PIM Message Type Space Extension and Reserved Bits

On compressions of self-adjoint extensions of a symmetric linear relation with unequal deficiency indices

Ukrainian Mathematical Bulletin ◽

10.37069/1810-3200-2019-16-4-8 ◽

2019 ◽

Vol 16 (4) ◽

pp. 567-587

Author(s):

Vadim Mogilevskii

Keyword(s):

Hilbert Space ◽

Boundary Conditions ◽

Linear Relation ◽

Deficiency Indices ◽

Space Extension ◽

Limit Value ◽

Abstract Boundary ◽

Symmetric Linear Relation ◽

Symmetric Operators

Let $A$ be a symmetric linear relation in the Hilbert space $\gH$ with unequal deficiency indices $n_-A <n_+(A)$. A self-adjoint linear relation $\wt A\supset A$ in some Hilbert space $\wt\gH\supset \gH$ is called an (exit space) extension of $A$. We study the compressions $C (\wt A)=P_\gH\wt A\up\gH$ of extensions $\wt A=\wt A^*$. Our main result is a description of compressions $C (\wt A)$ by means of abstract boundary conditions, which are given in terms of a limit value of the Nevanlinna parameter $\tau(\l)$ from the Krein formula for generalized resolvents. We describe also all extensions $\wt A=\wt A^*$ of $A$ with the maximal symmetric compression $C (\wt A)$ and all extensions $\wt A=\wt A^*$ of the second kind in the sense of M.A. Naimark. These results generalize the recent results by A. Dijksma, H. Langer and the author obtained for symmetric operators $A$ with equal deficiency indices $n_+(A)=n_-(A)$.

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Managerial Effects and Psychological Reaction Difference in Travel Product Option Framing : Interaction Effects of Tour Advertisement Message Type and Tour Destination

Journal of Tourism Studies ◽

10.21581/jts.2019.05.31.2.65 ◽

2019 ◽

Vol 31 (2) ◽

pp. 65-88

Author(s):

Jin-Ok Shin ◽

Chang-Sup Shim ◽

Chul Jeong

Keyword(s):

Interaction Effects ◽

Message Type ◽

Psychological Reaction

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Training may enhance early childhood educators’ self-efficacy to lead physical activity in childcare

BMC Public Health ◽

10.1186/s12889-021-10400-z ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Brianne A. Bruijns ◽

Andrew M. Johnson ◽

Jennifer D. Irwin ◽

Shauna M. Burke ◽

Molly Driediger ◽

...

Keyword(s):

Physical Activity ◽

Early Childhood ◽

Self Efficacy ◽

Critical Role ◽

Early Childhood Educators ◽

Outdoor Play ◽

Future Research ◽

Intervention Component ◽

Space Extension ◽

The Impact

Abstract Background Early childhood educators (ECEs) play a critical role in promoting physical activity (PA) among preschoolers in childcare; thus, PA-related training for ECEs is essential. The Supporting PA in the Childcare Environment (SPACE) intervention incorporated: 1. shorter, more frequent outdoor play sessions; 2. provision of portable play equipment; and, PA training for ECEs. An extension of the SPACE intervention (the SPACE-Extension) incorporated only the shorter, more frequent outdoor play periods component of the original SPACE intervention. The purpose of this study was to explore the individual impact of these interventions on ECEs’ PA-related self-efficacy and knowledge. Methods ECEs from the SPACE (n = 83) and SPACE-Extension (n = 31) were administered surveys at all intervention time-points to assess: self-efficacy to engage preschoolers in PA (n = 6 items; scale 0 to 100); self-efficacy to implement the intervention (n = 6 items); and, knowledge of preschooler-specific PA and screen-viewing guidelines (n = 2 items). A linear mixed effects model was used to analyze the impact of each intervention on ECEs’ self-efficacy and knowledge and controlled for multiple comparison bias. Results The SPACE intervention significantly impacted ECEs’ self-efficacy to engage preschoolers in PA for 180 min/day (main effect), and when outdoor playtime was not an option (interaction effect). Further, the interaction model for ECEs’ knowledge of the total PA guideline for preschoolers approached significance when compared to the main effects model. Participants within the SPACE-Extension did not demonstrate any significant changes in self-efficacy or knowledge variables. Conclusions Findings from this study highlight the benefit of ECE training in PA with regard to fostering their PA-related self-efficacy and knowledge. Future research should explore the impact of PA training for ECEs uniquely in order to determine if this intervention component, alone, can produce meaningful changes in children’s PA behaviours at childcare.

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Improving KKM Theory on General Metric Type Spaces

Topological Algebra and its Applications ◽

10.1515/taa-2020-0101 ◽

2021 ◽

Vol 9 (1) ◽

pp. 1-12

Author(s):

Sehie Park

Keyword(s):

Convex Space ◽

Metric Spaces ◽

Space Theory ◽

Type Space ◽

Generalized Metric ◽

Abstract Convex Space ◽

Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

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Some estimates for the commutators of multilinear maximal function on Morrey-type space

Open Mathematics ◽

10.1515/math-2021-0031 ◽

2021 ◽

Vol 19 (1) ◽

pp. 515-530

Author(s):

Xiao Yu ◽

Pu Zhang ◽

Hongliang Li

Keyword(s):

Maximal Function ◽

Morrey Space ◽

Morrey Spaces ◽

Bounded Mean Oscillation ◽

Generalized Morrey Spaces ◽

Type Space ◽

Bmo Function ◽

Mean Oscillation ◽

Multilinear Maximal Function ◽

Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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Understanding the Adoption of Incentivized Word-of-Mouth in the Online Environment

Journal of theoretical and applied electronic commerce research ◽

10.3390/jtaer16040056 ◽

2021 ◽

Vol 16 (4) ◽

pp. 992-1007

Author(s):

Bogdan Anastasiei ◽

Nicoleta Dospinescu ◽

Octavian Dospinescu

Keyword(s):

Latent Variables ◽

Word Of Mouth ◽

Electronic Word Of Mouth ◽

Argument Quality ◽

Message Type ◽

Source Expertise ◽

The One ◽

Random Groups ◽

The Relationship ◽

Adoption Intention

Nowadays, word-of-mouth is a very important component of e-commerce activity because consumers are very sensitive to other people’s opinions. Depending on the companies’ politics, these opinions can be incentivized or non-incentivized. One of the major dilemmas consists in establishing which kind of word-of-mouth has more influence on customers’ perceptions. The purpose of this study is to assess the relationships between perceived argument quality (PAQ) and perceived source expertise (PSE), on the one hand, and electronic word-of-mouth adoption intention on the other hand, for an incentivized message compared to a non-incentivized message. We processed answers from two different random groups by using adapted PAQ and PSE inventories of questions. The constructs, latent variables and items were analyzed in IBM Amos software, and our findings confirm the hypotheses regarding the relationship between the attributes of the message (argument quality and source expertise) and message credibility. Additionally, we found a significant positive relationship between message credibility and electronic word-of-mouth adoption intention. Our research also explores the moderating role of the message type (incentivized vs. non-incentivized) in the relationships above, and we discovered that the message type significantly moderates the relationship between perceived argument quality and credibility, but the type of message does not moderate the relationship between message credibility and eWOM adoption intention.

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What You Say and Where You Say It Matter: Effects of Facebook Message Publicity and Support Type on Evaluation of Support Message Quality

Social Science Computer Review ◽

10.1177/08944393211007311 ◽

2021 ◽

pp. 089443932110073

Author(s):

Yining Malloch ◽

Bo Feng

Keyword(s):

Social Support ◽

Emotional Support ◽

Communication Channel ◽

Computer Mediated Communication ◽

Communication Model ◽

Mediated Communication ◽

Message Type ◽

Computer Mediated ◽

Tangible Support ◽

The Impact

Guided by the masspersonal communication model, this study examined the impact of the communication channel (masspersonal vs. interpersonal) and support message type on evaluation of social support message quality in Facebook settings. An online factorial experiment with 480 participants revealed that support messages sent through interpersonal channels (e.g., private messaging) were perceived as higher in quality than those sent through masspersonal channels (e.g., status update). Regardless of channels, participants considered tangible support messages as higher quality than informational and emotional support messages. Implications for computer-mediated communication and social support theories and practices were discussed.

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New variable martingale Hardy spaces

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/prm.2021.17 ◽

2021 ◽

pp. 1-29

Author(s):

Yong Jiao ◽

Dan Zeng ◽

Dejian Zhou

Keyword(s):

Brownian Motion ◽

Hardy Space ◽

Hardy Spaces ◽

Stochastic Integral ◽

Lebesgue Spaces ◽

Type Space ◽

Variable Lebesgue Spaces ◽

Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

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