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Copyright of Opuntia Brava is the property of Universidad de Ciencias Pedagogicas de Las Tunas, Centro de Documentacion e Informacion Pedagogica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study rates of decay for C 0 -semigroups on Banach spaces under the assumption that the norm of the resolvent of the semigroup generator grows with | s | β log (| s |) b , β , b ≥ 0 , as | s | → ∞ , and with | s | - α log (1 / | s |) a , α , a ≥ 0 , as | s | → 0 . Our results do not suppose that the semigroup is bounded. In particular, for a = b = 0 , our results improve the rates involving Fourier types obtained by Rozendaal and Veraar (J Funct Anal 275(10):2845–2894, 2018). [ABSTRACT FROM AUTHOR]

In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series expansion whose coefficients are expressed in terms of specific Hessenberg determinants, present the decreasing property and concavity of the normalized tail of the Maclaurin power series expansion of the cosine function, deduce a new determinantal expression of the Bernoulli numbers, and verify the decreasing property for the ratio of the logarithms of the first two normalized tails of the Maclaurin power series expansion of the cosine function.

In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series expansion whose coefficients are expressed in terms of specific Hessenberg determinants, present the decreasing property and concavity of the normalized tail of the Maclaurin power series expansion of the cosine function, deduce a new determinantal expression of the Bernoulli numbers, and verify the decreasing property for the ratio of the logarithms of the first two normalized tails of the Maclaurin power series expansion of the cosine function. [ABSTRACT FROM AUTHOR]

Pre-service mathematics teachers’ (PMTs) subject competency continues to engage scholars and researchers. Understanding level of knowledge of concepts that PMTs bring to their learning in university is crucial to developing their teacher knowledge. This article examines genetic decomposition of schemas PMTs in one university in South Africa build (to know about rules) for solving logarithmic equations. A mixed methods approach, and the action-process-object-schema (APOS) theory were employed to examine mental construction the 19 purposively selected PMTs that responded to a 90-minute simple logarithm research task (LRT) made while solving problems. Analysis of task scripts using percentage score forms the basis of the qualitative phase of the research. Individual interview was useful to elicit PMTs’ views and perceptions of their encountered difficulties in solving LRT problems. One common difficulty was proving the logarithmic equation. This highlights gaps in PMTs’ prior knowledge of logarithmic concepts and basic rules. Implications of the findings for PMT subject competency were discussed. [ABSTRACT FROM AUTHOR]

Copyright of Revista Foco (Interdisciplinary Studies Journal) is the property of Revista Foco and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Applying an averaging technique for the adapted Prüfer angle, we obtain an oscillation criterion for linear second order differential equations whose coefficients consist of products of powers of natural logarithm and general (bounded or unbounded) continuous functions. The presented criterion is illustrated by new corollaries and examples. The novelty is caused by the used averaging technique over unbounded intervals. [ABSTRACT FROM AUTHOR]

The psychophysical laws governing the judgment of perceived numbers of objects or events, called the number sense, have been studied in detail. However, the behavioral principles of equally important numerical representations for action are largely unexplored in both humans and animals. We trained two male carrion crows (Corvus corone) to judge numerical values of instruction stimuli from one to five and to flexibly perform a matching number of pecks. Our quantitative analysis of the crows' number production performance shows the same behavioral regularities that have previously been demonstrated for the judgment of sensory numerosity, such as the numerical distance effect, the numerical magnitude effect, and the logarithmical compression of the number line. The presence of these psychophysical phenomena in crows producing number of pecks suggests a unified sensorimotor number representation system underlying the judgment of the number of external stimuli and internally generated actions. [ABSTRACT FROM AUTHOR]

The study examines the levels of understanding logarithmic expressions within the frames of a mathematical card game. The game is based on the popular card game Saboteur. In this paper, we analyse the progress of a group of six undergraduate students participating in a remedial course using games for recalling some fundamental mathematical concepts. The context of the game allowed us to observe and rank their levels of understanding logarithm and the change of these levels during the game. [ABSTRACT FROM AUTHOR]

Bland–Altman limits of agreement are very popular in method comparison studies on quantitative outcomes. However, a straightforward application of Bland–Altman analysis requires roughly normally distributed differences, a constant bias, and variance homogeneity across the measurement range. If one or more assumptions are violated, a variance-stabilizing transformation (e.g., natural logarithm, square root) may be sufficient before Bland–Altman analysis can be performed. Sometimes, fractional polynomial regression has been used when the choice of variance-stabilizing transformation was unclear and increasing variability in the differences was observed with increasing mean values. In this case, regressing the absolute differences on a function of the average and applying fractional polynomial regression to this end were previously proposed. This review revisits a previous inter-rater agreement analysis on the Agatston score for coronary calcification. We show the inappropriateness of a straightforward Bland–Altman analysis and briefly describe the nonparametric limits of agreement of the original investigation. We demonstrate the application of fractional polynomials, use the Stata packages fp and fp_select, and discuss the use of degree-2 (the default setting) and degree-3 fractional polynomials. Finally, we discuss conditions for evaluating the appropriateness of nonstandard limits of agreement. [ABSTRACT FROM AUTHOR]

The motive of the study was to find factors that influence the teaching and learning of logarithms at the senior High schools in the Kwahu East Municipality. The study employed a descriptive survey where a questionnaire was administered to Eighty-Six (86) teachers. The sample was selected using the Census method. After the SPSS software was used to analyse the data, the descriptive analysis revealed that most teachers positively perceive logarithms. Factors influencing Senior High School mathematics teachers' teaching of logarithm were identified. Teachers believe that suitable teaching methods can influence students' perceptions. Strategies to encourage positive perceptions should be promoted among teachers, and recommendations include developing innovative methods for teaching logarithms in Senior High School mathematics.

We give a formula for f (η) , where f : C → C is a continuously differentiable function satisfying f (z ¯) = f (z) ¯ , and η is a dual quaternion. Note this formula is straightforward or well known if η is merely a dual number or a quaternion. If one is willing to prove the result only when f is a polynomial, then the methods of this paper are elementary. [ABSTRACT FROM AUTHOR]

Linear forms in logarithms have an important role in the theory of Diophantine equations. In this paper, we prove explicit p -adic lower bounds for linear forms in p -adic logarithms of rational numbers using Padé approximations of the second kind. [ABSTRACT FROM AUTHOR]

In this paper, we first deduce the following Sobolev inequality with logarithmic term: (0.1) sup ⁡ { ∫ B | u | 2 ⁎ | ln ⁡ (τ + | u |) | | x | β d x : u ∈ H 0 , r a d 1 (B) , ‖ ∇ u ‖ L 2 (B) = 1 } < ∞ , where β > 0 , τ ≥ 0 are constants, B is the unit ball in R N , N ≥ 3 , and 2 ⁎ = 2 N / (N − 2) is the critical Sobolev exponent. Then we show that the supremum in (0.1) is attained when 0 < β < min ⁡ { N / 2 , N − 2 } and 1 ≤ τ < ∞. The inequality (0.1) can be used to prove the existence of positive solution for the following supercritical problem: (0.2) { − Δ u = u 2 ⁎ − 1 (ln ⁡ (τ + u)) | x | β + g (| x | , u) , u > 0 in B , u = 0 on ∂ B , where g (r , u) ∈ C ([ 0 , 1) × R) is a subcritical perturbation. As a consequence, we can deduce the existence of positive solution for the supercritical problem with non-power nonlinearity: (0.3) { − Δ u = u 2 ⁎ − 1 (ln ⁡ (τ + u)) | x | β , u > 0 in B , u = 0 on ∂ B. This is somewhat surprising, because the problem (0.3) has no nontrivial solution by Pohozaev's identity if the variable exponent | x | β is replaced by any non-negative constant. [ABSTRACT FROM AUTHOR]

Bland–Altman limits of agreement are very popular in method comparison studies on quantitative outcomes. However, a straightforward application of Bland–Altman analysis requires roughly normally distributed differences, a constant bias, and variance homogeneity across the measurement range. If one or more assumptions are violated, a variance-stabilizing transformation (e.g., natural logarithm, square root) may be sufficient before Bland–Altman analysis can be performed. Sometimes, fractional polynomial regression has been used when the choice of variance-stabilizing transformation was unclear and increasing variability in the differences was observed with increasing mean values. In this case, regressing the absolute differences on a function of the average and applying fractional polynomial regression to this end were previously proposed. This review revisits a previous inter-rater agreement analysis on the Agatston score for coronary calcification. We show the inappropriateness of a straightforward Bland–Altman analysis and briefly describe the nonparametric limits of agreement of the original investigation. We demonstrate the application of fractional polynomials, use the Stata packages fp and fp_select, and discuss the use of degree-2 (the default setting) and degree-3 fractional polynomials. Finally, we discuss conditions for evaluating the appropriateness of nonstandard limits of agreement.

In this paper, we study linear differential equations whose coefficients consist of products of powers of natural logarithm and very general continuous functions. Recently, using the Riccati transformation, we have identified a new type of conditionally oscillatory linear differential equations together with the critical oscillation constant. The studied equations are a generalization of these equations. Applying the modified Prüfer angle, we prove that they remain conditionally oscillatory with the same critical oscillation constant.

This article is a presentation of the analysis of new class of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback. Development of mathematical models of errors, quantitative assessment of these errors taking into account modern components and assessing the accuracy of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback were presented. (Logarithmic ADC with accumulation of charge and impulse feedback – analysis and modeling).

This article is a presentation of the analysis of new class of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback. LADC construction, principle of operation and dynamic properties were presented. They can also be part of more complex converters and systems based on LADC. LADC of this class is perspective for implementation in the form of integrated circuit, as the number of switched capacitors needed to conversion is minimized to one capacitor. (Logarithmic ADC with accumulation of charge and impulse feedback – construction, principle of operation and dynamic properties)

Sir Isaac Newton noticed that the values of the first five rows of Pascal's triangle are each formed by a power of 11, and claimed that subsequent rows can also be generated by a power of 11. Literally, the claim is not true for the 5th row and onward. His genius mind might have suggested a deep relation between binomial coefficients and a power of some integer that resembles the number 11 in some form. In this study, we propose and prove a general formula to generate the values in any row of Pascal's triangle from the digits of (10⋯0︸Θ zeros1)n. It can be shown that the numbers in the cells in nth row of Pascal's triangle may be achieved from Θ+1 partitions of the digits of the number (10⋯0︸Θ zeros1)n, where Θ is a non-negative integer. That is, we may generate the number in the cells in a row of Pascal's triangle from a power of 11, 101, 1001, or 10001 and so on. We briefly discuss how to determine the number of zeros Θ in relation to n, and then empirically show that the partition really gives us binomial coefficients for several values of n. We provide a formula for Θ and prove that the (n+1)th row of Pascal's triangle is simply Θ+1 partitions of the digits of (10⋯0︸Θ zeros1)n from the right.

Mathematics is the language of science, thus understanding mathematical concepts is a building block for understanding science, and so for understanding aspects of anaesthesia. The aim of this article is to discuss and hopefully demystify the principles of differentiation, exponentiation, integration, and logarithms; and to demonstrate how they apply to our practice as anaesthetists. [ABSTRACT FROM AUTHOR]

The speed of convergence of the classical sequence which defines the constant of Euler (or Euler-Mascheroni),... Further several new sequences with a faster convergence are defined either by modifying the argument of the logarithm (De Temple, 1993, Negoi 1997, Ivan 2002) or by modifying the last term 1/n of the harmonic sum (Vernescu 1999). Now we give a systematic study of these speeds of convergence and especially of the last ones. [ABSTRACT FROM AUTHOR]

We define a point-free construction of real exponentiation and logarithms, i.e. we construct the maps exp: (0, ∞) × R →(0, ∞), (x, ζ) 7→ x ζ and log: (1, ∞) × (0, ∞) → R, (b, y) 7→ logb (y), and we develop familiar algebraic rules for them. The point-free approach is constructive, and defines the points of a space as models of a geometric theory, rather than as elements of a set — in particular, this allows geometric constructions to be applied to points living in toposes other than Set. Our geometric development includes new lifting and gluing techniques in point-free topology, which highlight how properties of Q determine properties of real exponentiation. This work is motivated by our broader research programme of developing a version of adelic geometry via topos theory. In particular, we wish to construct the classifying topos of places of Q, which will provide a geometric perspective into the subtle relationship between R and Qp, a question of longstanding number-theoretic interest. [ABSTRACT FROM AUTHOR]

Logarithm has an important role in learning mathematics since various fields such as science, computer, finance, industry, and others are applied this material as one of the study subjects. In calculus, logarithm has an important role, especially natural logarithm. This study aims to determine pre-service mathematics teachers' difficulties in solving logarithm bases and numerus material. The subjects are students in the first semester in one university at Banda Aceh city who take elementary algebra course. The research was conducted with a descriptive approach to explain the difficulties that students faced, and it applied several steps such as providing logarithm test to students, determining the difficulties, and verifying it by interviewing students who had difficulties based on their answers. This study revealed that there were various difficulties that students faced such as; (1) lack of understanding of bases and numerus definitions of logarithms, (2) not being able to distinguish between expressions and logarithmic equations, (3) remembering too many formulas so that they do not understand the context of the problem, (4) couldn’t determine the position of irrational numbers on the number line.

The ever-increasing requirement for high-performance signal processing blocks in artificial intelligence, IoT, and neural networks has rendered the Logarithmic arithmetic as front runner of advanced processors. As they require complex mathematical operations such as multiplication and division but they can be quickly done in the logarithmic domain as they are reduced to addition and subtraction operations, respectively. The task, though, is to move from binary to logarithmic and vice versa. Several algorithms have been suggested for the logarithmic and antilogarithmic conversion, but there is a compromise between hardware difficulty and accuracy. Within this work, we are introducing the correction circuit for both logarithmic and antilogarithmic conversion that is based on Mitchell's algorithm. Here the correction terms are generated using a weighted average approach and are stored using 16 X 8 ROM. The terms for correction are selected using the characteristic of the logarithmic value. Then, these converters are used to design a logarithmic multiplier. To further simplify the multiplier, an optimized multiplier is proposed. It involves only the addition of a single term to the result before performing an antilogarithm operation, which also streamlined the application of the multiplier. The proposed multiplier and optimized multiplier involves only a memory unit and an adder apart from Mitchell's logarithmic multiplier, so the hardware metrics are closely similar to Mitchell's logarithmic multiplier while having a peak error rate of 9.4 % and 7.5 % which is 11.1 % for Mitchell's multiplier and has nearly 95 % of input combinations have less than 5 % error when multiplication is performed using proposed multipliers. [ABSTRACT FROM AUTHOR]

Mathematical communication skills are one of the standard abilities in mathematics learning that students must have. In fact, it was found that the grade 10 students at one of the senior high schools in Kupang were still lacking in communicating both orally and in writing in mathematics learning. They lacked the ability to describe mathematical ideas using written symbols and notations and also lacked the ability to make class presentations using mathematical language. The purpose of this study was to improve students' mathematical communication skills, both written and oral, by applying the Think-Talk-Write method. The method used in this research was classroom action research with the Kemmis and McTaggart model in three cycles. The research instruments used were observation sheets, questionnaires, rubric sheets for oral mathematic communication skills, written mathematical communication skills test sheets, and reflection journals. Based on the results of the analysis, the application of the Think-Talk-Write method can improve mathematical communication ability of grade 10 students at a senior high school in Kupang. In mathematical communication skills written algebraically or graphically using mathematical terms, the appropriate notation and formula symbols increased by 4.76%. Written communication skill with the arrangement of arguments and generalizations increased by 28.57%. Similarly, the ability to convey mathematical thinking using mathematical language increased by 23.81%. The application of the Think-Talk-Write method can improve students' mathematical communication skills with stages starting from the explanation of the model and learning objectives, the distribution of question worksheets and materials, the think stage, the talk stage, and the write stage. BAHASA INDONESIA ABSTRACT: Kemampuan komunikasi matematis merupakan salah satu standar kemampuan dalam pembelajaran matematika yang harus dimiliki siswa. Pada kenyataannya ditemukan bahwa siswa kelas X pada salah satu sekolah menengah atas Kupang masih kurang dalam berkomunikasi baik secara lisan maupun tulisan dalam pembelajaran matematika. Tujuan dari penelitian ini adalah untuk meningkatkan kemampuan komunikasi matematis siswa baik secara tulisan maupun lisan dengan menerapkan metode Think-Talk-Write. Metode penelitian yang digunakan adalah penelitian tindakan kelas dengan model Kemmis dan Mc. Taggart dalam tiga siklus. Instrumen penelitian yang digunakan dalam penelitian ini yaitu lembar observasi, lembar angket, lembar rubrik kemampuan komunikasi matematis lisan, lembar tes kemampuan komunikasi matematis tertulis, dan jurnal refleksi. Berdasarkan hasil analisis, kemampuan komunikasi matematis tertulis secara aljabar atau grafik yang menggunakan istilah matematika, simbol notasi dan formula baku yang sesuai mengalami peningkatan sebesar 4,76%. Pada kemampuan komunikasi tertulis dengan susunan argumen dan generalisasi mengalami peningkatan sebesar 28,57%. Begitu juga pada kemampuan menyampaikan pemikiran matematis menggunakan bahasa matematis mengalami peningkatan sebesar 23,81%. Sehingga dapat disimpulkan bahwa penerapan metode Think-Talk-Write dapat meningkatkan kemampuan komunikasi matematis siswa dengan tahapan mulai dari penjelasan model dan tujuan pembelajaran, pembagian lembar kerja soal dan materi, tahap Think, tahap Talk, dan tahap Write.

The integrated STEAM approach arises when a contextualized problem's resolution requires different contributions (views) from each discipline. In this descriptive article we discuss the views needed from chemistry, technology, design skills, mathematical modelling and the artistic support necessary for constructing a scientific model that explains the pH of the mouth when chewing gum. To do this, we focus on describing the implementation of a short sequence of video-recorded inquiry-based contextualized activities (didactic innovation) in two classrooms with students in their third year of compulsory secondary education (14–15 years old). The scenes taken from the analysis of the implementation videos support the proposal of the connections needed in the STEAM contributions. The difficulties encountered from each discipline and the resolutions we propose shed light on how well-selected problems make STEAM views necessary, thus avoiding the usual summative multidisciplinary approach. [ABSTRACT FROM AUTHOR]

This article is a presentation of the analysis of new class of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback. Development of mathematical models of errors, quantitative assessment of these errors taking into account modern components and assessing the accuracy of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback were presented. (Logarithmic ADC with accumulation of charge and impulse feedback - analysis and modeling). [ABSTRACT FROM AUTHOR]

This article is a presentation of the analysis of new class of logarithmic analog-to-digital converter (LADC) with accumulation of charge and impulse feedback. LADC construction, principle of operation and dynamic properties were presented. They can also be part of more complex converters and systems based on LADC. LADC of this class is perspective for implementation in the form of integrated circuit, as the number of switched capacitors needed to conversion is minimized to one capacitor. (Logarithmic ADC with accumulation of charge and impulse feedback - construction, principle of operation and dynamic properties). [ABSTRACT FROM AUTHOR]

Copyright of Afrika Statistika is the property of Statistics & Probability African Society and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the relationship between the existence of an -density of roots along the curves of regular rotation of an entire function of zero order and the regular behavior at infinity of its logarithm. [ABSTRACT FROM AUTHOR]

Purpose - Measurement of information has long been studied for many years from different perspectives. Acknowledging this diversity, the article aims at reviewing approaches to the information measurement. Design/methodology/approach -- Literature review method was used to analyze and interpret main approaches of measuring information. Findings - Logarithm, volume, syntax, probability and entropy, quantity, impact, value, and energy of information were identified and investigated in detail as the major approaches to the information measurement. Originality/value - Discussing strengths and weaknesses of each approach, it concludes that a multi-dimensional approach would help us measure the information more accurate. [ABSTRACT FROM AUTHOR]

In a CNN for image classification, a SoftMax layer is usually placed at the end. The exponentinal and logarithmic operations in the SoftMax layer are not adequate to be implemented in an accelerator circuit. The operations are usually implemented with look-up tables, and the exponential operation can be implemented in an iterative method. This paper proposes a successive approximation method to calculate a logarithm to remove a very large look-up table. By substituing the large table with two very small tables, the circuit can be reduced much. The experimental results show that the 85% area reduction can be reached with a small error degradation. [ABSTRACT FROM AUTHOR]

We present a CORDIC (Coordinate Rotation Digital Computer)-based method to compute the logarithm function with base 2 and validate this method by software simulation and hardware implementation. Technically, we overcome the limitation of traditional hyperbolic CORDIC and transform it based on the idea of generalized hyperbolic CORDIC so that it can be used to compute $log_{2}x\;(x\;\epsilon \;[1,2))$. The proposed method requires only simple shift-and-add operations and has a great tradeoff between precision (or speed) and area. In MATLAB, we provide different precisions corresponding to the iterations of the transformed CORDIC for user needs. Using a pipelined structure and setting the number of iterations to be 16 (the average relative error is $2.09\times 10^{-6}$), we implement an example hardware circuit. Synthesized under the SMIC 65nm CMOS technology, the circuit has an area of 24100 $\mu m^{2}$ and computation time of 11.1 ns, which can save 31.04% area and improve 6.92% computation speed averagely compared with existing methods. [ABSTRACT FROM AUTHOR]

This investigation assessed the economic and environmental impacts of small-scale wood logging by mules in the mixed broadleaved mountain forest. To develop a time prediction model, all measurements of time are replaced by their decadic logarithms. Unit cost was calculated by two methods: (i) as usual, division of the system cost by average productivity per hour, (ii) on the basis of the developed logarithmic models. To investigate the residual damage a 100% inventory method was employed in pre- and post-hauling, alongside the mule trail. A core sampling technique of bulk density was used for determining the degree of soil compaction, and soil disturbed widths were measured at a 5-m interval in the mule hauling direction. In this research, computed unit cost was 17.2 EUR.m-3 and estimated unit cost by the logarithmic model was 16.2 EUR.m-3. This result highlights the time consumption which estimated by the developed model was at a close ratio with real time (average at 95%). In terms of environmental impact, the results indicated that 5.7% of regenerations and 0% of trees were damaged. Also we found that the increased bulk density was not significant (P = 0.903) and only about 0.2% of the total area was disturbed.