On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmed S. Hendy ◽  
Mahmoud A. Zaky ◽  
Eid H. Doha
Keyword(s):  
Numerical Analysis ◽  
A Priori ◽  
Gronwall Inequality ◽  
Gronwall Lemma ◽  
Discrete Form ◽  
Left Hand ◽  
Grönwall Inequality ◽  
Difference Formula ◽  
The Right ◽  
The Given

Abstract The aim of this paper is to derive a novel discrete form of stochastic fractional Grönwall lemma involving a martingale. The proof of the derived inequality is accomplished by a corresponding no randomness form of the discrete fractional Grönwall inequality and an upper bound for discrete-time martingales representing the supremum in terms of the infimum. The release of a martingale term on the right-hand side of the given inequality and the graded L1 difference formula for the time Caputo fractional derivative of order 0 < α < 1 on the left-hand side are the main challenges of the stated and proved main theorem. As an example of application, the constructed theorem is used to derive an a priori estimate for a discrete stochastic fractional model at the end of the paper.

Temporal Coordination between Performing Musicians

2011 ◽  
Vol 64 (11) ◽  
pp. 2153-2167 ◽  
Author(s):  
Janeen D. Loehr ◽  
Caroline Palmer
Keyword(s):  
A Priori ◽  
Solo Performance ◽  
Action Simulation ◽  
Temporal Coordination ◽  
Left Hand ◽  
Right Hand ◽  
Mutual Adaptation ◽  
Temporal Grouping ◽  
Cross Correlations ◽  
The Right

Many common behaviours require people to coordinate the timing of their actions with the timing of others' actions. We examined whether representations of musicians' actions are activated in coperformers with whom they must coordinate their actions in time and whether coperformers simulate each other's actions using their own motor systems during temporal coordination. Pianists performed right-hand melodies along with simple or complex left-hand accompaniments produced by themselves or by another pianist. Individual performers' preferred performance rates were measured in solo performance of the right-hand melody. The complexity of the left-hand accompaniment influenced the temporal grouping structure of the right-hand melody in the same way when it was performed by the self or by the duet partner, providing some support for the action corepresentation hypothesis. In contrast, accompaniment complexity had little influence on temporal coordination measures (asynchronies and cross-correlations between parts). Temporal coordination measures were influenced by a priori similarities between partners' preferred rates; partners who had similar preferred rates in solo performance were better synchronized and showed mutual adaptation to each other's timing during duet performances. These findings extend previous findings of action corepresentation and action simulation to a task that requires precise temporal coordination of independent yet simultaneous actions.

Further Notes on the Sculpture of the Later Temple of Artemis at Ephesus

1914 ◽  
Vol 34 ◽  
pp. 76-88
Author(s):  
W. R. Lethaby
Keyword(s):  
British Museum ◽  
Female Figure ◽  
Left Hand ◽  
Right Hand ◽  
The Subject ◽  
Symmetrical Group ◽  
The Right ◽  
Vertical Joint ◽  
The Given

The Square Pedestals.—In some notes on the sculpture from the Artemision at the British Museum, printed in the last volume of this Journal (p. 87), I suggested that the fragment No. 1201 most probably belonged to a relief representing either Herakles in the Garden of the Hesperides or Herakles and the Hydra. Subsequent examination and the attempt to make a restoration from the given data have made me sure that the former was the subject of the sculpture. Only this would account for the quiet action of the left hand of Herakles and for the closely associated female figure. If this were indeed the subject, how could its normal elements be arranged so as to suit the conditions of the square pedestal having a vertical joint in the centre, and making proper use of the existing fragment of which Fig. 1 is a rough sketch? This question I have tried to answer. The fragment is now fixed in the side of a built-up pedestal close to its left-hand angle, but there is nothing which settles this position and it is a practically impossible one, for there is not room left in which to complete the figure of Herakles. If, however, we shift the piece to the right hand half of the pedestal, and sketch in the completion of the two figures, we at once see how perfectly the tree and serpent would occupy the centre of the composition and leave the left-hand space for the two other watching maidens—the whole making a symmetrical group.

scholarly journals Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1165
Author(s):  
Shahram Rezapour ◽  
Sotiris K. Ntouyas ◽  
Abdelkader Amara ◽  
Sina Etemad ◽  
Jessada Tariboon
Keyword(s):  
Differential Equation ◽  
Fixed Point Theorems ◽  
Research Study ◽  
Existence Results ◽  
Gronwall Inequality ◽  
Grönwall Inequality ◽  
Dependence Criterion ◽  
Uniqueness And Existence ◽  
The Right ◽  
Uniqueness And Existence Results

The main intention of the present research study is focused on the analysis of a Caputo fractional integro-differential boundary problem (CFBVP) in which the right-hand side of supposed differential equation is represented as a sum of two nonlinear terms. Under the integro-derivative boundary conditions, we extract an equivalent integral equation and then define new operators based on it. With the help of three distinct fixed-point theorems attributed to Krasnosel’skiĭ, Leray–Schauder, and Banach, we investigate desired uniqueness and existence results. Additionally, the dependence criterion of solutions for this CFBVP is checked via the generalized version of the Gronwall inequality. Next, three simulative examples are designed to examine our findings based on the procedures applied in the theorems.

scholarly journals Solving Equations in the lambda-Calculus using Syntactic Encapsulation

1995 ◽  
Vol 2 (49) ◽  
Author(s):  
Mayer Goldberg
Keyword(s):  
Normal Form ◽  
Lambda Calculus ◽  
Systems Of Equations ◽  
Left Hand ◽  
Right Hand ◽  
Solving Equations ◽  
The Right ◽  
The Given ◽  
Programming Calculi

<p>Syntactic encapsulation is a relation between an expression and one of<br />its sub-expressions, that constraints how the given sub-expression can<br />be used throughout the reduction of the expression. In this paper, we<br />present a class of systems of equations, in which the right-hand side of<br />each equation is syntactically encapsulated in the left-hand side. This<br />class is general enough to allow equations to contain self-application,<br />and to allow unknowns to appear on both sides of the equation. Yet<br />such a system is simple enough to be solvable, and for a solution<br />(though of course not its normal form) to be obtainable in constant<br />time.</p><p><br />Keywords: lambda-calculus, programming calculi.</p>

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Is the Future the Right Time?

2010 ◽  
Vol 57 (4) ◽  
pp. 308-314 ◽  
Author(s):  
Marc Ouellet ◽  
Julio Santiago ◽  
Ziv Israeli ◽  
Shai Gabay
Keyword(s):  
Auditory Task ◽  
English Speakers ◽  
Visual Modality ◽  
Opposite Pattern ◽  
Time Line ◽  
Temporal Reference ◽  
Left Hand ◽  
Reading Direction ◽  
Mental Time Line ◽  
The Right

Spanish and English speakers tend to conceptualize time as running from left to right along a mental line. Previous research suggests that this representational strategy arises from the participants’ exposure to a left-to-right writing system. However, direct evidence supporting this assertion suffers from several limitations and relies only on the visual modality. This study subjected to a direct test the reading hypothesis using an auditory task. Participants from two groups (Spanish and Hebrew) differing in the directionality of their orthographic system had to discriminate temporal reference (past or future) of verbs and adverbs (referring to either past or future) auditorily presented to either the left or right ear by pressing a left or a right key. Spanish participants were faster responding to past words with the left hand and to future words with the right hand, whereas Hebrew participants showed the opposite pattern. Our results demonstrate that the left-right mapping of time is not restricted to the visual modality and that the direction of reading accounts for the preferred directionality of the mental time line. These results are discussed in the context of a possible mechanism underlying the effects of reading direction on highly abstract conceptual representations.

scholarly journals Hand Preference and Performance in Basketball Tasks

2019 ◽  
Vol 16 (22) ◽  
pp. 4336 ◽  
Author(s):  
Emanuela Gualdi-Russo ◽  
Natascia Rinaldo ◽  
Alba Pasini ◽  
Luciana Zaccagni
Keyword(s):  
Professional Training ◽  
Factor Model ◽  
Hand Preference ◽  
Control Group ◽  
Basketball Players ◽  
Confirmatory Factor Analyses ◽  
Left Hand ◽  
Confirmatory Factor ◽  
And Performance ◽  
The Right

The aims of this study were to develop and validate an instrument to quantitatively assess the handedness of basketballers in basketball tasks (Basketball Handedness Inventory, BaHI) and to compare it with their handedness in daily activities by the Edinburgh Handedness Inventory (EHI). The participants were 111 basketballers and 40 controls. All subjects completed the EHI and only basketballers filled in the BaHI. To validate the BaHI, a voluntary subsample of basketballers repeated the BaHI. Exploratory and confirmatory factor analyses supported a two-factor model. Our results show that: (i) Handedness score (R) in daily actions did not differ between basketball players (R by EHI = 69.3 ± 44.6) and the control group (R by EHI = 64.5 ± 58.6); (ii) basketballers more frequently favored performing certain sport tasks with the left hand or mixed hands (as highlighted by R by BaHI = 50.1 ± 47.1), although their choice was primarily the right hand in everyday gestures; and (iii) this preference was especially true for athletes at the highest levels of performance (R by BaHI of A1 league = 38.6 ± 58.3) and for those playing in selected roles (point guard’s R = 29.4 ± 67.4). Our findings suggest that professional training induces handedness changes in basketball tasks. The BaHI provides a valid and reliable measure of the skilled hand in basketball. This will allow coaches to assess mastery of the ball according to the hand used by the athlete in the different tasks and roles.

scholarly journals Digit Variability in Carotenoid Scores Obtained with the Veggie Meter: A Pilot Study (P02-001-19)

2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Velarie Ansu ◽  
Stephanie Dickinson ◽  
Alyce Fly
Keyword(s):  
Indiana University ◽  
Left Hand ◽  
Funding Sources ◽  
Right Hand ◽  
Period Data ◽  
The Mean ◽  
The Right ◽  
Post Hoc ◽  
Main Effects ◽  
Mean Square Errors

Abstract Objectives To determine which digit and hand have the highest and lowest skin carotenoid scores, to compare inter-and-intra-hand variability of digits, and to determine if results are consistent with another subject. Methods Two subjects’ first(F1), second(F2), third(F3) and fifth(F5) digits on both hands were measured for skin carotenoids with a Veggie Meter, for 3 times on each of 18 days over a 37-day period. Data were subjected to ANOVA in a factorial treatment design to determine main effects for hand (2 levels), digits (4), and days (18) along with interactions. Differences between digits were determined by Tukey's post hoc test. Results There were significant hand x digit, hand x day, digit x day, and hand x digit x day interactions and significant simple main effects for hand, digit, and day (all P < 0.001). Mean square errors were 143.67 and 195.62 for subject A and B, respectively, which were smaller than mean squares for all main effects and interactions. The mean scores ± SD for F1, F2, F3, and F5 digits for the right vs left hands for subject A were F1:357.13 ± 45.97 vs 363.74 ± 46.94, F2:403.17 ± 44.77 vs. 353.20 ± 44.13, F3:406.76 ± 43.10 vs. 357.11 ± 45.13, and F5:374.95 ± 53.00 vs. 377.90 ± 47.38. For subject B, the mean scores ± SD for digits for the right vs left hands were F1:294.72 ± 61.63 vs 280.71 ± 52.48, F2:285.85 ± 66.92 vs 252.67 ± 67.56, F3:268.56 ± 57.03 vs 283.22 ± 45.87, and F5:288.18 ± 34.46 vs 307.54 ± 40.04. The digits on the right hand of both subjects had higher carotenoid scores than those on the left hands, even though subjects had different dominant hands. Subject A had higher skin carotenoid scores on the F3 and F2 digits for the right hand and F5 on the left hand. Subject B had higher skin carotenoid scores on F5 (right) and F1 (left) digits. Conclusions The variability due to hand, digit, and day were all greater than that of the 3 replicates within the digit-day for both volunteers. This indicates that data were not completely random across the readings when remeasuring the same finger. Different fingers displayed higher carotenoid scores for each volunteer. There is a need to conduct a larger study with more subjects and a range of skin tones to determine whether the reliability of measurements among digits of both hands is similar across the population. Funding Sources Indiana University.

scholarly journals Numerical Analysis of the Bond Strength between Two Methacrylic Polymers by Surface Modification

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3927
Author(s):  
Joanna Taczała ◽  
Katarzyna Rak ◽  
Jacek Sawicki ◽  
Michał Krasowski
Keyword(s):  
Numerical Analysis ◽  
Bond Strength ◽  
Angular Position ◽  
Fem Analysis ◽  
Groove Depth ◽  
Chemical Reagent ◽  
Shear Process ◽  
3D Geometry ◽  
The Right ◽  
Artificial Teeth

The creation of acrylic dentures involves many stages. One of them is to prepare the surfaces of artificial teeth for connection with the denture plates. The teeth could be rubbed with a chemical reagent, the surface could be developed, or retention hooks could be created. Preparation of the surface is used to improve the bond between the teeth and the plate. Choosing the right combination affects the length of denture use. This work focuses on a numerical analysis of grooving. The purpose of this article is to select the shape and size of the grooves that would most affect the quality of the bond strength. Two types of grooves in different dimensional configurations were analyzed. The variables were groove depth and width, and the distance between the grooves. Finally, 24 configurations were obtained. Models were analyzed in terms of their angular position to the loading force. Finite element method (FEM) analysis was performed on the 3D geometry created, which consisted of two polymer bodies under the shear process. The smallest values of the stresses and strains were characterized by a sample with parallel grooves with the grooving dimensions width 0.20 mm, thickness 0.10 mm, and distance between the grooves 5.00 mm, placed at an angle of 90°. The best dimensions from the parallel (III) and cross (#) grooves were compared experimentally. Specimens with grooving III were not damaged in the shear test. The research shows that the shape of the groove affects the distribution of stresses and strains. Combining the selected method with an adequately selected chemical reagent can significantly increase the strength of the connection.

scholarly journals Sea Surface Salinity Response to Tropical Cyclones Based on Satellite Observations

2021 ◽  
Vol 13 (3) ◽  
pp. 420
Author(s):  
Jingru Sun ◽  
Gabriel Vecchi ◽  
Brian Soden
Keyword(s):  
Tropical Cyclones ◽  
Sea Surface ◽  
Sea Surface Salinity ◽  
Surface Salinity ◽  
Translation Speed ◽  
Salinity Stratification ◽  
Left Hand ◽  
In Situ Data ◽  
Salinity Response ◽  
The Right

Multi-year records of satellite remote sensing of sea surface salinity (SSS) provide an opportunity to investigate the climatological characteristics of the SSS response to tropical cyclones (TCs). In this study, the influence of TC winds, rainfall and preexisting ocean stratification on SSS evolution is examined with multiple satellite-based and in-situ data. Global storm-centered composites indicate that TCs act to initially freshen the ocean surface (due to precipitation), and subsequently salinify the surface, largely through vertical ocean processes (mixing and upwelling), although regional hydrography can lead to local departure from this behavior. On average, on the day a TC passes, a strong SSS decrease is observed. The fresh anomaly is subsequently replaced by a net surface salinification, which persists for weeks. This salinification is larger on the right (left)-hand side of the storm motion in the Northern (Southern) Hemisphere, consistent with the location of stronger turbulent mixing. The influence of TC intensity and translation speed on the ocean response is also examined. Despite having greater precipitation, stronger TCs tend to produce longer-lasting, stronger and deeper salinification especially on the right-hand side of the storm motion. Faster moving TCs are found to have slightly weaker freshening with larger area coverage during the passage, but comparable salinification after the passage. The ocean haline response in four basins with different climatological salinity stratification reveals a significant impact of vertical stratification on the salinity response during and after the passage of TCs.

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