Gaussian width bounds with applications to arithmetic progressions in random settings

Motivated by problems on random differences in Szemer\'{e}di's theorem and on large deviations for arithmetic progressions in random sets, we prove upper bounds on the Gaussian width of point sets that are formed by the image of the $n$-dimensional Boolean hypercube under a mapping $\psi:\mathbb{R}^n\to\mathbb{R}^k$, where each coordinate is a constant-degree multilinear polynomial with 0-1 coefficients. We show the following applications of our bounds. Let $[\mathbb{Z}/N\mathbb{Z}]_p$ be the random subset of $\mathbb{Z}/N\mathbb{Z}$ containing each element independently with probability $p$. $\bullet$ A set $D\subseteq \mathbb{Z}/N\mathbb{Z}$ is $\ell$-intersective if any dense subset of $\mathbb{Z}/N\mathbb{Z}$ contains a proper $(\ell+1)$-term arithmetic progression with common difference in $D$. Our main result implies that $[\mathbb{Z}/N\mathbb{Z}]_p$ is $\ell$-intersective with probability $1 - o(1)$ provided $p \geq \omega(N^{-\beta_\ell}\log N)$ for $\beta_\ell = (\lceil(\ell+1)/2\rceil)^{-1}$. This gives a polynomial improvement for all $\ell \ge 3$ of a previous bound due to Frantzikinakis, Lesigne and Wierdl, and reproves more directly the same improvement shown recently by the authors and Dvir. $\bullet$ Let $X_k$ be the number of $k$-term arithmetic progressions in $[\mathbb{Z}/N\mathbb{Z}]_p$ and consider the large deviation rate $\rho_k(\delta) = \log\Pr[X_k \geq (1+\delta)\mathbb{E}X_k]$. We give quadratic improvements of the best-known range of $p$ for which a highly precise estimate of $\rho_k(\delta)$ due to Bhattacharya, Ganguly, Shao and Zhao is valid for all odd $k \geq 5$. We also discuss connections with error correcting codes (locally decodable codes) and the Banach-space notion of type for injective tensor products of $\ell_p$-spaces.Comment: 18 pages, some typos fixe

Measuring the Correlation Between Self-Efficacy Beliefs and English Language Attainments Among Thai University Students

This study examined the predictive value of Bandura’s 100 point self-efficacy scales among 208 third year university students (female; n = 108, male; n = 90) from three separate faculties; veterinary medicine (n = 60), business administration (n = 77) and engineering (n = 71) at a private institute of technology located on the outskirts of Bangkok. The central research question of this paper was to ascertain the extent to which one’s self-efficacy beliefs in English language attainments correspond with respective performance outcomes. Respondents were required to indicate their levels of self-efficacy in English as a general subject, as well as in domain specific matters relative to speaking proficiency, mid-term tests and final examinations. The results showed that the predictive value of subject related measures of self-efficacy across the sample population proved to be highly accurate, as the means of both sets of results were not significantly different (S.E: 68.12% vs. English: 66.28%; p <0.05), and were closely correlated (r = 0.692).The results from the domain specific scales, however, were less consistent. While there was no significant difference between declarations of self-efficacy and grade outcomes in both mid-term tests and final examinations (mid-term:62.59% vs. 64.33%; final: 63.22% vs.64.24%; p <0.05), and, both variables were also closely correlated (mid-term, r = 0.7018; final, r = 0.686); personal efficacy judgments for speaking proficiency were significantly inferior to respective attainments (58.46 vs. 68.25; p <0.05); resulting in a weaker correlation (r = 0.5248). Keywords: self-efficacy, beliefs, performance, subject, domain DOI: 10.7176/JEP/10-5-09Publication time:  February 28th, 201

On kk-layered numbers

A positive integer $n$ is said to be $k$-layered if its divisors can be partitioned into $k$ sets with equal sum. In this paper, we start the systematic study of these class of numbers. In particular, we state some algorithms to find some even $k$-layered numbers $n$ such that $2^{\alpha}n$ is a $k$-layered number for every positive integer $\alpha$. We also find the smallest $k$-layered number for $1\leq k\leq 8$. Furthermore, we study when $n!$ is a $3$-layered and when is a $4$-layered number. Moreover, we classify all $4$-layered numbers of the form $n=p^{\alpha}q^{\beta}rt$, where $\alpha$, $1\leq \beta\leq 3$, $p$, $q$, $r$, and $t$ are two positive integers and four primes, respectively. In addition, in this paper, some other results concerning these numbers and their relationship with $k$-multiperfect numbers, near-perfect numbers, and superabundant numbers are discussed. Also, we find an upper bound for the differences of two consecutive $k$-layered numbers for every positive integer $1\leq k\leq 5$. Finally, by assuming the smallest $k$-layered number, we find an upper bound for the difference of two consecutive $k$-layered numbers.Comment: 25 pages, 2 tables, comments are welcom

A Note On Asymptotic Smoothness Of The Extensions Of Zadeh

The concept of asymptotic smooth transformation was introduced by J. Hale [10]. It is a very important property for a transformation between complete metric spaces to have a global attractor. This property has also consequences on asymptotic stability of attractors. In our work we study the conditions under which the Zadeh's extension of a continuous map f : R n → R n is asymptotically smooth in the complete metric space JF(R n) of normal fuzzy sets with the induced Hausdorff metric d ∞ (see Kloeden and Diamond [8]).212141153Barros, L.C., Bassanezi, R.C., Tonelli, P.A., On the continuity of Zadeh's extension (1997) Proceedings Seventh IFSA World Congress, 2, pp. 3-8. , PragueBarros, L.C., Bassanezi, R.C., Tonelli, P.A., Fuzzy modeling in populations dynamics (2000) Ecological Modeling, 128, pp. 27-33Brumley, W.E., On the asymptotic behavior of solutions of differential difference equations of neutral type (1970) J. of Differential Equations, 7, pp. 175-188Cabrelli, C.A., Forte, B., Molter, U., Vrscay, E., Iterated Fuzzy Sets Systems: A new approach to the inverse for fractals and other sets (1992) J. of Math. Anal, and Appl., 171, pp. 79-100Cooperman, G., (1978) α-Condensing Maps and Dissipative Processes, , Ph. D. Thesis, Brown University, Providence, R. IDiamond, P., Chaos in iterated fuzzy systems (1994) J. of Mathematical Analysis and Applications, 184, pp. 472-484Diamond, P., Time Dependent Differential Inclusions, Cocycle Attractors and Fuzzy Differential Equations (1999) IEEE Trans. on Fuzzy Systems, 7, pp. 734-740Diamond, P., Kloeden, P., (1994) Metric Spaces of Fuzzy Sets: Theory and Applications, , World Scientific PubFriedmann, M., Ma, M., Kandel, A., Numerical solutions of fuzzy differential and integral equations (1999) Fuzzy Sets and Systems, 106, pp. 35-48Hale, J.K., Asymptotic Behavior of Dissipative Systems (1988) Math. Surveys and Monographs, 25. , American Mathematical Society, ProvidenceHüllermeier, E., An Approach to Modeling and Simulation of Uncertain Dynamical Systems (1997) J. Uncertainty, Fuzziness, Know Ledge-Bases Syst., 5, pp. 117-137Kloeden, P.E., Fuzzy dynamical systems (1982) Fuzzy Sets and Systems, 7, pp. 275-296Kloeden, P.E., Chaotic iterations of fuzzy sets (1991) Fuzzy Sets and Systems, 42, pp. 37-42Nguyen, H.T., A note on thé extension principle for fuzzy sets (1978) J. Math. Anal. Appl., 64, pp. 369-380Puri, M.L., Ralescu, D.A., Fuzzy Random Variables (1986) J. of Mathematical Analysis and Applications, 114, pp. 409-422Roman-Flores, H., Barros, L.C., Bassanezzi, R., A note on Zadeh's Extensions (2001) Fuzzy Sets and Systems, 117, pp. 327-331Roman-Flores, H., On the Compactness of E(X) (1998) Appl. Math. Lett., 11, pp. 13-17Zadeh, L.A., Fuzzy sets (1965) Inform. Control, 8, pp. 338-35

PO-184 Effects of resistance training and aerobic training on Fibronectin of Skeletal Muscle Extracellular Matrix and Satellite Cell in Aging Mice

Objective To investigate the effects of resistance and aerobic training on the content of fibronectin in skeletal muscle extracellular matrix and satellite cell in 9-month-old BALB/c mice, and then explore the effect of fibronectin content change on satellite cell and its intrinsic mechanism, which will provide a new research perspective and theoretical evidence for delaying sarcopenia. Methods 27 one-month-old BALB / c mice of SPF grade were purchased and fed for natural aging. At 9 months of age, the mice were divided into three groups randomly. Group R was resistance exercise training group (n=9), group A was aerobic exercise training group (n=9), and group C was control group (n=9). The load ladder model for resistance training in group R, the pyramid training program for 9 week training, 5 sets of load ladder training every time. 2 min for rest between sets, 1 min for rest between repetitions, 3 times a week. The treadmill training for aerobic training in group A for 9 weeks, the speed of 0.8km/h, 40min every time, 3 times a week. There is no training in group C. During the training, mouse grip strength was tested by the BIOSEB grip instrument once a week. After exercise intervention, the blood of mice was taken from the eyeball, and the gastrocnemius muscles were removed and placed in -80℃ temperature refrigerator to be freezed for tested . Immunofluorescence was used to detect FN and Pax7; The Real-time PCR was used to detect mRNA of FN, Sdc4, Fzd7, Wnt7a, c-Jun, Pax7; Western Blotting was used to detect the FN, sdc4, Fzd7, Wnt7a, c-Jun, p-c-Jun, Pax7 protein content. Results (1) Body weight, grip strength and skeletal muscle mass of mice: The body weight of group C and group R were significantly decreased after 9 weeks to compared with group A (P <0.05; P <0.05). The grip strength of group R and A was significantly increased in the ninth week to compared with group C, (P <0.01; P <0.05); The grip strength of group R and A in the ninth week were significantly higher than that in the first week (P <0.01; P <0.01)；  (2) FN in skeletal muscle extracellular matrix and it’s receptor Sdc4: The integrated optical density (IOD) of FN in group R was higher than that in group C and group A, but there was no significant difference among the three groups. The FN mRNA in group R was significantly increased to compared with group A (P<0.05). The FN protein content in group R was significantly increased to compared with group C and group A (P <0.01; P <0.01). There was no significant difference in the expression of Sdc4 mRNA in gastrocnemius muscle among the three groups. Compared with group C, the Sdc4 protein content was significantly down-regulated in both group R and group A (P<0.01; P<0.05). (3) Wnt7a/PCP signaling pathway: The Wnt7a mRNA and Wnt7a protein content in the gastrocnemius muscle of group R were significantly increased to compared with group C (P<0.05; P<0.01)). Compared with group A, Wnt7a protein content in group R was also significantly increased (P<0.05). There was no significant difference in Fzd7 mRNA in gastrocnemius muscle among the three groups; but the Fzd7 protein content in group R was significantly increased to compared with group A (P<0.05). The c-Jun mRNA in group R was significantly increased to compared with group C and A (P<0.05; P< 0.05). The content of c-Jun protein in group R was significantly increased to compared with group C and group A (P<0.01; P<0.01). The content of p-c-Jun protein in group R was significantly increased to compared with group C (P<0.05). (4) Pax7 : The number of Pax7 positive cells in group R was higher than that in group C and group A, but there was no significant difference among the three groups. Pax7 mRNA in group R and group A were significantly lower than that in group C (P<0.05; P<0.01), but Pax7 protein content in group R was significantly higher than group C and group A (P <0.05; P <0.05) Conclusions (1) Exercise can improve muscle strength of aging mice. (2) Resistance training can promote FN in skeletal muscle extracellular matrix and improve skeletal muscle extracellular matrix components of aging mice. (3) Resistance exercise training can promote Pax7 expression through the increase of FN and up-regulation of Wnt7a / PCP signaling pathway, thus make it possible for satellite cell proliferation

Numerical modelling of the coastal ocean off Tanzania

Includes bibliographical references (pages 71-89).In this model study of the coastal ocean off Tanzania, the Regional Ocean Modelling System (ROMS) was employed to model the coastal ocean off Tanzania over the domain of 5°N-15°S and 38-55°E. It was integrated for ten years with monthly mean Comprehensive Ocean and Atmosphere Data Sets (COADS) winds and heat fluxes. Initial and lateral boundary conditions were derived from the World Ocean Atlas. The model was used to simulate the annual cycle, and the sea surface temperature (SST) output compared with the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) sea surface temperature (SST) measurements for the same region. Although broadly comparable, the model SST was generally warmer than that of TMI data. The high SSTs in the Tanzanian coastal waters (greater than 28°C) occur from December to May while SSTs of less than 28°C occur during the rest of the year. The East African Coastal Current (EACC) experiences its lowest spatial and temporal average speeds (about 0.4ms- 1) in February and its maximum speed (1.7 ms⁻¹) in July. Speeds of greater than 1 ms⁻¹ occur during both transition seasons north of 6°S. The meridional wind stresses appear to be positively correlated with the EACC(r>0.6) in all locations and they are statistically significant (p<0.05). The annual cycle of the model flow in the southern Tanzanian waters seems to be positively correlated with the flow to the north of Madagascar (r=0.57 and p=O.O5). The flow in these regions changes in phase with each other from October to April and June to July with minimum speeds in November. For the other months, the flow in these regions is out of phase with each other. The model currents off southern Tanzania attain their maximum speeds in August when the South West monsoon is fully developed while the flow north of Madagascar attains its maximum speed in September when the South West monsoon fades. However, the flow in the southern Tanzanian waters is more affected by the reversal of winds over the tropical western Indian Ocean (r=0.69, p=0.01) than that north of Madagascar (r=0.51, p=0.09). This difference results in a larger annual speed range in the flow off southern Tanzania (about 0.4 ms⁻¹ ) than that to the north of Madagascar (about 0.3ms⁻¹). The ROMS model realistically simulates the annual cycle of the sea surface temperature and heat flux, the East African Coastal Current and the annual cycle of the flow entering the coastal ocean off the southern part of Tanzania. However, studies which integrate the large scale domain and regional coupled ocean-atmosphere interactions are needed to better understand of the East African climate and ocean variability. Such model results combined with suitable remote sensing and in situ observations will help improve understanding of the circulation and properties of the coastal ocean off Tanzania

YoBEKA (yoga, exercise, relaxation, concentration, mindfulness) in the elementary school – a non-randomized, controlled study

Background Children have been increasingly exposed to stress factors for years, especially in the school context. The aim of the present study is to investigate potential effects of the so-called YoBEKA intervention (yoga, exercise, relaxation, concentration, mindfulness) in the school context. Methodology In a controlled, non-randomized pilot study, students of the 3rd, 4th and 5th grade of three elementary school in Berlin were examined. The intervention group received 45 min of YoBEKA weekly for 16 weeks by a certified instructor and approximately 10 min of mindfulness- and yoga-based exercises daily by trained teaching staff. The control group received regular curricular lessons. Primary combined endpoint was stress vulnerability and stress symptomatology (SSKJ 3-8 R questionnaire, part 1 and part 3). Furthermore, general quality of life was assessed with the Kidscreen-27 (child and parent version) as well as demographic data, expectations, and evaluation (among children, parents, and teaching staff). Screening for somatoform disorders was performed by the SOMS-E (parents), and among teaching staff, occupational anxiety symptoms were assessed by the LASI and general stress symptomatology by the PSS. Data collection occurred at 3 time points: baseline, 4 and 12 months. Statistical analysis was performed using RM-ANOVA. Results Included were 263 students* (age: 9 3 years) from 12 classes. There were 196 complete data sets analyzed in the complete cases analysis (n = 136 intervention, n = 60 control). A total of n = 67 complete data sets were missing (n = 14 on V0, n = 15 on V1, n = 35 on V2), which were excluded from the analysis. No significant group difference was found on SSKJ 3-8 R [part 1: p = 0.053, F (1.95; 378.27) = 2.986; part 3: p = 0.464, F (1.93;374.55) = 0.761]. The Kidscreen-27 mean scores also showed no significant change when compared between groups [child version: p = 0.794, F (1.93; 372.524) = 0.221 and parent version: p = 0.54, F (1.955; 238.467) = 8.438]. A significant reduction [x2(3) = 63.0, p < 0.01, = 1.0] of children screened positive for somatoform disorders (SOMS-E) in the intervention group compared to the control group was demonstrated. Teacher questionnaires were not evaluated because of insufficient response. The qualitative evaluation by children and parents was overall positive. Summary The present study showed no effect of the intervention on the endpoints stress and quality of life of the pupils*, but a reduction of children positively screened for somatoform disorders. With increasing stress in the daily lives of many children and a significant increase in stress-associated disorders, further studies should investigate stress-reducing, relaxation-inducing interventions for students.Hintergrund Kinder sind insbesondere im Schulkontext seit Jahren zunehmend Stressfaktoren ausgesetzt. Ziel der vorliegenden Studie ist die Untersuchung potenzieller Effekte der sog. YoBEKAIntervention (Yoga, Bewegung, Entspannung, Konzentration, Achtsamkeit) im Schulkontext. Methodik In einer kontrollierten, nicht-randomisierten Pilotstudie wurden Schüler*innen der 3., 4. und 5. Klasse dreier Berliner Grundschulen untersucht. Die Interventionsgruppe erhielt über 16 Wochen wöchentlich 45 min YoBEKA durch eine zertifizierte Anleiterin sowie täglich ca. 10 min achtsamkeits- und yogabasierte Übungen durch geschultes Lehrpersonal. Die Kontrollgruppe erhielt regulären curricularen Unterricht. Primärer kombinierter Endpunkt war die Stressvulnerabilität und Stresssymptomatik (SSKJ 3-8 R Fragebogen, Teil 1 und Teil 3). Weiterhin wurden die allgemeine Lebensqualität mit dem Kidscreen-27 (Kinder- und Elternversion) sowie demographische Daten, Erwartungen und Evaluation (bei Kindern, Eltern und Lehrpersonal) erfasst. Ein Screening auf somatoforme Störungen erfolgte durch den SOMS-E (Eltern), beim Lehrpersonal wurden berufsbezogene Angstsymptome durch den LASI und die allgemeine Stresssymptomatik durch den PSS erfragt. Die Datenerhebung erfolgte zu 3 Zeitpunkten: zu Baseline, nach 4 und 12 Monaten. Die statistische Auswertung wurde mit RM-ANOVA durchgeführt. Ergebnisse Eingeschlossen wurden 263 Schüler*innen (Alter: 9 ± 3 Jahre) aus 12 Klassen. Es wurden 196 vollständige Datensätze im Rahmen der Complete Cases Analyse ausgewertet (n = 136 Intervention, n = 60 Kontrolle). Insgesamt fehlten n = 67 komplette Datensätze (n = 14 zu V0, n = 15 zu V1, n = 35 zu V2), die von der Analyse ausgeschlossen wurden. Es konnte kein signifikanter Gruppenunterschied beim SSKJ 3-8 R festgestellt werden [Teil 1: p = 0,053, F (1,95; 378,27) = 2,986; Teil 3: p = 0,464, F (1,93;374,55) = 0,761]. Auch beim Kidscreen-27 zeigten die Mittelwerte im Gruppenvergleich keine signifikante Veränderung [Kinderversion: p = 0,794, F (1,93; 372,524) = 0,221 und Elternversion: p = 0,54, F (1,955; 238,467) = 8,438]. Eine signifikante Reduktion [x2(3) = 63,0, p < 0,01, j = 1,0] der auf somatoforme Störungen positiv gescreenten Kinder (SOMS-E) in der Interventionsgruppe im Vergleich zur Kontrollgruppe konnte gezeigt werden. Auf eine Auswertung der Lehrerfragebögen wurde wegen unzureichendem Rücklauf verzichtet. Die qualitative Evaluation durch Kinder und Eltern war insgesamt positiv. Zusammenfassung Die vorliegende Studie zeigte keinen Effekt der Intervention auf die Endpunkte Stress und Lebensqualität der Schüler*innen, jedoch eine Reduktion der auf somatoforme Störungen positiv gescreenten Kinder. Bei steigender Stressbelastung im Alltag vieler Kinder und einer deutlichen Zunahme von stressassoziierten Erkrankungen sollte in weiteren Studien stressreduzierende, entspannungsinduzierende Interventionen für Schüler*innen untersucht werden