Ordinal Number Research Articles

<i>Pridёt Dvoje iz Larca:</i> an Experimental Study of Variable Agreement with Quantified Subjects

This paper presents an experimental study of predicative agreement in person and number with two types of quantified subjects containing a personal pronoun. Using two syntactic experiments with a rating task (the Likert scale), we compared the properties of the elective (dvoje iz nas ‘two of us’) and nominative (my dvoje ‘us two’) constructions regarding the preferred form of the verb in two configurations: with the preverbal and the postverbal position of the subject. Ordinal numbers (from dvoje ‘two of’ to semero ‘seven of’) and the quantifier word vse ‘all’ were compared as well. The results show that word order has a significant impact on the acceptability of different agreement strategies. For the elective construction, with the SV order, agreement by person and number of the quantifier is available, and the default agreement is rated as significantly less acceptable, while with the VS order, there are no significant differences between the ratings of the two agreement options. For a nominative construction with SV, only agreement by person and number of the pronoun is possible, while with VS, all strategies are rated as acceptable.

Ordinal processing differences between children with persistent dyscalculia and typically performing children.

Ordinal number processing skills are important for adults and children. Recent work demonstrates that children have difficulty with judging the ordinality of sequences that are in-order but do not match the typical count-list (i.e., in-order non-adjacent sequences, such as 2-4-6). Limited evidence in the literature suggests that dyscalculic children show a similar pattern of behavior. In the present study, we sought to explicitly test the hypothesis that children with developmental dyscalculia struggle primarily with extending notions of ordinality to sequences outside of the count-list. We test this hypothesis using a sample of children with persistent developmental dyscalculia, and a comparison group of typically performing children. Both groups completed an ordinality judgment task, in which triplet sequences were judged as being in-order (e.g., 3-4-5; 2-4-6) or in mixed-order (e.g., 3-5-4; 2-6-4). In line with our prediction, results demonstrate that children with persistent developmental dyscalculia make more errors, compared to typically performing children, but only on the in-order non-adjacent trials (e.g., 2-4-6). Broadly, this finding suggests that ordinality processing abilities are impaired in children with developmental dyscalculia, and that this characteristic appears primarily in extending notions of ordinality beyond adjacent sequences. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Association between days spent at home and functional status and health among persons living with dementia.

Many persons living with dementias (PLWD) prefer to remain at home as long as possible, and days spent at home (DAH)-defined as the time an individual spends outside of healthcare facilities-has emerged as a person-centred outcome measure in this population. We examined the association between DAH and functional status and health among PLWD. Utilizing a nationally representative cohort of individuals age 65 and older in the United States with dementia from the 2010-2018 Health and Retirement Study (HRS), we assessed the relationship between an ordinal categorical DAH variable and number of activities of daily living (ADLs) (range 0-10; 10 being independent), mobility (0-5; 5 being mobile), and self-rated health (SRH) (0-4; 4 being excellent), controlling for patient characteristics. DAH was defined as the number of self-reported days spent outside a hospital or nursing home in the time between survey waves, typically 730days. We identified 3002 participants (4192 observations, average 1.4 observations per participant). The mean DAH was 704.4days (SD 10.8days) and 64.9% spent all days at home (i.e. 730days). A 2-week decrease in DAH was associated with a lower ADL score by 0.32 points (95% confidence internal [CI]: 0.24-0.40, P-for-trend<0.001), a lower mobility score by 0.18 points (95% CI: 0.13-0.22, P-for-trend<0.001), and a lower SRH by 0.05 points (95% CI: 0.02-0.08, P-for-trend<0.001). We demonstrate that DAH is positively associated with important patient-reported outcomes among the dementia population, strengthening the argument for considering DAH as a meaningful outcome measure for PLWD.

Algorithm for determining tensions in a stay cable with a manufacturing defect

Purpose. Establishing the influence of presence of a longitudinal area, on which there is detachment of layers over a limited length of a composite orthotropic rope, on its stress-strain state. Research methodology. Development of a method for calculating the influence of presence of a longitudinal area, on which there is detachment of layers over a limited length of a composite orthotropic rope, on its stress-strain state by constructing and analytically solving a model of a stress-strain state of a composite tractive element, considering the conditions of interaction of a rope with a permanent structure using the methods of mechanics of layered composite materials with soft and hard layers. Findings. Analytical dependencies are obtained in a closed form, which allow determining a stress-strain state of a composite multi-layer rope with partial local detachment of a separate layer, considering the breakage of one reinforcing element. An algorithm for determining a stress-strain state of a composite multi-layer rope with partial detachment of a separate layer considering the breakage of one reinforcing element is established. Characteristics of a dependency of unevenness coefficients of load distribution in reinforcing elements, displacements and shear angle tangents on the ordinal number of a damaged cable in a presence of partial local detachment of a separate layer of a composite stay rope is established. Scientific novelty. Influence character of presence of a longitudinal area, on which there is detachment of layers over a limited length of a composite orthotropic rope, on its stress-strain state is established. A method of calculating the influence of presence of an area of detached layers in a rope on its stress-strain state is developed. Practical significance. Local detachment of layers is possible in a process of producing a composite multi-layer stay rope. The developed algorithm makes it possible to determine a stress-strain state of composite stay rope with local layer detachment. The known values of detachment allow implementing justified engineering solutions regarding the conditions of safe, temporary use of a composite rope in cable-stayed structure.

Asymptotic Series of the Associated Legendre Function with Respect to Seismic Surface Waves

The asymptotic series of the associated Legendre function is investigated for the angular degrees n=2-13 in the context of the amplitude and wavelength of seismic surface waves. The approximate formula for the associated Legendre function is used to determine the wavelength and phase velocity of free oscillations of the Earth and long-period surface waves. The approximate formula is derived from the first term of the asymptotic series and its error increases with decreasing n. In the present study, the effect of higher terms on the approximate formula is studied with respect to the amplitudes of the 1st term (a1), the 2nd term (a2), and the 3rd term (a3). For the colatitude angle θ of π/3≦θ≦2π/3, the amplitude ratios a2/a1 are approximately 3.5％-1.0％ for n=2-11 and are less than 1.0％ for n ≧ 12, while the amplitude ratios a3/a1 are approximately 0.4％ - 0.03％ for n=2-13. The effect of amplitudes of higher terms on the 1st term increases as the colatitude angle approaches the pole or the antipode. The wavelengths of the 1st term (λ1) , the 2nd term (λ2) , and the 3rd term (λ3) are in the sequence λ1 &gt;λ2 &gt;λ3. The wavelength ratiosλ2 /λ1 and λ3 &gt;λ1 for n=2-13 are 0.71%-0.93% and 0.55%-0.87%, respectively. The relationship of the wavelengths between the different angular degrees may be expressed as λ n k =λn-1k+1, where n and k are respectively the angular degree and the ordinal number of the asymptotic series.

A first semantics for &lt;i&gt;at first&lt;/i&gt; and &lt;i&gt;at last&lt;/i&gt;

This paper offers the first ever semantic analysis of a puzzling restriction on the distribution of ordinal numbers in English: while the temporal adverbials at first and at last are felicitous, putting any other ordinal in this environment is degraded (#at second, #at third). My analysis builds on the notion that assertions are relativized to a salient time interval, known in the literature as reference time or topic time. On my semantics, at first and at last further relativize an assertion to a salient subinterval of the topic time that shares an infimum (first point) or supremum (last point) with it. On the standard assumption that time-intervals are dense, the infelicity of #at second, #at third, etc. follows from this semantics. Since at first and at last invoke the first and last points of a time-interval on my analysis, #at second will attempt to invoke the second (i.e. second earliest) point of a time-interval. Invoking the first and last points of a dense interval is coherent, but invoking the second point (i.e. the point closer to the first point than any other) is not. My analysis makes interesting predictions about the interaction of at first/at last with present tense and frame adverbials, and it opens up several avenues for future research.

Interface state-based bound states in continuum and below-continuum-resonance modes with high-Q factors in the rotational periodic system

Abstract In thispaper, we have introduced a new approach to calculate the orbital angular momentum (OAM) of bound states in the continuum (BICs) and below-continuum-resonance (BCR) modes in the rotational periodic system nested inside and outside by transforming the Bloch wave number from the translational periodic system. We extensively classify and study these BICs and BCR modes, which exhibit high-quality (high-Q) factors, in different regions relative to the interface of system. These BICs and BCR modes with high-Q factor have been studied in detail based on the distinctive structural parameters and scattering theory. Outcomes of this research break the periodic limitation of interface state-based BICs, and realize more and higher symmetry interface state-based BICs and BCR modes. Moreover, we can control the region that light captured by adjusting the frequency, and show that Q factor of BICs is more closely related to the ordinal number of rings and rotational symmetry number of the system.

The far-field diffraction of a plane wave on a system of randomly and in average periodically located point scatterers: the Debye-Waller factor

The description of the superposition field of a system of point sources with a random and, on average, periodic structure is considered. The description is given in the far field and the point sources are considered as centers of secondary sphere waves generated by an external plane wave. In contrast to the traditional approach, where description of the diffraction pattern is given on the base of wave field averaging, here the intensity is averaged.In the framework of the suggested approach the analytic formula of dependence of the average intensity on the direction observation is found. The influence of disorder on the values of intensity of main maximums of a periodic structure is investigated. It is shown that this influence depends on the ordinal numbers of the maximum and in the case of central main maximum this influence vanishes. The question of applicability of the Debye-Weller factor for describing of the statistic of diffracted field is discussed.

Pressure-volume-temperature analysis of Caspian oil to improve the analytical delumping procedure

Compositional modeling of the reservoir isn’t complete without calculations of phase equilibrium and is a complex process involving many calculations. In nature, hydrocarbons don’t occur as separate components, they’re mainly mixtures. When modeling the reservoir composition for phase equilibrium calculations, in order to reduce computational costs, in practice, hydrocarbon mixtures are grouped into pseudo-components. The number of grouped pseudo-components varies from 4 to 10. This grouping process is called lumping. However, when crude oil comes to the surface, it’s important to know its detailed composition, since mixtures grouped into pseudo-components don’t allow you to know this. In this regard, modeling of the detailed composition of hydrocarbons is the main tool for understanding the detailed phase separation and design of surface facilities. In practice, this process is called delumping. In the case of this process, the detailed composition of the fluid is presented and the amount reaches up to 36 components, sometimes more. The delumping process, due to the precise separation of heavy plus fractions into carbons with single ordinal numbers (C7, C8, etc.), makes it possible to clearly recognize non-zero BIP’s in the equation of state. The new analytical approach has not previously been applied to the oils of the Caspian region, so this approach has an important role for the oil industry in the Caspian region. Analytical delumping in this paper was done to improve the PVT modeling. This paper presents the results of PVT research of Caspian oil and presents a comparison of analytical and numerical methods of delumping. As a result of the study, it was found that the analytical approach is in excellent agreement with experimental data and data from software such as PVTsim

Multidimensional Multi-Connected Fuzzy Interval-Logic Controller

The key features and the principle of operation of a multidimensional fuzzy interval-logic controller with interconnected adjustable parameters developed by the authors are considered. The scheme of interpretation of continuous physical quantities by an equivalent set of terms and the basic version of the block diagram of the regulator are presented. The main elements of the logical output block are described, including the block of production rules, which includes a predefined database of values of control actions on control objects in the form of ordinal numbers of terms of output continuous quantities. The advantages and features of setting up the mutual connections between the input and output continuous values of the regulator are considered, which is expressed in determining the functional dependencies between them. The set of parameters possessed by the terms of input continuous quantities in relation to specific output continuous quantities of the regulator is described. The methods of defuzzification of the values of output continuous quantities within the boundaries of their terms are shown. The possibility of combining input and output continuous quantities into groups when setting up mutual connections between them is described. The mechanism of determining groups of interrelated continuous quantities is illustrated, the total number of which is determined by forming a matrix of relationships, according to the author’s scheme. The algorithm of sequential processing of the contents of the cells of the matrix of relationships, consisting of three steps, is considered. Expressions are given for calculating the basic parameters of a multidimensional fuzzy interval-logic controller with interrelated adjustable parameters. The results of a computational experiment to reduce the system of production rules of the regulator in determining the relationships between input and output continuous quantities are presented.

Ordinal numbers: Not superlatives, but modifiers of superlatives

The few existing accounts of the semantics of ordinal numbers attribute to them all or almost all of the semantic properties of superlatives. This work discusses a construction problematic for existing theories of ordinals: the ordinal superlative construction (e.g. Joel climbed the third highest mountain). Existing theories give ordinals and superlatives such similar semantics that they struggle to explain how an ordinal and a superlative could join together and form a complex modifier. As an alternative, I propose a semantics according to which ordinals are exceptive modifiers of superlatives. For example, the n-th highest mountain is the mountain that, with n - 1 exceptions, is the highest. When an ordinal does not co-occur with an overt superlative (e.g. the second train), I posit a covert superlative adjective that represents the contextual ordering. Not only does this approach account for the ordinal superlative construction, but it lends itself to a principled explanation of differences between ordinals and superlatives with respect to plurality.

What is wellness? Investigating the importance of different domains of wellness among laypeople and experts: A survey study.

Lack of consensus on wellness has led to a vast number of different conceptualisations, which hinder international efforts to monitor individual-level wellness and social progress comparably. This study aimed to aid in the harmonisation of the concept by contributing to the scarce research on laypeople's views on wellness. The study investigates whether the importance of different areas of wellness varies depending on age, gender, education or socio-economic position. Furthermore, considering that wellness models are often constructed by expert panels, this study aimed to shed light on how experts' and laypeople's views on wellness vary. Altogether, 1152 laypeople and 23 Finnish experts rated the importance of 61 systematic review-based wellness domains. Each domain received an ordinal number, which, together with the Mann-Whitney U-test or Kruskal-Wallis test, was used to examine the differences between the groups. Thirteen wellness domains were found at the top of the lists, regardless of whether the results were analysed based on gender, age, education or socio-economic position. When looking at the priority order of different domains, we were able to identify several differences between the expert panel and laypeople. To ensure the relevance of wellness models, it is vital to understand the areas that laypeople consider to be important for their comprehensive wellness. This study offers 13 domains that could be combined with an expert view on wellness and used as a starting point for creating a more comprehensive, inclusive and better-suited wellness instrument.

Dimension of uncountably generated submodules

In this article we introduce and study the concepts of uncountably generated Krull dimension and uncountably generated Noetherian dimension of an $R$-module, where $R$ is an arbitrary associative ring. These dimensions are ordinal numbers and extend the notion of Krull dimension and Noetherian dimension.&#x0D; They respectively rely on the behavior of descending and ascending chains of uncountably generated submodules.&#x0D; It is proved that a quotient finite dimensional module $M$ has uncountably generated Krull dimension if and only if it has Krull dimension, but&#x0D; the values of these dimensions might differ.&#x0D; Similarly, a quotient finite dimensional module $M$ has uncountably generated Noetherian dimension if and only if it has Noetherian dimension.&#x0D; We also show that the Noetherian dimension of a quotient finite dimensional module $M$ with uncountably generated Noetherian dimension $\beta$ is less than or equal to $\omega _{1}+\beta $, where $\omega_{1}$ is the first uncountable ordinal number.

Functorial Fast-Growing Hierarchies

Abstract We prove an isomorphism theorem between the canonical denotation systems for large natural numbers and large countable ordinal numbers, linking two fundamental concepts in Proof Theory. The first one is fast-growing hierarchies. These are sequences of functions on $\mathbb {N}$ obtained through processes such as the ones that yield multiplication from addition, exponentiation from multiplication, etc. and represent the canonical way of speaking about large finite numbers. The second one is ordinal collapsing functions, which represent the best-known method of describing large computable ordinals. We observe that fast-growing hierarchies can be naturally extended to functors on the categories of natural numbers and of linear orders. The isomorphism theorem asserts that the categorical extensions of binary fast-growing hierarchies to ordinals are isomorphic to denotation systems given by cardinal collapsing functions. As an application of this fact, we obtain a restatement of the subsystem $\Pi ^1_1$ - ${\mathsf {CA_0}}$ of analysis as a higher-type well-ordering principle asserting that binary fast-growing hierarchies preserve well-foundedness.

Determiner Morphology of Ale

This study was focused on describing the determiner of the Ale language. Therefore, the study followed a descriptive research design and language consultants were selected using purposeful sampling. Then, the linguistic data was collected using interviews, focus group discussions and elicitation. The collected data were analyzed using qualitative methods. The findings show that the demonstrative determiner in Ale is used to show something is near to the speaker/ listener, expressed by husi 'This' for singular and hisi 'These' for plural. Oppositely, to describe some things far from the speaker /listeners are indicated by husa 'That' for singular and hisa 'Those' for plural nouns. Ale's Demonstrative determiners begin with the similar consonant sounds/h-/ and vowel ending. Possessive determiners in Ale show that something belongs to someone. These determiners of Ale are used to describe the belongs of something for someone by inserting before nouns. Quantifiers are also determiners that modify a noun to indicate its quantity. Quantifiers like he tiikisa 'a few', tiikisa 'a little', he kisha' many'. On the other hand, in Ale, quantifiers may describe cardinal and ordinal numbers. Cardinal numbers refer to the number of or quantity of something. Cardinal number quantifiers are; to'on 'one', laki 'two', and izzex 'three'. Ordinal numbers refer to the numeral positions of something. The sample of ordinal quantifiers in Ale is Paayoote' first', lanka' second, and isxxa 'third'.

The Archimedean Origin of Modern Positional Number Systems

A symbolic analysis of Archimedes’s periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented by remarking on the cruciality of this topic in number theory. Periods of ordinal numbers and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship between numbers and information, which shed new light on a red line passing through the whole history of mathematics.

FEATURES OF ELEMENTS ACCUMULATION IN FRUIT AND BERRY PLANTS CULTIVATED IN THE VICINITY OF ZELENOGORSK CITY, KRASNOYARSK REGION

The aim of the study is to identify the peculiarities of the elemental composition of berries (fruits) and leaves of raspberry (Rubus idaeus L.), rowan (Sorbus aucuparia L.), black currant (Ribes nigrum L.), sour cherry (Cerasus vulgaris L.), serviceberry (Amelanchier ovalis Medik.) collected in the vicinity of Zelenogorsk, Krasnoyarsk Region, with an assessment of their potential use as sources of elements, ecological safety of use, as well as patterns of distribution of elements between plants, soil, and the surrounding environment. The elemental composition was analyzed using the method of arc atomic emission spectroscopy with a multi-channel analyzer of emission spectra (DAES with MAES) after ashing. As a result, the presence of 30 elements was determined in the ash of the studied plants, 25 of which belong to trace elements, and 22 are (conditionally) essential. The belongingness of the minimum extremes of content to mostly odd ordinal numbers of elements in the Mendeleev table was established, while the maximum extremes belonged to even ones. It is proposed to represent the revealed regularities in the form of combinations of extrema with the corresponding serial numbers of atoms, which clearly indicates the plant's ability to concentrate certain chemical elements. Based on the degree of accumulation from the soil, which indicates the ability of plants to accumulate elements, the highest indicator for all studied species and their raw materials is K, for all raspberry and blackcurrant raw materials – Ca, for cherry and raspberry leaves with berries (fruits) and separately for cherry fruits – Mg, only for blackcurrant leaves with berries (fruits) – Ti, for blackcurrant leaves with berries (fruits) – Sr and Ag. The study identified only Ti and Ag as having a "strong accumulation" in the biological absorption of elements, while the others were common for vegetation. Raspberry was found to have the highest biogeochemical activity among the studied fruit and berry plants (regardless of the raw material), followed by blackcurrant. It is shown that the raw materials "leaves + berries (fruits)" in all the studied cases contain much more trace elements, in contrast to individual berries (fruits). The study demonstrated the potential use of these plant species as sources of macroelements and trace elements, including essential ones.

More of me: Self-prioritization of numeric stimuli.

People process stimuli that have been arbitrarily associated with the self versus with a stranger preferentially, but congruence effects can modulate self-prioritization, as when the self is paired with, for example, symmetrical versus asymmetrical stimuli. In two experiments, we examined the interaction of self-prioritization with number magnitude when participants associated the self or a stranger with specific number symbols such as "2" presented as natural, negative, and ordinal number types (Experiment 1), or abstract numeric concepts, such as "larger than 5" (Experiment 2). Empathy and personal distance were also assessed. While self-prioritization emerged in both experiments, number type (natural, ordinal, and negative) had no effect on performance. Furthermore, correlations with empathy and personal distance did not emerge consistently. An interaction between number magnitude and self-assignment was observed for the magnitude comparison matching task (e.g., > 5) (Experiment 2), but not in the specific number (e.g., "8") matching task (Experiment 1). The null interaction may reflect the fact that encoding symbol identity, but not number magnitude, was sufficient for the symbol-matching task. The order of numbers and self-associations also had an effect. In sum, this study is the first to show that self-prioritization emerges for symbolic numbers and can even occur with abstract categories, such as a range of numbers (e.g., > 5). Furthermore, congruence effects between number concepts and labels (e.g., for the stranger, less is better) may also affect performance. However, this would appear to depend on the task context, such as whether numeric magnitude was needed to complete the task. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

The concept of infinity and the development of set theory solutions

The concept of infinity is intricately connected to and comprehended via the framework of cardinal and ordinal numbers. Cardinal and ordinal numbers are fundamental mathematical ideas within the field of set theory. The cardinal number is used to denote the quantity of items inside a given set while ordinal defines basic algorithms. This article demonstrates how the discipline of set theory may be used as a tool to investigate the nature of infinity, or at the very least give some insights into the subject. The idea of infinity may be better understood by looking at it through the lens of set theory and the commutative property. In addition to that, this research presents the connection and compatibility examination of Cohens operation upon the Zermelo Freankel axiomatic framework. These accomplishments are discussed in this article as illuminating insights for readers to consider while imagining the ultimate solution to the problems posed by the Continuum Hypothesis and the nature of infinity. Through the use of examples from contemporary researchers, the multiverse and indeterminism are introduced as potential approaches to the problem of how to solve Cantors legacy in the future.

Phonological Alternation in Numerals in Sungai Penuh Dialect of Kerinci

Kerinci is a Malayic language spoken primarily in Sungai Penuh City and Kerinci Regency, Sumatra which is considered unique as most lexicons have two or more forms, differing in the phonological realisation of their final syllables. These word-final syllable rhymes are referred to as Absolute and Oblique forms since they bear syntactic functions. This paper describes phonological alternation in numerals and their morphosyntactic functions based on data from a synchronic descriptive study conducted in Koto Renah village, Sungai Penuh, Kerinci. The study reveals that most cardinal and ordinal numbers have two or more forms. The last unit of a compound numeral is the absolute form, while all preceding units are oblique forms. The phrasal alternations in numerals lends credence to the view that the Kerinci language is indeed unique.