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linear function for calibrating capacitance and frequency domain reflectometry (EC-5) for soil water monitoring by introducing slope-intercept relationship

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SOIL SCIENCE AND PLANT NUTRITION 2020年第4期66卷 531-540页

作者： Mochizuki, Hidetoshi Sakaguchi, Iwao NARO Western Reg Agr Res Ctr Fukuyama Hiroshima Japan

New calibration method of the capacitance and frequency domain reflectometry (ECH2O EC-5) for soil water monitoring was developed by introducing the slope-intercept relationship derived from the relationship between the RAW data recorded by the Em50 datalogger and the thermogravimetrically measured volumetric water content of soil. Numerous soil samples taken from paddy-upland rotational fields in western Japan were used for precise soil-specific calibration experiments to determine the variables of slope-intercept relationship. By using these identified variables and an easily available dataset of the measured volumetric water content and the RAW data, the developed linear function predicted volumetric water content of soils. The developed linear function was validated with the reported literature data, the agricultural fields experiment, and the laboratory experiment. From those three validations, the developed linear function was evaluated to be practically available for laboratory and field researches. Also, it is implied that the developed linear function is extendable to dataloggers except for the Em50 and monitoring devices excluding the EC-5.

关键词： Calibration frequency domain reflectometry volumetric water content linear function ec-5

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linear function based Transformation Scheme for Preserving Database Privacy in Cloud Computing

Linear Function based Transformation Scheme for Preserving D...

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19th IEEE International Conference on Parallel and Distributed Systems (ICPADS)

作者： Yoon, Min Kim, Hyeong-Il Jang, Miyoung Chang, Jae-Woo Chonbuk Natl Univ Dept Comp Engn Jeonju 561756 South Korea

ISBN: (纸本)9781479920815

Because much interest in spatial database in cloud computing has been attracted, studies on preserving location data privacy in cloud computing have been actively done. However, since the existing spatial transformation schemes are weak to proximity attack, they cannot preserve the privacy of users who enjoy location-based services from the cloud computing. Therefore, a transformation scheme for providing a safe service to users is required. So, we, in this paper, propose a new transformation scheme based on a line symmetric transformation (LST). The proposed scheme performs both LST-based data distribution and error injection transformation for preventing proximity attack effectively. Finally, we show from our performance analysis that the proposed scheme greatly reduces the success rate of the proximity attack while performing the spatial transformation in an efficient way.

关键词： Cloud computing Location data protection Spatial transformation scheme linear function

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CANONICAL REPRESENTATION - FROM PIECEWISE-linear function TO PIECEWISE-SMOOTH functionS

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS 1993年第7期40卷 461-468页

作者： LIN, JN UNBEHAUEN, R Lehrstuhl für Allgeineine und Theoretiache Elektrotechnik Universität Erlangen-Nürnberg Erlangen Germany Lehrstuhl für Allgeineine und Theoretiache Elektrotechnik Universität Erlangen-Nünberg Erlangen Germany

The canonical representation of piecewise-linear (PWL) functions provides a global compact formulation of continuous PWL functions, which has significant advantages in the research and applications concerning nonlinear systems. This paper studies the generalization of the canonical representation from PWL functions to piecewise-smooth (PWS) functions. At first, a class of PWS functions, called the regular PWS function, is defined as a generalization of the continuous PWL function. An important example of the regular PWS functions is the continuous piecewise-polynomial function. The continuous PWL function with a PWL partition is also covered by the regular PWS function. Then, the canonical representation of the PWS function is defined and the existence conditions are discussed. The PWS generalization of the canonical representation is significant in applications where a PWS scheme can improve the performance of a PWL scheme in the approximation of a nonlinear function, i.e., in approximating the input/output relation of a nonlinear system or a mapping neural network or in nonlinear signal processing.

关键词： Smooth function Generalization power level linear function Canonical nonlinear functions Nonlinear systems function

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Formula Complexity of a linear function in a k-ary Basis

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MATHEMATICAL NOTES 2021年第3-4期109卷 445-458页

作者： Sergeev, I. S. Res Inst Kvant Moscow 125438 Russia

The Khrapchenko method of finding a lower bound for the complexity of binary formulas is extended to formulas in k-ary bases. The resulting extension makes it possible to evaluate the complexity of linear Boolean functions and a majority function of n variables when realized by formulas in the basis of all k-ary monotone functions and negation as Omega(n(g(k))), where g(k) = 1 + Theta(1/ln k). For a linear function, the complexity bound in this form is unimprovable. For k = 3, the sharper lower bound Omega(n(1.53)) is proved.

关键词： Boolean formulas linear function majority function Khrapchenko method bipartite graphs lower bounds for complexity

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Fusion genes and rearranged genes as a linear function of chromosome aberrations in cancer

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NATURE GENETICS 2004年第4期36卷 331-334页

作者： Mitelman, F Johansson, B Mertens, F Univ Hosp Dept Clin Genet SE-22185 Lund Sweden

Cytogenetic aberrations have been reported in 45,000 human neoplasms. Structural balanced rearrangements are associated with distinct tumor subtypes with remarkable specificity and have been essential for identifying genes involved in tumorigenesis(1,2). All balanced rearrangements that have been characterized molecularly act by deregulating a gene in one of the breakpoints or by creating a fusion gene(3-6). Because most recurrent aberrations and rearranged genes have been found in hematological disorders, whereas numerous genomic imbalances have been identified in solid tumors(7,8), it has become generally accepted that there are pathogenetic differences between these neoplasms. We here show that in every tumor type, the numbers of recurrent balanced chromosome abnormalities, fusion genes and genes rearranged as a consequence of balanced aberrations are simply a function of the number of cases with an abnormal karyotype. Hence, there may not be any fundamental tissue-specific differences in the genetic mechanisms by which neoplasia is initiated.

关键词： physiological aspects Neoplasms Fusion NOS fusion gene 肿瘤 Physiological aspects FUSION Gene Fusion ASSAY SCALE linear function Neoplasms Hematological Disease Breakpoints Chromosome Aberrations NOT OTHERWISE SPECIFIED

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Entire functions, analytic continuation, and the fractional parts of a linear function

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MATHEMATICAL NOTES 1999年第3-4期66卷 442-450页

作者： Pavlov, AI Russian Acad Sci VA Steklov Math Inst Moscow Russia

The main result of the paper is as follows. Theorem. Suppose that G(z) is an entire function satisfying the following conditions: 1) the Taylor coefficients of the function G(z) are nonnegative;2) for some fixed C > 0 and A > 0 and for \ Z \ > R-0, the following inequality holds: \ G(z)\ < exp(C \ z \/In-A\ z \) Further, suppose that for same fixed alpha > 0 the deviation D-N of the sequence x(n) = {alpha n}, n = 1,2,..., as N --> infinity has the estimate D-N = O(ln(B) N/N). Then if the function G(z) is not an identical constant and the inequality B + 1 < A holds, then the power series Sigma(n=0) infinity G(\alpha n \)z(n) converging in the disk \ z \ < 1 cannot be analytically continued to the region \ z \ > 1 across any are of the circle \ z \ =1.

关键词： entire function linear function analytic continuation Cauchy theorem Wigert's theorem Hecke's theorem

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On the complexity of realization of the linear function by formulas over finite Boolean bases

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Discrete Mathematics and Applications 2000年第2期10卷 147-157页

作者： Cherukhin, D. Yu.

We completely describe the set of bases over which the complexity of realization of the function x1 direct sum ... direct sum xn is of order n. For all bases not belonging to this set, we obtain the lower bound for the complexity of realization of the function x1 direct sum ... direct sum xn, which is of the form nc, where c gt;1 and c does not depend on n. Basing on this bound for complexity, we give a more simple proof of existence of an infinite (descending) sequence of Boolean bases.

关键词： Complexity GRANTS formula linear function

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Optimal Search for Locally Feasible Solutions of a linear function on Permutations

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CYBERNETICS AND SYSTEMS ANALYSIS 2022年第1期58卷 29-35页

作者： Donets, G. P. Biletskyi, V., I Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

We consider the problem of optimal search for locally feasible solutions of a linear function on the permutations where the linear function takes the values from the given interval. We describe a new method of solving... 详细信息

关键词： linear function permutation transposition balance position operation

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Understanding linear function: a Comparison of Selected Textbooks from England and Shanghai

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INTERNATIONAL JOURNAL OF SCIENCE AND MATHEMATICS EDUCATION 2017年第1期15卷 131-153页

作者： Wang, Yuqian Barmby, Patrick Bolden, David Univ Durham Durham England Univ Witwatersrand Johannesburg South Africa

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students' understanding towards a structural view of linear function.

关键词： Comparative study linear function Textbook analysis Understanding

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In which ways and to what extent do English and Shanghai students understand linear function?

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RESEARCH IN MATHEMATICS EDUCATION 2017年第1期19卷 66-90页

作者： Wang, Yuqian Barmby, Patrick Bolden, David Univ Durham Sch Educ Durham England Univ Witwatersrand Sch Educ Johannesburg South Africa

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship;Connecting Representations;Property Noticing;Object Analysis;and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing that the English cohort generally operated at the levels of Property Noticing and Object Analysis, whereas the Shanghai cohort reached the higher level of Inventising. The main study explored understanding levels and students' errors within each cohort in detail, in order to gain insights into reasons for apparent differences. The instrument used in the main study included two overlapping items, which were the same for both cohorts, while others were pitched at levels of understanding revealed in the pilot. Analysis of students' solutions revealed that the English students' errors were manifested in a lack of basic skills including dealing with negative numbers, while the Shanghai students showed weaknesses in their ability to use graphs. The discussion highlights different views of understanding as a possible background reason for the contrasts observed. Errors and apparent difficulties suggest implications for teaching linear function in each context.

关键词： abstraction linear function understanding

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