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In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a general radial weight. We give necessary conditions when the symbol is of the form g1+g2‾, where g1 and g2 are analytic on the annulus z∈ℂ,1/2<|z|<1. [ABSTRACT FROM AUTHOR]

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form ψ+φ‾, where ψ and φ are analytic on the annulus z∈ℂ,1/2<|z|<1. [ABSTRACT FROM AUTHOR]

Dog therapy is implemented in various healthcare fields because of its unique ability to reduce perceived anxiety and hormonal stress, increase positive patient relationships with practitioners, and assist with demonstrating procedures. However, implementation of dog therapy in a clinical athletic training setting is not frequently discussed in relevant literature. This article outlines recommendations for the use and efficacy of therapy dogs in an athletic training facility, based on data from several studies across various healthcare fields. We provide information regarding best practice recommendations to incorporate therapy dogs into athletic training services, as well as the necessary administrative aspects and safeguards. Athletic trainers can use these recommendations and framework to explore the implementation of dog therapy into clinical practice. [ABSTRACT FROM AUTHOR]

For a prime number p and an integer m ≥ 2 , we prove that the symbol length of all elements of m -fold Massey products in H 2 (G , F p) , for pro- p groups G of elementary type, is bounded by (m 2 / 4) + m. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro- p Galois groups G = G F (p) of fields F which contain a root of unity of order p. More generally, we provide such a uniform bound for the symbol length of all pullbacks ρ ⁎ (ω ¯) of a given cohomology element ω ¯ ∈ H n (G ¯ , F p) , where G ¯ is a finite p -group, n ≥ 2 , and ρ : G → G ¯ is a pro- p group homomorphism. [ABSTRACT FROM AUTHOR]

Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay). [ABSTRACT FROM AUTHOR]

Knowledge of symbols, which can be influenced by school ethos, informs identity construction in primary school children. This study aimed to explore Gaelscoil (Irish-medium) and English-medium primary school children's familiarity with Irish and European symbols. Thirty 9–12-year-old children in Ireland participated in this study; 15 from two Irish-medium and 15 from an English-medium primary school. A draw-and-tell data collection design was used and qualitative data was analysed using the constant comparative method. Results indicate children from both school types shared a number of Irish symbols, namely Irish emblems, Irish mythology, sports and material aspects of culture. Irish-medium primary school children had two further Irish symbol categories, the past as a symbol and physical characteristics of Ireland. European symbols shared across children from both school types included signifiers of the European Union (EU), monetary symbols and European countries. The Irish-medium primary school children had two further categories, Europe through an Irish lens and European cuisine, while the English-medium children had one further category, sport. The results suggest that by middle childhood, children in both school types have knowledge about a number of symbols associated with both national and European identities. Implications for future research are discussed. [ABSTRACT FROM AUTHOR]

Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non‐symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non‐symbolic quantities. Preschool children (3‐year‐olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4‐year‐olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset‐knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence. Research Highlights: Children are more accurate in mapping between finger patterns and symbols (number words and Arabic digits) than in mapping finger patterns and quantities, indicating that fingers are processed holistically as symbolic codes.Children can map finger patterns to symbols above their corresponding cardinality level even in subset‐knowers.Finger patterns may play a role in the process by which children learn to map symbols to quantities.Fingers patterns' use in the classroom context may be an adequate instructional and diagnostic tool. [ABSTRACT FROM AUTHOR]

This paper aims to bring to light and edit nine Byzantine funerary inscriptions discovered in the town of El-'Irāq (western Governorate of Karak, southern Jordan). All these pieces belong to the period ranging from the 5th to the 6th centuries ce. Like the majority of the inscriptions from the area, these epigraphs consist of short epitaphs engraved on rectangular tombstones made of local limestone and adorned with Christian symbols. The main novelty of this work is the appearance of two anthroponyms that have not been attested to date in the local epigraphic record: Γομολλα and Ἠλίος. [ABSTRACT FROM AUTHOR]

We extend the stability and spectral invariance of convolution-dominated matrices to the case of quasi-Banach algebras p < 1 . As an application, we construct a spectrally invariant quasi-Banach algebra of pseudodifferential operators with non-smooth symbols that generalize Sjöstrand's results. [ABSTRACT FROM AUTHOR]

In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of weighted modulation spaces. Further, we investigate the periodic multilinear Fourier integral operator. Finally, we study continuity of bilinear pseudo-differential operators on modulation spaces for certain symbol classes, namely 퐒퐆 -class. [ABSTRACT FROM AUTHOR]

The present article, realized by using analytical method and library research, has discussed the different roles of colors in French and Persian terms. On the one hand, these terms have been studied in the field of linguistics, especially in terms of vocabulary and syntactic structure, and on the other hand, their hidden and obvious symbols have been analyzed by the intercultural point of view. In order to be aware of the commonality and differentiation of the colors’ role in the terms of both French and Persian languages and to create order and coherence in the text of the article, the authors have categorized them into six groups, according to their own initiative: conceptual metaphor, terms structured by noun and adjective, metonymy, political domain, abstract concepts and terms based on infinitive. It is noteworthy that by referring to specialized books and dictionaries, the body of research consisting of qualified terms for each group has been conceived and for each of them, equivalent has been chosen in the target language. In addition to examining each term, the authors of the article have provided an analytical study of the examples, citing the views of linguists. Also, by referring to the book Le Proverbe : Vers une définition linguistique (2012) by Sonia Gomez-Jordana Ferari, the syntactic structure of the examples of the research body has been examined.. [ABSTRACT FROM AUTHOR]

Similar visual forms can have different meanings and the messages that symbols carry are context specific. Some of the symbols are inevitably contested due to their historical uses. This article explores what is probably the most notorious of contested symbols: the swastika and its local variant in Latvia, the ugunskrusts (Cross of Fire). With the aim of analyzing vernacular narratives connected with contemporary uses of the ugunskrusts in Latvia, the article focuses on situations in which there is a conscious choice to use the ugunskrusts with the intention of reclaiming and rehabilitating the symbol for artistic and spiritual reasons, based on a belief in the symbol's benign nature and with the help of narratives of cultural heritage. Despite these claims, however, the cases are not just about symbols or cultural heritage, but are just as much about historical conflicts in the past and current political affairs. Thus, the article shows how different national experiences of crimes committed by totalitarian regimes of the twentieth century determine the interpretation of, and attitude toward, the use of symbols connected with these regimes. I examine how collective memory battles are mirrored in the use of this contested symbol. Despite the voices that deny the negative connotation of the symbol locally, the image of the swastika in the western world is inevitably tied to Nazism. Therefore, I look at how the attitude toward this symbol correlates with the interpretation of World War II in the collective memory of Latvia. The article is based on in-depth ethnographic interviews conducted since 2017. [ABSTRACT FROM AUTHOR]

Background Deaf and hard of hearing people persistently experience barriers accessing health services, largely due to ineffective communication systems, a lack of flexible booking arrangements, and a lack of Deaf awareness training for health professional staff. Methods Face to face focus groups were conducted with 66 Deaf and hard of hearing people in Deaf clubs across Wales, UK. Thematic analysis was undertaken. Results Responses identified from focus groups are reported as barriers faced using health services, improvements that would make a difference, impact of accessibility of health services, and a potential Sign language badge for healthcare staff. Conclusions Deaf people report that health professionals lack training on Deaf awareness and do not know how to communicate effectively with Deaf and hard of hearing people. Further research into Deaf awareness and training resources for health professionals are needed to establish what improves Deaf cultural competencies, and ultimately makes healthcare experiences more positive for people who are Deaf. [ABSTRACT FROM AUTHOR]

Locally repairable codes (LRCs) are linear codes with locality properties for code symbols, which have important applications in distributed storage systems. In this paper, we completely classify all the possible code parameters of optimal ternary LRCs achieving the Singleton-like bound proposed by Gopalan et al. Explicit constructions of optimal ternary LRCs are given for each group of possible code parameters. Moreover, it is also proved that optimal ternary LRCs with maximal minimum distance 6 are unique up to the equivalence of linear codes. [ABSTRACT FROM AUTHOR]

Wittgenstein was hostile towards set theory; see his remark in §22 of RFM II: ‘I believe and hope that a future generation will laugh at this hocus pocus’. At the same time, he says that what philosophy owes set theory is ‘tremendous’ and that this is something ‘deep’. I want to clarify these two statements and to reconcile them. The hocus‐pocus remark is mainly directed at the temptation to talk about an own world of sets, focussing on extensions and thereby forgetting the actual mathematical manoeuvres leading to them. Wittgenstein does not shy away from using set‐theoretical symbols and expressions, but he regularly deprives them of their genuine set‐theoretical character. When speaking of the ‘depth’ we encounter with regard to set theory, what he means is the depth explained in PI §111: It arises ‘through a misinterpretation of our forms of language’, and this is particularly so in set theory. [ABSTRACT FROM AUTHOR]

Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indices and variables of these polynomials is also determined. Particular limits on the parameters entering the polynomials allow to define several Griffiths polynomials of other types. One special limit connects them to the original Griffiths polynomials (of Krawtchouk type). Finally, a connection with the 9j symbols is made. [ABSTRACT FROM AUTHOR]

The article focuses on the approach in developing a branding and marketing strategy to bolster the effectiveness of the 2019-2024 U.S. Health Resources and Services Administration (HRSA) Geriatric Workforce Enhancement Program (GWEP). Topics discussed include the names, logos and taglines proposed to established the program's identity, Brand identity, position and strategy, and the program's marketing strategy for its partners.

This paper focuses on the global protests that condemn the war on Gaza following the Al-Aqsa Flood on October 7, 2023. These protests were unprecedented in their broad scope and innovative forms. The paper argues that this protest movement is fundamentally memorydriven, as it represents an extension of the 2019-2020 demonstrations against racism and colonialism, utilizing and reusing mnemonic media and symbols. In contrast, this global surge of memory is facing official suppression of protest dynamics, employing mnemonic strategies used by authorities within memory policies. This is prominently illustrated through the German model, characterized by practices of silence, forgetting, and accompanying repressive measures falling under a culture of cancellation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a precise Wigner–Weyl calculus for the models defined on the honeycomb lattice. We construct two symbols of operators: the B symbol, which is similar to the one introduced by F. Buot, and the W (or, Weyl) symbol. The latter possesses the set of useful properties. These identities allow us to use it in physical applications. In particular, we derive topological expression for the Hall conductivity through the Wigner-transformed Green function. This expression may be used for the description of the systems with artificial honeycomb lattice, when magnetic flux through the lattice cell is of the order of elementary quantum of magnetic flux. It is worth mentioning that, in the present paper, we do not consider the effect of interactions. [ABSTRACT FROM AUTHOR]

Operator precedence grammars (OPG) are context-free grammars (CFG) that are characterized by the absence of two adjacent non-terminal symbols in the body of each production (right-hand side). Operator precedence languages (OPL) are deterministic and context-free. Three possible precedence relations between pairs of terminal symbols are established for these languages. Many CFGs are not OPGs because the operator precedence cannot be applied to them as they do not comply with the basic rule. To solve this problem, we have conducted a thorough redefinition of the Left and Right sets of terminals that are the basis for calculating the precedence relations, and we have defined a new Leftmost set. The algorithms for calculating them are also described in detail. Our work's most significant contribution is that we establish precedence relationships between terminals by overcoming the basic rule of not having two consecutive non-terminals using an algorithm that allows building the operator precedence table for a CFG regardless of whether it is an OPG. The paper shows the complexities of the proposed algorithms and possible exceptions to the proposed rules. We present examples by using an OPG and two non-OPGs to illustrate the operation of the proposed algorithms. With these, the operator precedence table is built, and bottom-up parsing is carried out correctly. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the incomplete beta matrix function $ \mathbb {B}^{z}(M,K),\;z\in \mathbb {C} $ B z (M , K) , z ∈ C , for parameter matrices M and K in $ \mathbb {C}^{{m}\times {m}} $ C m × m using the neutrix limit and evaluation methods on their the partial derivatives. Also, we define a new extension of the Pochhammer matrix symbol in terms of the incomplete beta matrix functions. Furthermore, we then apply this extended matrix symbol for the incomplete first Appell hypergeometric matrix functions and obtain some of their properties. [ABSTRACT FROM AUTHOR]

Let \Omega be a bounded pseudoconvex domain in \mathbb {C}^n with Lipschitz boundary and \phi be a continuous function on \overline {\Omega }. We show that the Toeplitz operator T_{\phi } with symbol \phi is compact on the weighted Bergman space if and only if \phi vanishes on the boundary of \Omega. We also show that compactness of the Toeplitz operator T^{p,q}_{\phi } on \overline {\partial }-closed (p,q)-forms for 0\leq p\leq n and q\geq 1 is equivalent to \phi =0 on \Omega. [ABSTRACT FROM AUTHOR]

We introduce a class of uniformly 2‐nondegenerate CR hypersurfaces in CN$\mathbb {C}^N$, for N>3$N>3$, having a rank 1 Levi kernel. The class is first of all remarkable by the fact that for every N>3$N>3$ it forms an explicit infinite‐dimensional family of everywhere 2‐nondegenerate hypersurfaces. To the best of our knowledge, this is the first such construction. Besides, the class contains infinite‐dimensional families of nonequivalent structures having a given constant nilpotent CR symbol for every such symbol. Using methods that are able to handle all cases with N>5$N>5$ simultaneously, we solve the equivalence problem for the considered structures whose symbol is represented by a single Jordan block, classify their algebras of infinitesimal symmetries, and classify the locally homogeneous structures among them. We show that the remaining considered structures, which have symbols represented by a direct sum of Jordan blocks, can be constructed from the single block structures through simple linking and extension processes. [ABSTRACT FROM AUTHOR]

This work explores the polynomial fuzzy stabilization for positive systems. The traditional quadratic Lyapunov function and basic stability analysis may not be favourable for stability investigation due to the absence of the positivity property and membership functions. Therefore, a fuzzy co-positive polynomial Lyapunov–Krasovskii (FCPL) function which considers the positivity is proposed firstly through an imperfect premise matching (IPM) approach. Secondly, the symbol transfer technique which takes into account fuzzy membership knowledge relaxes the stability conditions. The number of symbols is reduced by two constraints: (1) the last and next moments of the membership functions of the FCPL function; (2) membership functions of the fuzzy model and the controller. Finally, the polynomial fuzzy controller with symbols is obtained. Two examples are implemented to verify the proposed methods. • Favourable fuzzy co-positive polynomial Lyapunov–Krasovskii functional candidate: we propose a FCPL candidate to favour the relaxed stability. The original membership function elements in stability conditions are retained and the information of membership function is considered to relax the results. • Solvable polynomial fuzzy controller whose feedback gains with nonlinear polynomial terms: the controller is designed whose feedback gains with polynomial terms of system states and membership characteristics. Adequate nonlinear information is considered and it makes the controller design process robust. • Favourable symbol transfer technique design: the symbol transfer technique is employed for reducing the stability conservativeness. Membership grades are carried by symbols in the control. The next moment of membership functions is replaced by the symbol to solve the non-convex problem. [ABSTRACT FROM AUTHOR]

The present study focuses on the asymptotic behavior of fractional stochastic FitzHugh-Nagumo lattice systems with multiplicative noise. First, we investigate the well-posedness of solutions for these stochastic systems and subsequently establish the existence and uniqueness of tempered random uniform attractors. [ABSTRACT FROM AUTHOR]

In 2002 Mauduit and Sárközy started to study finite sequences of k symbols... is a finite set of k symbols. Bérczi estimated the pseudorandom measures for a truly random sequence EN of k symbol. In this paper, we shall study the minimal values of correlation measures for the sequences of k symbols, developing the methods similar to those introduced by Alon, Anantharam, Gyarmati, and Schmidt, among others. [ABSTRACT FROM AUTHOR]

We first describe commuting Toeplitz operators with harmonic symbols on weighted harmonic Bergman spaces. Then, a sufficient condition for hyponormality on weighted Bergman spaces of the punctured unit disk, when the analytic part of the symbol is a monomial, is shown. [ABSTRACT FROM AUTHOR]

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This study explores how receiving identical information from different sources affects learning and cognitive load, focusing on two types of redundancy: modal redundancy, where redundant information comes from two visual sources (images and written text), and codal redundancy, where redundant information comes from two sources of different modalities which utilize the same symbol system (spoken and written text). Using a 2 × 2 between-subjects design involving modal (yes/no) and codal (yes/no) redundancy, 158 participants completed twenty learning tasks, consisting of ten construction and ten recall tasks. Additionally, they rated their cognitive load by indicating their perceived task difficulty and mental load. Overall, results indicate positive main effects of modal redundancy and negative effects of codal redundancy on learning and cognitive load. Furthermore, significant interaction effects suggest that modal redundancy may counterbalance the negative effects of codal redundancy, implying a compensatory mechanism in cognitive processing for construction tasks. These results highlight the importance of considering both modal and codal redundancy and their interaction in instructional design. [ABSTRACT FROM AUTHOR]

In this article, we present a coding method called expanding-window zigzag decodable fountain code with unequal error protection property (EWF-ZD UEP code) to achieve scalable multimedia transmission. The key idea of the EWF-ZD UEP code is to utilize bit-shift operation and expanding-window strategy to improve the decoding performance of the high-priority data without performance deterioration of the low-priority data. To provide more protection for the high-priority data, we precode the different importance level using LDPC codes of varying code rates. The generalized variable nodes of different importance levels are further grouped into several windows. Each window is associated with a selection probability and a bit-shift distribution. The combination of bit-shift and symbol exclusive-or operations is used to generate an encoded symbol. Theoretical and simulation results on input symbols of two importance levels reveal that the proposed EWF-ZD UEP code exhibits UEP property. With a small bit shift, the decoding delay for recovering high-priority input symbols is decreased without degrading the decoding performance of the low-priority input symbols. Moreover, according to the simulation results on scalable video coding, our scheme provides better basic video quality at a lower proportion of received symbols compared to three state-of-art UEP fountain codes. [ABSTRACT FROM AUTHOR]

In this paper, using standard pairs, we present a method to construct symbols satisfying the sum rules of order p for any given p. It is shown that using matrix polynomial theory symbols, symmetric or non-symmetric, satisfying the sum rules of order p can be constructed efficiently. The construction is illustrated using various examples. [ABSTRACT FROM AUTHOR]

To examine the level of number line estimation (NLE) in Chinese children with respect to representations of both numerical (Arabic numerals) and nonnumerical symbols (dots), a total of 192 Chinese preschoolers aged between 4 and 5 years participated in four different NLE tasks. These tasks were paired to evaluate the accuracy and patterns of children's estimations in both numerical and non-numerical symbol contexts. Our findings indicate that, for Chinese preschoolers, relatively precise numerical symbol representations begin to emerge as early as 4 years of age. The accuracy of number line estimates for both 4- and 5-year-old children gradually increases in tasks involving both numerical and non-numerical symbols. Additionally, the development and patterns observed in the number line estimates of 4- and 5-year-old Chinese preschoolers are similar in both numerical symbol and non-numerical symbol tasks. These results indicate that the initiation of relatively precise numerical symbol representation and the turning point in the developmental trajectory, where the relatively precise representation for numerical symbols surpasses that of non-numerical ones, occur earlier in Chinese children than in their Western counterparts. [ABSTRACT FROM AUTHOR]

The aim of this article is to characterize the use of algebraic language by grade 9 students, with regard to strategies, meanings and difficulties. For that, we discuss the productions resulting from solving an algebraic task by six students. The results show the use of symbolic strategies and strategies based on informal reflection and the attribution of appropriate meanings to symbols, but a limited willingness to search and revise the meanings of algebraic expressions. Using parentheses, multiplying monomials and expressing relationships present in the context of the problem stand out as the students' main difficulties. [ABSTRACT FROM AUTHOR]

This paper presents a conceptual analysis and critical review of the notion of 'affordance' and its uptake, transformation and application in the work of Gunther Kress. It traces its origins and explores how Kress, co-founder of social semiotics, (re)conceptualised affordance and incorporated it in his social semiotic theory of sign making, defining affordance in terms of the "potentials and limitations of specific modes". The paper discusses how his take on the term was received, and develops a radical critique questioning the analytical merits of affordance. It concludes with a call for a return to Kress's original question of exactly what it is about a form (signifier) that makes it suitable, in the eyes of the sign maker, for what they want to express (signified), and to consider materiality and social convention alongside the sign maker's lifeworld, audience, situation, and conditions of sign making. [ABSTRACT FROM AUTHOR]

Let k be a field, let n ≥ 2 be a nonsquarefree integer not divisible by the characteristic of k. Assume that all roots of unity of degree n are contained in k. In the first part of the paper we consider pairs of symbol algebras over k with common slots D 1 ≃ (e , x) n ≃ (r , u) n , D 2 ≃ (e , y) n ≃ (r , v) n , exp D 1 = exp D 2 = n , and show that in general (e , x , y) n ≠ (r , u , v) n. As a consequence we prove that in general it is impossible to connect the pair { (e , x) n ; (e , y) n } and the pair { (r , u) n ; (r , v) n } by a chain of pairs of symbol algebras with a common slot and isomorphic to (D 1 ; D 2) in such a way that any two neighboring pairs in the chain are obtained from one another by a "natural" transformation. In the second part of the paper we prove that in contrast to the case n = 2 for any n divisible by 4 there exist symbol algebras D 1 , D 2 with deg ⁡ D 1 = deg ⁡ D 2 = n and exp D 1 = exp D 2 = n without common slot such that i D 1 + j D 2 is a symbol algebra of degree n for any i , j ∈ Z. [ABSTRACT FROM AUTHOR]

Background: Clostridioides difficile (C. diff) infection causes significant morbidity for hospitalized patients. A large medical intensive care unit had an increase in C. diff infection rates. Objectives: The aim of this project was to reduce the C. diff polymerase chain reaction (PCR) test positivity rate and the rate of C. diff PCR tests ordered. Rates were compared between preintervention (July 2017 to December 2019) and postintervention (January 2021 to December 2022) timeframes. Methods: Unit leadership led a robust quality improvement project, including use of quality improvement tools such as A3, Gemba walks, and plan-do-study-act cycles. Interventions were tailored to the barriers identified, including standardization of in-room supply carts; use of single-packaged oral care kits; new enteric precautions signage; education to staff, providers, and visitors; scripting for patients and visitors; and use of a C. diff testing algorithm. Statistical process control charts were used to assess for improvements. Results: The average rate of C. diff PCR test positivity decreased from 34.9 PCR positive tests per 10 000 patient days to 12.3 in the postintervention period, a 66% reduction. The average rate of PCR tests ordered was 28 per 1000 patient days in the preintervention period; this decreased 44% to 15.7 in the postintervention period. Discussion: We found clinically significant improvements in the rate of C. diff infection and PCR tests ordered as a result of implementing tailored interventions in a large medical intensive care unit. Other units should consider using robust quality improvement methods and tools to conduct similar initiatives to reduce patient harm and improve care and outcomes. [ABSTRACT FROM AUTHOR]

The article focuses on the legal challenges posed by the use of emojis in the context of securities law. It examines how emojis, originally intended for emotional emphasis in digital communication, are now being scrutinized for their potential to convey misleading information that could constitute securities fraud. It highlights the complexities of interpreting these symbols in legal contexts traditionally governed by textual communication.

In this paper, we study the radial symmetry and monotonicity of nonnegative solutions to nonlinear equations involving the logarithmic Schrödinger operator (1 + Δ)log corresponding to the logarithmic symbol log(1 + |ξ|²) which is a singular integral operator given by (I+ Δ)log u(x) = cNP.V. u(x)-u(y) /∫ℝN u(x)-u(y)/|x-y|n k(|x-y|dy, where cN = π - N/2, k(r) =21-N/2 r N/2 K N/2 (r)and Kv is the modified Bessel function of the second kind with index v. The proof hinges on a direct method of moving planes for the logarithmic Schrödinger operator. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the various properties of the Toeplitz operators acting on the Dirichlet spaces. First, we consider the matrix representation of Toeplitz operators with harmonic and monomial symbols. Second, we establish the expansivity and contractivity of the Toeplitz operators T φ with monomial symbols φ . Third, we give a necessary and sufficient conditions for the normality and hyponormality of the Toeplitz operators T φ with such symbols on the Dirichlet spaces. [ABSTRACT FROM AUTHOR]

The article deals with decommunization in Ukraine from 2014 to 2020, examining the motives and actions of the main actors of this policy and societal responses and recounting its most significant developments and outcomes. The decommunization in Ukraine in 2014–2020 was a successful, though belated, effort initiated at a time when Communist symbols had lost their original ideological sense as well as social, cultural, and political significance. The promoters of decommunization reanimated it and managed to contextualize it under actual threat from Russia to justify their policy, which they used to promote a nationalist narrative of memory. [ABSTRACT FROM AUTHOR]

A low power clock generator with self-calibration for UHF RFID tags compatible with the EPCglobal Class-1 Gen-2 (EPC Gen2) standard is presented. By utilizing the timing information of the reader to tag (R ⇒ T) link symbols, the frequency accuracy of the calibrated clock can meet the stringent requirement of the standard. Designed in a 0.18 μ m standard CMOS technology, simulation results show that the frequency error of the clock source is only from − 2.07 to + 1.4% of the target frequency of 2.56 MHz. The power consumption is only 720 nW. [ABSTRACT FROM AUTHOR]

Shared symbolism and ideology at dark heritage sites construct the narrative of a collective national destiny. Visitors' experiences with such sites necessarily involve decoding signs and symbols. The commonality in interpretative practices is rooted in "collateral knowledge" and forms the identity of place. Yet, cultural materiality, collective identities, and semiotics have been overlooked by dark tourism academia. In broader tourism studies, semiotic attempts lack methodological homogeneity and congruence and efforts to transpose Charles Peirce's semiotic theory into practical experiential methodologies are scarce. This study introduces a practical, systematic, and replicable semiotic methodology for reading the identity of dark heritage sites. This methodology revolves around three interconnected Peircean concepts: the sign, the collateral knowledge, and the sign's relationship to its dynamical object. It is proposed that reading the indexical, iconical, and symbolical functions of signs through the filter of collateral knowledge can ensure a systematic meaning-making process and reveal subtle influences. [ABSTRACT FROM AUTHOR]

Tai chi culture has a widespread influence on the world. Tai-chi diagrams, as the symbol of Tai chi culture, express the balance between Yin and Yang through the centrosymmetric pattern, but the balance connotation of Tai-chi diagrams needs a comprehensive understanding in more aspects, e.g., the balance in mechanics. In this work, we propose a mechanics theory to investigate the intrinsic mechanism of Yin–Yang equilibrium in ancient and modern Tai-chi diagrams. The model based on the minimum potential energy theory can effectively describe the interface curves of the Yin–Yang equilibrium by modifying boundary conditions, which is proven by experiments. The results show that the balance of Tai-chi diagrams is not only manifested in its symmetrical appearance but also reflected in its intrinsic balance configuration in mechanics. The model presented herein provides a new perspective to understand the balance of Tai-chi diagrams, which may provide useful insights into the applications of Tai-chi diagrams. [ABSTRACT FROM AUTHOR]

Background: Early language delay is exacerbated by social disadvantage. Factors such as parents' low levels of literacy, confidence and self‐perception can affect the capacity to act on advice received, critical to empowerment. Methods used to achieve successful health outcomes in socially disadvantaged clinical populations may need enhancing. Aims: To compare the impact of standard parent‐based intervention (PBI) to enhanced PBI for young children with speech, language and communication needs (SCLN) and their families living in more socially disadvantaged populations. Methods and Procedures: A multicentre clustered blind randomised controlled trial was used to compare the effect of parent‐based group interventions to improve early language development with children (mean age 27.5 months) from more socially disadvantaged populations with an expressive vocabulary of 40 or less single words. Intervention sessions were delivered by a speech and language therapist, over a 20‐week period. Participants received one of two interventions: (1) Standard Care – indirect group PBI – (PBI) (2) Enhanced Care: indirect group enhanced PBI – (EPBI). Both standardised and non‐standardised measures were used as outcomes. Parent engagement in the intervention was captured through analysis of attendance and the Parent Activation Measure – Speech & Language Therapy (PAM‐SLT) (Insignia Health, 2014). The PAM measures a person's knowledge, skills and confidence to manage their own health and well‐being (NHS England, 2018). In this study, activation referred to parents' knowledge, skills and confidence to manage their child's language development. Outcomes and Results: One hundred fifty‐five participants were randomised at baseline. Children in both groups made significant improvements in the outcome on MacArthur‐Bates Communicative Development Inventories Sentence Length, from pre‐intervention to post‐intervention and 6 months post‐intervention (p < 0.05). Changes in vocabulary and expressive language skills were more equivocal, showing wide variation in confidence intervals for both groups. Where parents attended at least one intervention session almost all effect sizes were in favour of the EPBI intervention. Parents' activation levels significantly increased for both groups (EPBI p < 0.001, PBI p = 0.003), with a moderate effect size in favour of EPBI (Hedges' G 0.37, confidence interval –0.02 to 0.76), although wide variation was found. Conclusions and Implications: This trial provides some evidence of facilitating the language development of children with SLCN from more socially disadvantaged areas through supporting caregivers. However, we found variation in outcomes; some children made excellent progress, whilst others did not. Further exploration of parent engagement and its relationship to child language outcomes will be valuable to understanding more about mechanisms of change in interventions that involve parents. WHAT THIS PAPER ADDS: What is already known on the subject: Speech, language and communication needs (SLCN) have a knock‐on effect on emotional well‐being, school readiness, literacy and school attainment, putting children at increased risk of long‐term consequences such as poor literacy, mental health problems and unemployment. In disadvantaged areas, the prevalence of language difficulties is higher than elsewhere. Factors such as parents' low levels of literacy, confidence and self‐perception can affect the capacity to act on advice received, critical to empowerment. What this paper adds to existing knowledge: Children with SLCN from more socially disadvantaged areas can make improvements in their language development through parent intervention, although wide individual variation was found. There was some evidence that children achieve better outcomes with EPBI, which employed an interagency collaborative approach. Parent's engagement (activation levels) increased significantly over time with intervention, with the increase twice as big for EPBI. What are the potential or actual clinical implications of this work?: This trial provides some evidence that it is possible to facilitate the language development of children from more socially disadvantaged areas through supporting their caregivers. Further research would be useful to determine whether increases in parent engagement are related to adherence to intervention and change in child outcomes. [ABSTRACT FROM AUTHOR]

Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset O in terms of datasets I) is a logical specification involving two distinguished sets of relational symbols. One set of relations is for the "source data" I, and the other is for the "interface data" O. Such a specification is a valid definition of O in terms of I, if any two models of the specification agreeing on I agree on O. In contrast, an explicit definition is a transformation (or "query" below) that produces O from I. Variants of Beth's theorem [Bet53] state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be converted to explicit definitions in the nested relational calculus (NRC). We first provide a model-theoretic argument for this result, which makes some additional connections that may be of independent interest, between NRC queries, interpretations, a standard mechanism for defining structure-to-structure translation in logic, and between interpretations and implicit to definability "up to unique isomorphism". The latter connection uses a variation of a result of Gaifman concerning "relatively categorical" theories. We also provide a proof-theoretic result that provides an effective argument: from a proof witnessing implicit definability, we can efficiently produce an NRC definition. This will involve introducing the appropriate proof system for reasoning with nested sets, along with some auxiliary Beth-type results for this system. As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views. [ABSTRACT FROM AUTHOR]

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges" and captures various description logics with counting, but without constant symbols. We show that the satisfiability problem for this logic is EXP-complete. While the lower bound already holds for the standard two-variable guarded fragment logic, the upper bound is established by a novel, yet simple deterministic graph-based algorithm. [ABSTRACT FROM AUTHOR]

Let u$u$ be a subharmonic function on the open unit disc D$\mathbb {D}$, centered at the origin of the complex plane, and let φ:D→D$\varphi:\mathbb {D}\rightarrow \mathbb {D}$ be a holomorphic function such that φ(0)=0$\varphi (0)=0$. A classical result, known as Littlewood subordination principle, states Iu∘φ(r)⩽Iu(r)$\mathrm{I}_{u\circ \varphi }(r)\leqslant \mathrm{I}_u(r)$, where Iu∘φ(r)$\mathrm{I}_{u\circ \varphi }(r)$ and Iu(r)$\mathrm{I}_u(r)$ are integral means over the circle of radius 0⩽r<1$0\leqslant r<1$ centered at the origin, of the functions u∘φ$u\circ \varphi$ and u$u$, respectively. In this note, we obtain an unexpected improvement of Littlewood subordination principle in the case when the function φ$\varphi$ is univalent, by proving that Iu∘φ(r)⩽Iu(r)−κ∫0rIu(r)−Iu(t)dt,$$\begin{equation*} \hspace*{40pt}\mathrm{I}_{u\circ \varphi }(r)\leqslant \mathrm{I}_u(r)-\kappa \int _0^{r}{\left(\mathrm{I}_u(r)-\mathrm{I}_u(t)\right)}\mathrm{d}t, \end{equation*}$$where κ=(1−|φ′(0)|)/2$\kappa =(1-|\varphi ^{\prime }(0)|)/2$. We also list some applications of this result including an improved variant of Rogosinski theorem with univalent symbol. [ABSTRACT FROM AUTHOR]

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The 26 letters of the English alphabet are undoubtedly, within the scope of the most recognizable forms globally even some of the non-English speaking communities. The English alphabet has been subjected to varied elements from speaking to writing. The words used in most local parlances are formulated and written by means of the letters of the English alphabet. However, this English alphabet from the design perspective, as this paper intends to unravel, there is so much to be extracted from the letters of the English alphabet, which has not been addressed. Digital applications were used to harness the abstracted design concepts that emanated from this study. Finally, the recurrent issues of concept generation will be given a significant boost as intrinsic findings from this study show that the methodical exploitation of the letters of the English alphabet can be used to generate infinite thematic genre of abstracted art or flourishes worthy of a variety of elucidations. [ABSTRACT FROM AUTHOR]