the ascent duration (ASC) and RM) one predicts an ASC longer than 48 mo for cycle 24; hence, maximum amplitude occurrence should be after December 2012. Application of the Hathaway-Wilson-Reichmann shape-fitting function, using an RM = 70 and ASC = 56 mo, is found to adequately fit the early sunspot number growth of cycle 24.

The behavior of ascent duration, maximum amplitude, and period for cycles 1 to 21 suggests that they are not mutually independent. Analysis of the resultant three-dimensional contingency table for cycles divided according to rise time (ascent duration), size (maximum amplitude), and duration (period) yields a chi-square statistic (= 18.59) that is larger than the test statistic (= 9.49 for 4 degrees-of-freedom at the 5-percent level of significance), thereby, inferring that the null hypothesis (mutual independence) can be rejected. Analysis of individual 2 by 2 contingency tables (based on Fisher's exact test) for these parameters shows that, while ascent duration is strongly related to maximum amplitude in the negative sense (inverse correlation) - the Waldmeier effect, it also is related (marginally) to period, but in the positive sense (direct correlation). No significant (or marginally significant) correlation is found between period and maximum amplitude. Using cycle 22 as a test case, we show that by the 12th month following conventional onset, cycle 22 appeared highly likely to be a fast-rising, larger-than-average-size cycle. Because of the inferred correlation between ascent duration and period, it also seems likely that it will have a period shorter than average length.

A simple method for monitoring the nearness and size of conventional cycle maximum for an ongoing sunspot cycle is examined. The method uses the observed maximum daily value and the maximum monthly mean value of international sunspot number and the maximum value of the 2-mo moving average of monthly mean sunspot number to effect the estimation. For cycle 23, a maximum daily value of 246, a maximum monthly mean of 170.1, and a maximum 2-mo moving average of 148.9 were each observed in July 2000. Taken together, these values strongly suggest that conventional maximum amplitude for cycle 23 would be approx. 124.5, occurring near July 2002 +/-5 mo, very close to the now well-established conventional maximum amplitude and occurrence date for cycle 23-120.8 in April 2000.

By definition, the conventional onset for the start of a sunspot cycle is the time when smoothed sunspot number (i.e., the 12-month moving average) has decreased to its minimum value (called minimum amplitude) prior to the rise to its maximum value (called maximum amplitude) for the given sunspot cycle. On the basis (if the modern era sunspot cycles 10-22 and on the presumption that cycle 22 is a short-period cycle having a cycle length of 120 to 126 months (the observed range of short-period modern era cycles), conventional onset for cycle 23 should not occur until sometime between September 1996 and March 1997, certainly between June 1996 and June 1997, based on the 95-percent confidence level deduced from the mean and standard deviation of period for the sample of six short-pei-iod modern era cycles. Also, because the first occurrence of a new cycle, high-latitude (greater than or equal to 25 degrees) spot has always preceded conventional onset of the new cycle by at least 3 months (for the data-available interval of cycles 12-22), conventional onset for cycle 23 is not expected until about August 1996 or later, based on the first occurrence of a new cycle 23, high-latitude spot during the decline of old cycle 22 in May 1996. Although much excitement for an earlier-occurring minimum (about March 1996) for cycle 23 was voiced earlier this year, the present study shows that this exuberance is unfounded. The decline of cycle 22 continues to favor cycle 23 minimum sometime during the latter portion of 1996 to the early portion of 1997.

Examined are single- and bi-variate geomagnetic precursors for predicting the maximum amplitude (RM) of a sunspot cycle several years in advance. The best single-variate fit is one based on the average of the ap index 36 mo prior to cycle minimum occurrence (E(Rm)), having a coefficient of correlation (r) equal to 0.97 and a standard error of estimate (se) equal to 9.3. Presuming cycle 24 not to be a statistical outlier and its minimum in March 2008, the fit suggests cycle 24 s RM to be about 69 +/- 20 (the 90% prediction interval). The weighted mean prediction of 11 statistically important single-variate fits is 116 +/- 34. The best bi-variate fit is one based on the maximum and minimum values of the 12-mma of the ap index; i.e., APM# and APm*, where # means the value post-E(RM) for the preceding cycle and * means the value in the vicinity of cycle minimum, having r = 0.98 and se = 8.2. It predicts cycle 24 s RM to be about 92 +/- 27. The weighted mean prediction of 22 statistically important bi-variate fits is 112 32. Thus, cycle 24's RM is expected to lie somewhere within the range of about 82 to 144. Also examined are the late-cycle 23 behaviors of geomagnetic indices and solar wind velocity in comparison to the mean behaviors of cycles 2023 and the geomagnetic indices of cycle 14 (RM = 64.2), the weakest sunspot cycle of the modern era.

Examined are single- and bi-variate geomagnetic precursors for predicting the maximum amplitude (RM) of a sunspot cycle several years in advance. The best single-variate fit is one based on the average of the ap index 36 mo prior to cycle minimum occurrence (E(Rm)), having a coefficient of correlation (r) equal to 0.97 and a standard error of estimate (se) equal to 9.3. Presuming cycle 24 not to be a statistical outlier and its minimum in March 2008, the fit suggests cycle 24 s RM to be about 69 +/- 20 (the 90% prediction interval). The weighted mean prediction of 11 statistically important single-variate fits is 116 +/- 34. The best bi-variate fit is one based on the maximum and minimum values of the 12-mma of the ap index; i.e., APM# and APm*, where # means the value post-E(RM) for the preceding cycle and * means the value in the vicinity of cycle minimum, having r = 0.98 and se = 8.2. It predicts cycle 24 s RM to be about 92 +/- 27. The weighted mean prediction of 22 statistically important bi-variate fits is 112 32. Thus, cycle 24's RM is expected to lie somewhere within the range of about 82 to 144. Also examined are the late-cycle 23 behaviors of geomagnetic indices and solar wind velocity in comparison to the mean behaviors of cycles 2023 and the geomagnetic indices of cycle 14 (RM = 64.2), the weakest sunspot cycle of the modern era.