scholarly journals The (C, α) integrability of functions by weighted mean methods

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1209-1214 ◽  
Author(s):  
İbrahim Çanak ◽  
Ümit Totur
Keyword(s):  
Continuous Function ◽  
Weighted Mean ◽  
Integrability Of Functions

Let p(x) be a nondecreasing continuous function on [0, ?) such that p(0) = 0 and p(t) ? ? as t ? ?. For a continuous function f (x) on [0, ?), we define s(t)= ?0t f(u)du and ?? (t) =?0t? (1- p(u)/p(t))? f(u)du. We say that a continuous function f (x) on [0, ?) is (C, ?) integrable to a by the weighted mean method determined by the function p(x) for some ? > ?1 if the limit limt?? ?? (t) = a exists. We prove that if the limit limt?? ?? (t) = a exists for some ? > ?1, then the limit limt?? ??+h (t) = a exists for all h > 0. Next, we prove that if the limit limt?? ?? (t) = a exists for some ? > 0 and p(t)/p?(t) f(t)= O(1), t ? ?, then the limit limt?? ???1 (t) = a exists.

scholarly journals Erdös-Turán mean convergence theorem for Lagrange interpolation at Lobatto points

1986 ◽  
Vol 34 (3) ◽  
pp. 375-381 ◽  
Author(s):  
William E. Smith
Keyword(s):  
Continuous Function ◽  
Weight Function ◽  
Convergence Theorem ◽  
Lagrange Interpolation ◽  
Mean Square ◽  
Lagrange Polynomial ◽  
Weighted Mean ◽  
Product Integration ◽  
Lagrange Polynomials ◽  
Mean Convergence

Let {Qn} denote the orthogonal polynomials associated with the weight function p on [−1, 1] and let denote the zeros of (1−x2) Qn (x). Consider the Lagrange polynomials which interpolate a given continuous function at these points. It is shown that, as n → ∞, the Lagrange polynomial converges to the function in the W weighted mean square sense, where w (x) = ρ(x)\(1−x2), provided that W is integrable. An application to numerical product integration is noted.

Indikatoren schulischen Wohlbefindens bei gesunden und chronisch kranken Kindern: Psychometrische Prüfung und Validierung adaptierter FEESS-Skalen

2020 ◽  
Vol 34 (3-4) ◽  
pp. 201-219
Author(s):  
Kathleen Schnick-Vollmer ◽  
Christiane Diefenbach ◽  
Christine Gräf ◽  
Dorle Hoffmann ◽  
Isabell Hoffmann ◽  
...  
Keyword(s):  
Item Response ◽  
Mean Square ◽  
Weighted Mean ◽  
Externe Validität ◽  
Chronisch Kranke

Zusammenfassung. Das schulbezogene Wohlbefinden (SBWB) ist eine wichtige Voraussetzung für schulischen Erfolg. Trotzdem existieren – insbesondere mit Blick auf die Erfassung des SBWB von Erstklässlern – im deutschsprachigen Raum nur vereinzelt Studien. Dies lässt sich möglicherweise durch das Fehlen geeigneter Instrumente begründen. Dies gilt auch und insbesondere dann, wenn der Gesundheitszustand der Kinder berücksichtigt werden soll. Das Ziel der vorliegenden Arbeit besteht in der Validierung des adaptierten Fragebogens zur Erfassung von emotionalen und sozialen Schulerfahrungen (FEESS 1 – 2; Rauer & Schuck, 2004 ) mit Fokus auf die Eignung des Instruments für chronisch kranke und gesunde Kinder. Dafür wird zunächst das Konstrukt Wohlbefinden (WB) resp. SBWB definiert und in einschlägige Theorien – die Selbstbestimmungstheorie nach Deci und Ryan (1985) und das Erwartung-mal-Wert-Modell nach Wigfield und Eccles (2000) – eingebettet. Die Bedeutung der verwendeten FEESS-Skalen und ihr Zusammenhang zum schulischen Erfolg werden aufgezeigt. 1491 Kinder wurden zu ihrer Lernfreude (LF), sozialen Integration (SI) und zu ihrem schulbezogenen Fähigkeitsselbstkonzept (SK) befragt. Die Erfassung des Gesundheitszustands wurde über Elternfragebögen und Schuleingangsuntersuchungen eruiert. Zudem wurden die Eltern zur gesundheitsbezogenen Lebensqualität (LQ) ihrer Kinder mit Hilfe eines Fragebogens zur Erfassung der Lebensqualität von Kindern (KINDL; Bullinger, Mackensen & Kirchberger, 1994 ) befragt. Die psychometrische Qualität der adaptierten FEESS-Skalen wurde für beide Gruppen (erkrankt / gesund) auf Skalen- und Itemebene untersucht. Hierzu kamen sowohl klassische Verfahren als auch Verfahren der Item-Response-Theorie zum Einsatz. Die Ergebnisse untermauern die Validität des Konstruktes SBWB und stützen die Annahme der Dreidimensionalität (LF, SI, SK). Alle drei Skalen zeigen eine zufriedenstellende bis sehr gute Reliabilität. Die Items zeigen sehr gute MNSQ-Werte (weighted mean-square; gewichtete Abweichungsquadrate) und geeignete Trennschärfen. Die externe Validität, für deren Berechnung der Zusammenhang zwischen den Angaben der Kinder und den Angaben der Eltern zur gesundheitsbezogenen LQ untersucht wurde, konnte noch nicht ausreichend nachgewiesen werden. Bis auf diese Einschränkung kann mit Hilfe der adaptierten FEESS-Skalen im nächsten Schritt das SBWB von gesunden und erkrankten Kindern verglichen werden, um mögliche Chancenungleichheiten auszugleichen.

The Relationship Between Immorality and Cleansing

2018 ◽  
Vol 49 (5) ◽  
pp. 303-309 ◽  
Author(s):  
Jedidiah Siev ◽  
Shelby E. Zuckerman ◽  
Joseph J. Siev
Keyword(s):  
Effect Size ◽  
Meta Analysis ◽  
Weighted Mean ◽  
The Relationship

Abstract. In a widely publicized set of studies, participants who were primed to consider unethical events preferred cleansing products more than did those primed with ethical events ( Zhong & Liljenquist, 2006 ). This tendency to respond to moral threat with physical cleansing is known as the Macbeth Effect. Several subsequent efforts, however, did not replicate this relationship. The present manuscript reports the results of a meta-analysis of 15 studies testing this relationship. The weighted mean effect size was small across all studies (g = 0.17, 95% CI [0.04, 0.31]), and nonsignificant across studies conducted in independent laboratories (g = 0.07, 95% CI [−0.04, 0.19]). We conclude that there is little evidence for an overall Macbeth Effect; however, there may be a Macbeth Effect under certain conditions.

Generalized ʎ-Closed Sets and (ʎ-ʏ)*-Continuous Function

2017 ◽  
Vol 4 (ICBS Conference) ◽  
pp. 1-17 ◽  
Author(s):  
Alias Khalaf ◽  
Sarhad Nami
Keyword(s):  
Continuous Function ◽  
Closed Sets

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

Minimally Empirical Double Hybrid Functionals Trained Against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

2019 ◽  
Author(s):  
Golokesh Santra ◽  
Nitai Sylvetsky ◽  
Gershom Martin
Keyword(s):  
Substantial Improvement ◽  
Viable Alternative ◽  
Mean Absolute Deviation ◽  
Dispersion Correction ◽  
Training Set ◽  
Weighted Mean ◽  
Absolute Deviation ◽  
Hybrid Functionals ◽  
Scaling Algorithms

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed wB97M(2) empirical double hybrid (with 16 empirical parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, our xrevDSD-PBEP86-D4 functional reaches a statistically equivalent WTMAD2=2.22 kcal/mol, using just a handful of empirical parameters, and the xrevDOD-PBEP86-D4 functional reaches 2.25 kcal/mol with just opposite-spin MP2 correlation, making it amenable to reduced-scaling algorithms. In general, the D4 empirical dispersion correction is clearly superior to D3BJ. If one eschews dispersion corrections of any kind, noDispSD-SCAN offers a viable alternative. Parametrization over the entire GMTKN55 dataset yields substantial improvement over the small training set previously employed in the DSD papers.

Minimally Empirical Double Hybrid Functionals Trained Against the GMTKN55 Database: revDSD-PBEP86-D4, revDOD-PBE-D4, and DOD-SCAN-D4

2019 ◽  
Author(s):  
Golokesh Santra ◽  
Nitai Sylvetsky ◽  
Gershom Martin
Keyword(s):  
Substantial Improvement ◽  
Viable Alternative ◽  
Mean Absolute Deviation ◽  
Dispersion Correction ◽  
Training Set ◽  
Weighted Mean ◽  
Absolute Deviation ◽  
Hybrid Functionals ◽  
Scaling Algorithms

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed wB97M(2) empirical double hybrid (with 16 empirical parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, our xrevDSD-PBEP86-D4 functional reaches a statistically equivalent WTMAD2=2.22 kcal/mol, using just a handful of empirical parameters, and the xrevDOD-PBEP86-D4 functional reaches 2.25 kcal/mol with just opposite-spin MP2 correlation, making it amenable to reduced-scaling algorithms. In general, the D4 empirical dispersion correction is clearly superior to D3BJ. If one eschews dispersion corrections of any kind, noDispSD-SCAN offers a viable alternative. Parametrization over the entire GMTKN55 dataset yields substantial improvement over the small training set previously employed in the DSD papers.

FACILITATING SKILLS OF GRADE SCHOOL TEACHERS IN INCREASING LEARNING RETENTION AMONG GRADE SCHOOL PUPILS

2019 ◽  
Author(s):  
GARRY LINGON
Keyword(s):  
Learning Styles ◽  
Learning Process ◽  
Learning Activities ◽  
Survey Questionnaire ◽  
Grade School ◽  
School Teachers ◽  
Weighted Mean ◽  
Daily Lives ◽  
Learning Retention ◽  
Materials Used

<p>Teachers are a facilitator of the learning process. Teachers give pupils an ample time to discover new things on their own. Many challenges faced by the teachers in facilitating the activity of learners such as planning, creating, preparing, and selecting the materials used in the activity. Because of this, the task of the teachers is multi-faceted. Many things to be considered in making learning activities, must suit the capability of the learners, this activity can be adapted to different learning styles, and the activity must stimulate the interest of the learners. But not all activities are fitted for all learners because learners are diverse and unique in nature. The needs of pupils are the major concern of the teachers, to retain the learning of the pupils and especially the learning could apply in their daily lives for meaningful learning. The research dealt with the challenges of the teachers in increasing the learning retention among pupils and possible activities that stimulate the interest of the learners. This research measure the responses measured in getting the frequency, percentage, and weighted mean using formulas to analyze the data gathered. Utilize descriptive design with a survey questionnaire as the research instrument. This research has two sets of respondents the grade school teachers and pupils. <br></p>

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