Darboux Approach to Mα-integration

It is known that one can develop Riemann integration theory via Darboux approach. Themain idea in the Darboux approach is to define an integral using upper and lower Riemannsums. In this study we look at how -integration can be develop via Darboux approach.Here is a brief discussion of the methodology. We define an equivalence relation on the set of-divisions of , - such that for - divisions *(, - )+ and *(, - )+ wesay that if and only if the intervals in are exactly the intervals in . Given agauge on , - and a -fine division *(, - )+ of , -, we set, - * + Given a function on , -, and a -fine - division , we define the upper and lowersums (respectively) in the following manner( ) , -( ) ( )( ) and ( ) , -( ) ( )( )provided these values exists. We were able to show that a function on , - is -ntegrable if and only if the following exists and are equal:() ∫̅̅̅̅̅ ( ) and () ∫ ( ) In this approach we were able to prove the basic properties of the -integral. It is our nextgoal to extend -integration to other spaces via Darboux approach

The N-integral

In this paper, we introduced a Henstock-type integral named $N$-integral of a real valued function $f$ on a closed and bounded interval $[a,b]$. The $N$-integrable functions lie entirely between Riemann integrable functions and Henstock integrable functions. It was shown that for a Henstock integrable function $f$ on $[a,b]$ the following are equivalent: \begin{enumerate} \item[$(1)$] The function $f$ is $N$-integrable; \item[$(2)$] There exists a null set $S$ for which given $\epsilon \u3e0$ there exists a gauge $\delta$ such that for any $\delta$-fine partial division $D=\{(\xi,[u,v])\}$ of $[a,b]$ we have $$(\phi_S(D)\cap \Gamma_{\epsilon})\sum |f(v)-f(u)||v-u|\u3c\epsilon$$ where $\phi_S(D)=\{(\xi,[u,v])\in D:\xi \notin S\}$ and $$\Gamma_{\epsilon}=\{(\xi,[u,v]): |f(v)-f(u)|\geq \epsilon\}$$ \end{enumerate} and \begin{enumerate} \item[$(3)$] The function $f$ is continuous almost everywhere. \end{enumerate} A characterization of continuous almost everywhere functions was also given

Characterizing Convergence Conditions for the Mα-Integral

Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries

Cauchy Extension of Mα-Integral and Absolute Mα-Integrability

Park, Ryu, and Lee recently introduced a Henstock-type integral, which lies between the Mcshane and the Henstock integrals. This paper proves the closure property of this new integral under Cauchy extension, and presents a characterization on absolute Mα-integrabilit

Relationship of Knowledge on Healthy Lifestyle to Dietary Practices and Physical Activity as Moderated by Age

Lifestyle – related diseases remained to be on the top ten killer according to the World HealthOrganization. Literature indicates that diseases are highly related to lifestyle practices. Onthe other hand, optimal health is a perceived goal of the greater population, however, puttingit into practice is a challenge. The study determined the following: 1) the level of knowledgeon healthy lifestyle, dietary practices and physical activity; 2) the relationship of knowledgeon healthy lifestyle to dietary practices and physical activities, and 3) the relationship ofknowledge to dietary practice and relationship of knowledge to physical activities accordingto age group. A Descriptive-correlational design was employed. The data were gatheredamong 66 randomly selected university students staying in the dormitories; who are at least18 years of age, in which 24 are males and 42 are females, and 40 have earned at most abachelor’s degree and 26 have at least earned units in a master’s program. Utilizing adaptedinstruments, respondents were scored on a 12-item instrument in knowledge where in eachcorrect answer correspond to one point, 27-item instrument on healthy lifestyle in terms ofdiet where in each appropriate response correspond to one point, and 4-item instrument onhealthy lifestyle in terms of physical activities. In turn, the highest possible score ofknowledge, diet, and physical activities are 12, 27, and 4, respectively. Descriptive resultsrevealed that respondents have high knowledge on healthy lifestyle, have fair dietarypractices and moderate practice of physical activities. Furthermore, knowledge on healthylifestyle is not significantly correlated to dietary practices physical activities. However, asignificant relationship was found when respondents were grouped according to age; onlythose 24 years old and above were found to have significant results. Hence, arecommendation to increase the accessibility and reinforcement values of exercise andphysical activity that will have immediate and long term health benefits for college students

Relationship of Knowledge on Healthy Lifestyle to Dietary Practices and Physical Activity as Moderated by Age

Lifestyle – related diseases remained to be on the top ten killer according to the World HealthOrganization. Literature indicates that diseases are highly related to lifestyle practices. On theother hand, optimal health is a perceived goal of the greater population, however, putting it intopractice is a challenge. The study determined the following: 1) the level of knowledge onhealthy lifestyle, dietary practices and physical activity; 2) the relationship of knowledge onhealthy lifestyle to dietary practices and physical activities, and 3) the relationship ofknowledge to dietary practice and relationship of knowledge to physical activities according toage group. A Descriptive-correlational design was employed. The data were gathered among66 randomly selected university students staying in the dormitories; who are at least 18 yearsof age, in which 24 are males and 42 are females, and 40 have earned at most a bachelor’sdegree and 26 have at least earned units in a master’s program. Utilizing adapted instruments,respondents were scored on a 12-item instrument in knowledge where in each correct answercorrespond to one point, 27-item instrument on healthy lifestyle in terms of diet where in eachappropriate response correspond to one point, and 4-item instrument on healthy lifestyle interms of physical activities. In turn, the highest possible score of knowledge, diet, and physicalactivities are 12, 27, and 4, respectively. Descriptive results revealed that respondents havehigh knowledge on healthy lifestyle, have fair dietary practices and moderate practice ofphysical activities. Furthermore, knowledge on healthy lifestyle is not significantly correlatedto dietary practices physical activities. However, a significant relationship was found whenrespondents were grouped according to age; only those 24 years old and above were found tohave significant results. Hence, a recommendation to increase the accessibility andreinforcement values of exercise and physical activity that will have immediate and long termhealth benefits for college students

Relating Group Size and Posting Activity of an Online Community of Financial Investors: Regularities and Seasonal Patterns

Group size can potentially affect collective activity and individual propensity to contribute to collective goods. Mancur Olson, in his Logic of Collective Action, argued that individual contribution to a collective good tends to be lower in groups of large size. Today, online communication platforms represent an interesting ground to study such collaborative dynamics under possibly different conditions (e.g., lower costs related to gather and share information). This paper examines the relationship between group size and activity in an online financial forum, where users invest time in sharing news, analysis and comments with other investors. We looked at about 24 million messages shared in more than ten years in the finanzaonline.com online forum. We found that the relationship between the number of active users and the number of posts shared by those users is of the power type (with exponent α\u3e1) and is subject to periodic fluctuations, mostly driven by hour-of-the-day and day-of-the-week effects. The daily patterns of the exponent showed a divergence between working week and weekend days. In general, the exponent was lower before noon, where investors are typically interested in market news, higher in the late afternoon, where markets are closing and investors need better understanding of the situation. Further research is needed, especially at the micro level, to dissect the mechanisms behind these regularities

NMDA receptor content of synapses in stratum radiatum of the hippocampal CA1 area

Glutamate receptors activated by NMDA (NMDARs) or AMPA (AMPARs) are clustered on dendritic spines of pyramidal cells. Both the AMPAR-mediated postsynaptic responses and the synaptic AMPAR immunoreactivity show a large intersynapse variability. Postsynaptic responses mediated by NMDARs show less variability. To assess the variability in NMDAR content and the extent of their coexistence with AMPARs in Schaffer collateral-commissural synapses of adult rat CA1 pyramidal cells, electron microscopic immunogold localization of receptors has been used. Immunoreactivity of NMDARs was detected in virtually all synapses on spines, but AMPARs were undetectable, on average, in 12% of synapses. A proportion of synapses had a very high AMPAR content relative to the mean content, resulting in a distribution more skewed toward larger values than that of NMDARs. The variability of synaptic NMDAR content [coefficient of variation (CV), 0.64-0.70] was much lower than that of the AMPAR content (CV, 1.17-1.45). Unlike the AMPAR content, the NMDAR content showed only a weak correlation with synapse size. As reported previously for AMPARs, the immunoreactivity of NMDARs was also associated with the spine apparatus within spines. The results demonstrate that the majority of the synapses made by CA3 pyramidal cells onto spines of CA1 pyramids express both NMDARs and AMPARs, but with variable ratios. A less-variable NMDAR content is accompanied by a wide variability of AMPAR content, indicating that the regulation of expression of the two receptors is not closely linked. These findings support reports that fast excitatory transmission at some of these synapses is mediated by activation mainly of NMDARs

Attribution of recent temperature behaviour reassessed by a neural-network method

Abstract Attribution studies on recent global warming by Global Climate Model (GCM) ensembles converge in showing the fundamental role of anthropogenic forcings as primary drivers of temperature in the last half century. However, despite their differences, all these models pertain to the same dynamical approach and come from a common ancestor, so that their very similar results in attribution studies are not surprising and cannot be considered as a clear proof of robustness of the results themselves. Thus, here we adopt a completely different, non-dynamical, data-driven and fully nonlinear approach to the attribution problem. By means of neural network (NN) modelling, and analysing the last 160 years, we perform attribution experiments and find that the strong increase in global temperature of the last half century may be attributed basically to anthropogenic forcings (with details on their specific contributions), while the Sun considerably influences the period 1910–1975. Furthermore, the role of sulphate aerosols and Atlantic Multidecadal Oscillation for better catching interannual to decadal temperature variability is clarified. Sensitivity analyses to forcing changes are also performed. The NN outcomes both corroborate our previous knowledge from GCMs and give new insight into the relative contributions of external forcings and internal variability to climate