Characteristics of numerals and classifiers in Darmdo Minyag

Based on first-hand data obtained during fieldwork, our article analyses numerals and frequently employed numeral classifiers of Darmdo Minyag. Numeral classifiers are obligated to follow a numeral when counting. There are three different roots for ‘ten’: /ɦa~ʁo/ used in the numbers 10–19; /ʁuɑ/ used in the numbers 20–49; and /ɡa/ used in the numbers 50–99. The presence of multiple roots for ‘ten’ with an initial glottal, uvular or velar stop or fricative has been attested in many languages of the Qiangic area. Although Tibetan forms may be used for all numerals, native forms 99 have been attested in Darmdo Minyag. The influence of Tibetan on cardinal and ordinal numerals, approximate, multiple and fractional numbers is noted as well. Darmdo Minyag has a rich inventory of sorting and mensural classifiers. Shape is the most important feature according to which nouns are categorized. Mensural classifiers may be divided into arrangement classifiers and units of measure. Units of measure are of two types: the first acts as a classifier, the second type is a [noun numeral+classifier] construction. Darmdo Minyag has two types of verbal action classifiers: several verbal action classifiers of unknown origin which modify semantically rich verbs, and numeral-verb combinations which modify a semantically empty verb. The main functions of classifiers are classification and individualization.

Blowup results for the fractional Schrödinger equation without gauge invariance

<p style='text-indent:20px;'>This paper is concerned with the nonexistence of global solutions to the fractional Schrödinger equations with order <inline-formula><tex-math id="M1">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> and nongauge power type nonlinearity <inline-formula><tex-math id="M2">\begin{document}$ |u|^p $\end{document}</tex-math></inline-formula> for any space dimensions, where <inline-formula><tex-math id="M3">\begin{document}$ \alpha\in (0, 2] $\end{document}</tex-math></inline-formula> is assumed to be any fractional numbers. A modified test function is employed to overcome some difficulties caused by the fractional operator and to establish blowup results. Some restrictions with respect to <inline-formula><tex-math id="M4">\begin{document}$ \alpha, p $\end{document}</tex-math></inline-formula> and initial data in the previous literature are removed.</p>

பண்டைய தமிழர்களின் எண்கணித முறை

No one looks back on the mathematical system of the ancient Tamils in this age of science and mathematics. Contemporary mathematicians are not much interested either. This is due to the long gap between the old ancient mathematical system and today’s mathematical system. Not only that but it is not easy to understand.Looking at the mathematical method of the ancients it is possible to know that they had a very subtle knowledge.The ancients calculated by putting fractional numbers. If the fractional number is the number 1/8, 1/4, 3/4, 1/2 then we know the fraction. But they have also used more subtle fractional numbers than this.

SET EXPRESSIONS WITH CARDINAL NUMERALS IN THE LANGUAGE OF NEWS MEDIA

The article is focused on set expressions with cardinal numerals in Spanish newspaper language. These fixed expressions are part of linguistic expressive means, which realize one of mass media functions. The purpose of the article is to analyze set expressions with cardinal numerals, classify them according to some criteria and determine newspaper spheres in which they are most frequently used. Fixed expressions with cardinal numerals are more numerous in number than those with ordinal ones, or multiple, partible or fractional numbers, and include expressions with numbers from zero to eight and numbers with a hundred, a thousand, and a million.For the purposes of the research fixed expressions with cardinal numerals are divided into two groups: the invariable expressions with a fixed cardinal numeral, and the variable expressions with a changeable cardinal numeral. In the article there are provided classifications of set expressions with cardinal numerals based on grammatical and semantic criteria, and their components. There is analyzed the use of fixed expressions in the language of newspapers. Set expressions with cardinal numerals form part of the phraseological thesaurus of the Spanish language and the language of news media in particular.

KRUNA WILANGAN BASA BALI KUNO SAJERONING KAMUS BASA BALI KUNO LAN PEPADANNYANE RING BASA BALI ANYAR

This study aims to describe (1) type of numbers in old Balinese, and (2) type of numbers in new Balinese. The subject of this study is the ancient Balinese inscription while the object is the numbers. The documentation method is used in order to collect the data. Then, the data analysis uses several techniques such as, data identification, data reduction, data classification, and data summarization. The result of this study was found that (1) type of the numbers in the old Balinese such as distributive numbers, collective numbers, indefinite distributive numbers, klitik numbers, measurement numbers, and fractional numbers, and (2) type of numbers in New Balinese which based on the same meanings, such as the equivalent forms, the similar forms, and the different forms.

MEASURING PERSPECTIVE OF FRACTION KNOWLEDGE: INTEGRATING HISTORICAL AND NEUROCOGNITIVE FINDINGS

In this theoretical investigation, we describe the origins and cognitive difficulties involved in the common conception of fractional numbers, where a fraction corresponds to some parts of an equally partitioned whole. As an alternative, we present a new notion of fraction knowledge, called the perspective of measure-proportionality. It is informed both by the historical-cultural analysis of the emergence of fractions in social practice and by neuroscientific evidence of the propensity of human beings to perceive from childhood nonsymbolic proportionality between pairs of quantities. We suggest that this natural neurocognitive propensity of individuals may be an instructional link to develop students’ robust knowledge about fractional numbers.

Teaching Fraction Concepts Using the Concrete-Representational-Abstract Sequence

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence of instruction has been shown to be an effective means of teaching conceptual understanding of fractional numbers. The purpose of this study was to compare the effects of CRA with remedial multitiered systems of support (MTSS) Tier 2 instruction for teaching fraction concepts. Thirty-one fifth-grade students participated in two different Tier 2 interventions; one group received typical Tier 2 instruction with their general education teachers and the other received CRA instruction with the researchers. The researchers measured student performance using a pretest and posttest and found significant differences in progress favoring the CRA group. Results and implications are discussed.

Developing Module of Fractional Numbers using Contextual Teaching and Learning Approach

The purpose of this study was to develop a learning module of fractional numbers using Contextual Teaching and Learning (CTL) approach. The stages of development adhered to the stages of development proposed by Plomp (2007). To assess the quality of the module, Neeven’s assessment of product quality (2007) was used. This assessment focused on three things: the validity, practicality, and effectiveness of the developed module. The validity of the module was determined by validators. Once the module was confirmed valid by the validators, the try-outs were administered to see the practicality and effectiveness. The practicality of the module was assessed from students’ activity and students’ responses on learning using the module. Meanwhile, the effectiveness of the module was assessed from the results of daily tests and final tests. The try-outs were conducted in class four times, and the percentage of students’ scores in each meeting was above 90%, which means that students did not experience difficulties and felt comfortable in shaping their learning experience, and students’ response was also positive. Meanwhile, the average daily test results of students for each meeting and the average final test results of all students were above 75. The results of these try-outs indicate that the developed module met the criteria of practicality and effectiveness.