Garay, Mauricio
2012-01-01
Arithmetic class are closed subsets of the euclidean space which generalise arithmetical conditions encoutered in dynamical systems, such as diophantine conditions or Bruno type conditions. I prove density estimates for such sets using Dani-Kleinbock-Margulis techniques.
DEFF Research Database (Denmark)
Gil, J. I. Burgos; Feliu, Elisenda
2012-01-01
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov co...... and is endowed with a product structure, which is commutative and associative....
Reversible arithmetic logic unit
zhou, Rigui; Shi, Yang; Zhang, Manqun
2011-01-01
Quantum computer requires quantum arithmetic. The sophisticated design of a reversible arithmetic logic unit (reversible ALU) for quantum arithmetic has been investigated in this letter. We provide explicit construction of reversible ALU effecting basic arithmetic operations. By provided the corresponding control unit, the proposed reversible ALU can combine the classical arithmetic and logic operation in a reversible integrated system. This letter provides actual evidence to prove the possib...
Reversible arithmetic logic unit for quantum arithmetic
DEFF Research Database (Denmark)
Thomsen, Michael Kirkedal; Glück, Robert; Axelsen, Holger Bock
2010-01-01
This communication presents the complete design of a reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The presented ALU is garbage free and uses reversible updates to combine the standard reversible arithmetic...
Rastegar, Arash
2015-01-01
By Grothendieck's anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number-fields encode all the arithmetic information of these curves. The Goal of this paper is to develop an arithmetic Teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number-...
Visser, A.
2008-01-01
This paper is concerned with the 'logical structure' of arithmetical theories. We survey results concerning logics and admissible rules of constructive arithmetical theories. We prove a new theorem: the admissible propositional rules of Heyting Arithmetic are the same as the admissible propositional
[Acquisition of arithmetic knowledge].
Fayol, Michel
2008-01-01
The focus of this paper is on contemporary research on the number counting and arithmetical competencies that emerge during infancy, the preschool years, and the elementary school. I provide a brief overview of the evolution of children's conceptual knowledge of arithmetic knowledge, the acquisition and use of counting and how they solve simple arithmetic problems (e.g. 4 + 3). PMID:18198117
Oller-Marcén, Antonio M.
2012-01-01
An integer $n$ is said to be \\textit{arithmetic} if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we characterize arithmetic numbers. As an application, in Section 2, we give an interesting characterization of Mersenne numbers.
Gil, J I Burgos
2009-01-01
We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.
Dominici, Diego
2011-01-01
This work introduces a distance between natural numbers not based on their position on the real line but on their arithmetic properties. We prove some metric properties of this distance and consider a possible extension.
Ganea, Mihai
2009-01-01
Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be mutually interpretable with TC, a weak theory of concatenation introduced by Grzegorczyk. Furthermore, TC is shown to be interpretable in the theory F studied by Tarski and Szmielewa, thus confirming their claim that F is essentially undecidable.
Dominici, Diego
2009-01-01
What is the distance between 11 (a prime number) and 12 (a highly composite number)? If your answer is 1, then ask yourself "is this reasonable?" In this work, we will introduce a distance between natural numbers based on their arithmetic properties, instead of their position on the real line.
Marklof, J
2005-01-01
The central objective in the study of quantum chaos is to characterize universal properties of quantum systems that reflect the regular or chaotic features of the underlying classical dynamics. Most developments of the past 25 years have been influenced by the pioneering models on statistical properties of eigenstates (Berry 1977) and energy levels (Berry and Tabor 1977; Bohigas, Giannoni and Schmit 1984). Arithmetic quantum chaos (AQC) refers to the investigation of quantum system with additional arithmetic structures that allow a significantly more extensive analysis than is generally possible. On the other hand, the special number-theoretic features also render these systems non-generic, and thus some of the expected universal phenomena fail to emerge. Important examples of such systems include the modular surface and linear automorphisms of tori (`cat maps') which will be described below.
Arithmetic of Complex Manifolds
Lange, Herbert
1989-01-01
It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms. In recent years such problems, which are simultaneously of arithmetic and geometric interest, have become increasingly important. This proceedings volume contains 12 original research papers. Its main topics are theta functions, modular forms, abelian varieties and algebraic three-folds.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Towards an arithmetical logic the arithmetical foundations of logic
Gauthier, Yvon
2015-01-01
This book offers an original contribution to the foundations of logic and mathematics, and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic, and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of l...
Yablo's Paradox And Arithmetical Incompleteness
Leach-Krouse, Graham
2011-01-01
In this short paper, I present a few theorems on sentences of arithmetic which are related to Yablo's Paradox as G\\"odel's first undecidable sentence was related to the Liar paradox. In particular, I consider two different arithemetizations of Yablo's sentences: one resembling G\\"odel's arithmetization of the Liar, with the negation outside of the provability predicate, one resembling Jeroslow's undecidable sentence, with negation inside. Both kinds of arithmetized Yablo sentence are undecida...
Introduction to cardinal arithmetic
Holz, M; Weitz, E
1999-01-01
This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice (ZFC). A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, König and Tarski between 1870 and 1930. Next, the development in the 1970s led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the 1970s.Reviews:'The authors aim their text at beginners in set theory. They start
Arithmetic soft-core accelerators
Calderon Rocabado, D.R.H.
2007-01-01
In this dissertation, we address the design of multi-functional arithmetic units working with the most common fixed-point number representations, namely: unsigned, sign-magnitude, fractional, ten's and two's complement notations. The main design goal is to collapse multiple complex arithmetic operat
Valuations on arithmetic surfaces
Institute of Scientific and Technical Information of China (English)
XU Ning
2009-01-01
In this paper,we give the definition of the height of a valuation and the definition of the big field Cp,G,where p is a prime and G R is an additive subgroup containing 1.We conclude that Cp,G is a field and Cp,G is algebraically closed.Based on this the author obtains the complete classification of valuations on arithmetic surfaces.Furthermore,for any m ≤ n ∈ Z,let Vm,n be an R-vector space of dimension n - m + 1,whose coordinates are indexed from rn to n.We generalize the definition of Cp,G,where p is a prime and G C Vm,n is an additive subgroup containing 1.We also conclude that Cp,G is a field if m ≤ 0 ≤ n.
Valuations on arithmetic surfaces
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we give the definition of the height of a valuation and the definition of the big field Cp,G, where p is a prime and GR is an additive subgroup containing 1. We conclude that Cp,G is a field and Cp,G is algebraically closed. Based on this the author obtains the complete classification of valuations on arithmetic surfaces. Furthermore, for any m ≤n∈ Z, let Vm,n be an R-vector space of dimension n-m + 1, whose coordinates are indexed from m to n. We generalize the definition of Cp,G, where p is a prime and GVm,n is an additive subgroup containing 1. We also conclude that Cp,G is a field if m ≤0 ≤n.
Arithmetic the foundation of mathematics
2015-01-01
Arithmetic factors into our lives on a daily basis, so it's hard to imagine a world without the six basic operations: addition, subtraction, multiplication, division, raising to powers, and finding roots. Readers will get a solid overview of arithmetic, while offering useful examples of how they are used in routine activities, such as social media applications. It reinforces Common Core math standards, including understanding basic math concepts and how they apply to students' daily lives and challenges. A history of arithmetic helps provide a contextual framework for the course of its develop
Pavlichin, Dmitri S.; Mabuchi, Hideo
2014-06-01
Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.
Markov, Svetoslav; Hayes, Nathan
2010-01-01
An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from fa...
Neuropsychology of childhood arithmetic disorders.
Batchelor, E S
1989-01-01
The arithmetic learning disability literature was reviewed and critiqued. Due to the paucity of research in this area, few conclusions may be inferred. In general, the available research has provided tentative hypotheses about the nature of arithmetic disabilities. A variety of psychosocial variables notwithstanding, childhood arithmetic disability may directly result from cerebral dysfunction, poor motivation, and emotional/behavioral disturbance. However, further research is necessary in order to clarify the effects of maturation on arithmetic skills acquisition. Indeed, one approach to identification of the disorder would consider individual differences in neuropsychological development and performance affecting arithmetic achievement. It was concluded that a more comprehensive approach to investigating and diagnosing childhood arithmetic disability is needed. Reformulations and methods of study were articulated. Six related lines of research were outlined. A diagnostic rating scale was suggested which would account for type and severity of disorder. Diagnostic criteria were recommended based on the degree and definition of disability. Needs for remediation research were briefly explored. PMID:2485827
Counting arithmetic lattices and surfaces
Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner
2010-01-01
We give estimates on the number $AL_H(x)$ of arithmetic lattices $\\Gamma$ of covolume at most $x$ in a simple Lie group $H$. In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most $x$. Our main result is for the classical case $H=PSL(2,R)$ where we compute the limit of $\\log AL_H(x) / x\\log x$ when $x\\to\\infty$. The proofs use several different techniques: geometric (bounding the number of generators of $\\Gamma$ as a function of its covolu...
The Development of Arithmetical Abilities
Butterworth, Brian
2005-01-01
Background: Arithmetical skills are essential to the effective exercise of citizenship in a numerate society. How these skills are acquired, or fail to be acquired, is of great importance not only to individual children but to the organisation of formal education and its role in society. Method: The evidence on the normal and abnormal…
The retrieval and selection of arithmetic facts in oral arithmetic.
Megías, Patricia; Macizo, Pedro
2016-10-01
We examined the co-activation and the selection of arithmetic facts in oral arithmetic. In two experiments, participants had to verify whether simple additions were correct or not. In Experiment 1, additions were presented in the auditory-verbal format; in Experiment 2, additions were presented in the digit format but simulating the temporal sequence of auditory problems of Experiment 1. Results were similar in both experiments. Firstly, participants took the same time to respond when an addition was incorrect but the result was that of multiplying the operands (e.g., 2+4=8) relative to a control addition with unrelated result. Secondly, participants took more time to respond when the result of multiplying the operands of the first trial was presented again in a correct addition problem (e.g., 2+6=8) relative to a control addition. This pattern of results is discussed in terms of the temporal resolution to which auditory problems are resolved and the role of an inhibitory mechanism involved in the selection of arithmetic facts.
FAST TRACK COMMUNICATION: Reversible arithmetic logic unit for quantum arithmetic
Kirkedal Thomsen, Michael; Glück, Robert; Axelsen, Holger Bock
2010-09-01
This communication presents the complete design of a reversible arithmetic logic unit (ALU) that can be part of a programmable reversible computing device such as a quantum computer. The presented ALU is garbage free and uses reversible updates to combine the standard reversible arithmetic and logical operations in one unit. Combined with a suitable control unit, the ALU permits the construction of an r-Turing complete computing device. The garbage-free ALU developed in this communication requires only 6n elementary reversible gates for five basic arithmetic-logical operations on two n-bit operands and does not use ancillae. This remarkable low resource consumption was achieved by generalizing the V-shape design first introduced for quantum ripple-carry adders and nesting multiple V-shapes in a novel integrated design. This communication shows that the realization of an efficient reversible ALU for a programmable computing device is possible and that the V-shape design is a very versatile approach to the design of quantum networks.
Arithmetic Aspects of Bianchi Groups
Sengun, Mehmet Haluk
2012-01-01
We discuss several arithmetic aspects of Bianchi groups, especially from a computational point of view. In particular, we consider computing the homology of Bianchi groups together with the Hecke action, connections with automorphic forms, abelian varieties, Galois representations and the torsion in the homology of Bianchi groups. Along the way, we list several open problems and conjectures, survey the related literature, presenting concrete examples and numerical data.
Some results on uniform arithmetic circuit complexity
DEFF Research Database (Denmark)
Frandsen, Gudmund Skovbjerg; Valence, Mark; Barrington, David A. Mix
1994-01-01
and polynomial-size unbounded fan-in arithmetic circuits satisfying a natural uniformity constraint (DLOGTIME-uniformity). A 1-input and 1-output arithmetic function over the fieldsF2n may be identified with ann-input andn-output Boolean function when field elements are represented as bit strings. We prove...... that if some such representation is X-uniform (where X is P or DLOGTIME), then the arithmetic complexity of a function (measured with X-uniform unbounded fan-in arithmetic circuits) is identical to the Boolean complexity of this function (measured with X-uniform threshold circuits). We show the existence...
Joint source channel coding using arithmetic codes
Bi, Dongsheng
2009-01-01
Based on the encoding process, arithmetic codes can be viewed as tree codes and current proposals for decoding arithmetic codes with forbidden symbols belong to sequential decoding algorithms and their variants. In this monograph, we propose a new way of looking at arithmetic codes with forbidden symbols. If a limit is imposed on the maximum value of a key parameter in the encoder, this modified arithmetic encoder can also be modeled as a finite state machine and the code generated can be treated as a variable-length trellis code. The number of states used can be reduced and techniques used fo
The Arithmetic of Supersymmetric Vacua
Bourget, Antoine
2016-01-01
We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. These form a key ingredient in the semi-classical calculation of the number of massive vacua of N=1* gauge theories with gauge algebra su(n) compactified on a circle. Using arithmetic, we express that number in an SL(2,Z) duality invariant manner. We confirm our tally of massive vacua of the N=1* theories by a count of inequivalent extrema of the exact superpotential.
Memory Updating and Mental Arithmetic.
Han, Cheng-Ching; Yang, Tsung-Han; Lin, Chia-Yuan; Yen, Nai-Shing
2016-01-01
Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM) as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc) could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults. PMID:26869971
Memory updating and mental arithmetic
Directory of Open Access Journals (Sweden)
Cheng-Ching eHan
2016-02-01
Full Text Available Is domain-general memory updating ability predictive of calculation skills or are such skills better predicted by the capacity for updating specifically numerical information? Here, we used multidigit mental multiplication (MMM as a measure for calculating skill as this operation requires the accurate maintenance and updating of information in addition to skills needed for arithmetic more generally. In Experiment 1, we found that only individual differences with regard to a task updating numerical information following addition (MUcalc could predict the performance of MMM, perhaps owing to common elements between the task and MMM. In Experiment 2, new updating tasks were designed to clarify this: a spatial updating task with no numbers, a numerical task with no calculation, and a word task. The results showed that both MUcalc and the spatial task were able to predict the performance of MMM but only with the more difficult problems, while other updating tasks did not predict performance. It is concluded that relevant processes involved in updating the contents of working memory support mental arithmetic in adults.
Weak Theories of Concatenation and Arithmetic
Horihata, Yoshihiro
2012-01-01
We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.
Arithmetic for First Graders Lacking Number Concepts
Kamii, Constance; Rummelsburg, Judith
2008-01-01
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
From Arithmetic Sequences to Linear Equations
Matsuura, Ryota; Harless, Patrick
2012-01-01
The first part of the article focuses on deriving the essential properties of arithmetic sequences by appealing to students' sense making and reasoning. The second part describes how to guide students to translate their knowledge of arithmetic sequences into an understanding of linear equations. Ryota Matsuura originally wrote these lessons for…
Plain Polynomial Arithmetic on GPU
Anisul Haque, Sardar; Moreno Maza, Marc
2012-10-01
As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently parallelized on GPUs. Remarkably, it outperforms (highly optimized) FFT-based multiplication up to degree 212 while on CPU the same threshold is usually at 26. We also report on a GPU implementation of the Euclidean Algorithm which is both work-efficient and runs in linear time for input polynomials up to degree 218 thus showing the performance of the GCD algorithm based on systolic arrays.
Computer arithmetic and verilog HDL fundamentals
Cavanagh, Joseph
2009-01-01
Verilog Hardware Description Language (HDL) is the state-of-the-art method for designing digital and computer systems. Ideally suited to describe both combinational and clocked sequential arithmetic circuits, Verilog facilitates a clear relationship between the language syntax and the physical hardware. It provides a very easy-to-learn and practical means to model a digital system at many levels of abstraction. Computer Arithmetic and Verilog HDL Fundamentals details the steps needed to master computer arithmetic for fixed-point, decimal, and floating-point number representations for all prima
Arithmetic area for m planar Brownian paths
Desbois, Jean
2012-01-01
We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.
Quality of Arithmetic Education for Children with Cerebral Palsy
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.; Withagen, Floortje
2010-01-01
The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…
Statistical based MQ arithmetic coder
Noikaew, Nopphol; Chitsobhuk, Orachat
2014-01-01
Embedded block coding with optimized truncation (EBCOT) is a key algorithm in JPEG 2000 image compression system. Recently, the bit-plane coder architectures are capable of producing symbols at a higher rate than the capability of the existing MQ arithmetic coders. To solve this problem, a design of a multiple-symbol processor for statistical MQ coder architecture on FPGA is proposed. The proposed architecture takes advantage of simplicity of single-symbol architecture while integrates several techniques in order to increase the coding rate (more than one symbol per clock), reduce critical path, thus accelerate the coding speed. The repeated symbol statistics has been analyzed prior to the proposed architecture using lookahead technique. This allows the proposed architecture to support encoding rate of maximum 8 symbols per clock cycle without stalls and without excessively increasing the hardware cost. This helps to accelerate encoding process, which leads to greatly increase throughput. From the experiments, for lossy wavelet transform, the proposed architecture offers high throughput of at least 233.07 MCxD/S with effectively reducing the number of clock cycles more than 35.51%.
Recursive formula for arithmetic Asian option prices
Kyungsub Lee
2013-01-01
We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return process and European option prices. The computation of arithmetic Asian option prices is straightforward whenever European option prices are available. Applications with numerical results under the Black-Scholes framework and the exponential L\\'evy model are...
How to be Brilliant at Mental Arithmetic
Webber, Beryl
2010-01-01
How to be Brilliant at Mental Arithmetic addresses the twin pillars of mental arithmetic - mental recall and mental agility. Mental recall depends on familiarity with number bonds and plenty of opportunity to practise. Mental agility depends more on confidence with the number system and the four operations. Using the worksheets in this book, students will learn about: tens and units; addition, subtraction, multiplication and division; addition shortcuts; product squares; quick recall; number se
Herbrand consistency of some arithmetical theories
Salehi, Saeed
2012-01-01
G\\"odel's second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the witnesses of bounded formulas, due to Z. Adamowicz [Herbrand consistency and bounded arithmetic, \\textit{Fundamenta Mathematicae} 171 (2002) 279--292]. In that paper, it was shown that one cannot always shrink the witness of a bounded formula logarithmically, but in the presence of Herbrand consistency, for theories ...
Design of optimized Interval Arithmetic Multiplier
Directory of Open Access Journals (Sweden)
Rajashekar B.Shettar
2011-07-01
Full Text Available Many DSP and Control applications that require the user to know how various numericalerrors(uncertainty affect the result. This uncertainty is eliminated by replacing non-interval values withintervals. Since most DSPs operate in real time environments, fast processors are required to implementinterval arithmetic. The goal is to develop a platform in which Interval Arithmetic operations areperformed at the same computational speed as present day signal processors. So we have proposed thedesign and implementation of Interval Arithmetic multiplier, which operates with IEEE 754 numbers. Theproposed unit consists of a floating point CSD multiplier, Interval operation selector. This architectureimplements an algorithm which is faster than conventional algorithm of Interval multiplier . The costoverhead of the proposed unit is 30% with respect to a conventional floating point multiplier. Theperformance of proposed architecture is better than that of a conventional CSD floating-point multiplier,as it can perform both interval multiplication and floating-point multiplication as well as Intervalcomparisons
Arithmetic area for m planar Brownian paths
International Nuclear Information System (INIS)
We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable Sn1,n2,...,nm(m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2,..., and nm times by path m. Various results are obtained in the asymptotic limit m→∞. A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area
Arithmetic area for m planar Brownian paths
Desbois, Jean; Ouvry, Stéphane
2012-05-01
We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable Sn1, n2,..., nm(m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2,..., and nm times by path m. Various results are obtained in the asymptotic limit m\\to \\infty . A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area.
Arithmetic Self-Similarity of Infinite Sequences
Hendriks, Dimitri; Endrullis, Joerg; Dow, Mark; Klop, Jan Willem
2012-01-01
We define the arithmetic self-similarity (AS) of a one-sided infinite sequence sigma to be the set of arithmetic progressions through sigma which are a vertical shift of sigma. We classify the AS of several well-known sequences, such as the Thue-Morse sequence, the period doubling sequence, and the regular paperfolding sequence. The latter two are examples of (completely) additive sequences as well as of Toeplitz words. We investigate the intersection of these families. We give a complete characterization of single-gap patterns that yield additive Toeplitz words, and classify their AS. Moreover, we show that every arithmetic progression through a Toeplitz word generated by a one-gap pattern is again a Toeplitz word. Finally, we establish that generalized Morse sequences are specific sum-of-digits sequences, and show that their first difference is a Toeplitz word.
Learning, Realizability and Games in Classical Arithmetic
Aschieri, Federico
2010-01-01
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully...
Arithmetic geometry over global function fields
Longhi, Ignazio; Trihan, Fabien
2014-01-01
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009–2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the con...
Arithmetic area for m planar Brownian paths
Desbois, Jean; Ouvry, Stephane
2012-01-01
We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE informatio...
Derivations and Generating Degrees in the Ring of Arithmetical Functions
Indian Academy of Sciences (India)
Alexandru Zaharescu; Mohammad Zaki
2007-05-01
In this paper we study a family of derivations in the ring of arithmetical functions of several variables over an integral domain, and compute the generating degrees of the ring of arithmetical functions over the kernel of these derivations.
Training of Attention in Children With Low Arithmetical Achievement.
Maria Guarnera; Antonella D’Amico
2014-01-01
This study focuses on the role of attentional processes in arithmetical skills and examines if training of basic attentive skills may improve also working memory abilities reducing arithmetic difficulties. In order to study the efficacy of attentional treatment in arithmetic achievement and in enhancing working memory abilities a test-treatment-retest quasi experimental design was adopted. The research involved 14 children, attending fourth and fifth grades, with Arithmetical Learning Disabil...
Arithmetic and Cognitive Contributions to Algebra
Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.
2013-01-01
Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…
Retrieval-Induced Forgetting of Arithmetic Facts
Campbell, Jamie I. D.; Thompson, Valerie A.
2012-01-01
Retrieval-induced forgetting (RIF) is a widely studied phenomenon of human memory, but RIF of arithmetic facts remains relatively unexplored. In 2 experiments, we investigated RIF of simple addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 x 3 = 6). In both experiments, robust RIF expressed in response times occurred…
Goldbach Conjecture and First-Order Arithmetic
Revilla, Fernando
2007-01-01
Using the concepts of Hyperbolic Classification of Natural Numbers, Essential Regions and Goldbach Conjecture Function we prove that the existence of a proof of the Goldbach Conjecture in First-Order Arithmetic would imply the existence of another proof in a certain extension that would not be valid in all states of time associated to natural numbers created by means of adequate dynamic processes.
Intuitionistic fixed point theories over Heyting arithmetic
Arai, Toshiyasu
2010-01-01
In this paper we show that an intuitionistic theory for fixed points is conservative over the Heyting arithmetic with respect to a certain class of formulas. This extends partly the result of mine. The proof is inspired by the quick cut-elimination due to G. Mints.
Relating arithmetical techniques of proportion to geometry
DEFF Research Database (Denmark)
Wijayanti, Dyana
2015-01-01
The purpose of this study is to investigate how textbooks introduce and treat the theme of proportion in geometry (similarity) and arithmetic (ratio and proportion), and how these themes are linked to each other in the books. To pursue this aim, we use the anthropological theory of the didactic...
Single electron tunneling based arithmetic computation
Lageweg, C.R.
2004-01-01
In this dissertation we investigate the implementation of computer arithmetic operations with Single Electron Tunneling (SET) technology based circuits. In our research we focus on the effective utilization of the SET technologys specific characteristic, i.e., the ability to control the transport of
Specificity and overlap in skills underpinning reading and arithmetical fluency
V. van Daal; A. van der Leij; H. Adèr
2012-01-01
The aim of this study was to examine unique and common causes of problems in reading and arithmetic fluency. 13- to 14-year-old students were placed into one of five groups: reading disabled (RD, n = 16), arithmetic disabled (AD, n = 34), reading and arithmetic disabled (RAD, n = 17), reading, arith
Personal Experience and Arithmetic Meaning in Semantic Dementia
Julien, Camille L.; Neary, David; Snowden, Julie S.
2010-01-01
Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…
Ray system in lasers, nonlinear arithmetic pyramid and nonlinear arithmetic triangles
Yurkin, Alexander
2013-01-01
The paper describes a system of rays declining at small angles in lasers. The correlation between a group of rays and binomial coefficients is shown. The correlation of distribution of rays in the system of numbers placed in a three-dimensional table, the nonlinear arithmetic pyramid is shown. Two types of nonlinear arithmetic triangles are considered. Various types of partitions of integers is described.
Directory of Open Access Journals (Sweden)
K. Anup Kumar
2012-07-01
Full Text Available In this investigation, we have modified the Feistel cipher by taking the plaintext in the form of a pair of square matrices. Here we have introduced the operation multiplication with the key matrices and the modular arithmetic addition in encryption. The modular arithmetic inverse of the key matrix is introduced in decryption. The cryptanalysis carried out in this paper clearly indicate that this cipher cannot be broken by the brute force attack and the known plaintext attack.
Learning, Realizability and Games in Classical Arithmetic
Aschieri, Federico
2010-12-01
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel modified realizability to a classical fragment of first order Arithmetic, Heyting Arithmetic plus EM1 (Excluded middle axiom restricted to Sigma^0_1 formulas). We introduce a new realizability semantics we call "Interactive Learning-Based Realizability". Our realizers are self-correcting programs, which learn from their errors and evolve through time. Secondly, we extend the class of learning based realizers to a classical version PCFclass of PCF and, then, compare the resulting notion of realizability with Coquand game semantics and prove a full soundness and completeness result. In particular, we show there is a one-to-one correspondence between realizers and recursive winning strategies in the 1-Backtracking version of Tarski games. Third, we provide a complete and fully detailed constructive analysis of learning as it arises in learning based realizability for HA+EM1, Avigad's update procedures and epsilon substitution method for Peano Arithmetic PA. We present new constructive techniques to bound the length of learning processes and we apply them to reprove - by means of our theory - the classic result of Godel that provably total functions of PA can be represented in Godel's system T. Last, we give an axiomatization of the kind of learning that is needed to computationally interpret Predicative classical second order Arithmetic. Our work is an extension of Avigad's and generalizes the concept of update procedure to the transfinite case. Transfinite update procedures have to learn values of transfinite sequences of non computable functions in order to extract witnesses from classical proofs.
Recursive double-size fixed precision arithmetic
Chabot, Christophe; Fousse, Laurent; Giorgi, Pascal
2011-01-01
This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture).
Dictionary of algebra, arithmetic, and trigonometry
Krantz, Steven G
2000-01-01
Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geom...
Arithmetic Operand Ordering for Equivalence Checking
Institute of Scientific and Technical Information of China (English)
WENG Yanling; GE Haitong; YAN Xiaolang; Ren Kun
2007-01-01
An information extraction-based technique is proposed for RTL-to-gate equivalence checking. Distances are calculated on directed acyclic graph (AIG). Multiplier and multiplicand are distinguished on multiplications with different coding methods, with which the operand ordering/grouping information could be extracted from a given implementation gate netlist, helping the RTL synthesis engine generate a gate netlist with great similarity. This technique has been implemented in an internal equivalence checking tool, ZD_VIS. Compared with the simple equivalence checking, the speed is accelerated by at least 40% in its application to a class of arithmetic designs, addition and multiplication trees. The method can be easily incorporated into existing RTL-to-gate equivalence checking frameworks, increasing the robustness of equivalence checking for arithmetic circuits.
Arithmetic Properties of the Ramanujan Function
Indian Academy of Sciences (India)
Florian Luca; Igor E Shparlinski
2006-02-01
We study some arithmetic properties of the Ramanujan function (), such as the largest prime divisor ( ()) and the number of distinct prime divisors (()) of () for various sequences of . In particular, we show that ( ()) ≥ $(\\log n)^{33/31+(1)}$ for infinitely many , and $$P((p)(p^2)(p^3))>(1+(1))\\frac{\\log\\log p\\log\\log\\log p}{\\log\\log\\log\\log p}$$ for every prime with $(p)≠ 0$.
Calculation Methodology for Flexible Arithmetic Processing
García Chamizo, Juan Manuel; Mora Pascual, Jerónimo Manuel; Mora Mora, Higinio; Signes Pont, María Teresa
2003-01-01
A new operation model of flexible calculation that allows us to adjust the operation delay depending on the available time is presented. The operation method design uses look-up tables and progressive construction of the result. The increase in the operators’ granularity opens up new possibilities in calculation methods and microprocessor design. This methodology, together with the advances in technology, enables the functions of an arithmetic unit to be implemented on the basis of techniques...
Time-Precision Flexible Arithmetic Unit
García Chamizo, Juan Manuel; Mora Pascual, Jerónimo Manuel; Mora Mora, Higinio; Signes Pont, María Teresa
2003-01-01
A new conception of flexible calculation that allows us to adjust an operation depending on the available time computation is presented. The proposed arithmetic unit is based on this principle. It contains a control operation module that determines the process time of each calculation. The operation method design uses precalculated data stored in look-up tables, which provide, above all, quality results and systematization in the implementation of low level primitives that set parameters for ...
Coinductive Formal Reasoning in Exact Real Arithmetic
Niqui, Milad
2008-01-01
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by coinductive streams. The algorithms work on coinductive stream of M\\"{o}bius maps and form the basis of the Edalat--Potts exact real arithmetic. We use the machinery of the Coq proof assistant for the coinductive types to present the formalisation. The form...
Arithmetic Operators for Pairing-Based Cryptography
Beuchat, Jean-Luc; Brisebarre, Nicolas; Detrey, Jérémie; Okamoto, Eiji
2007-01-01
Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we first study an accelerator for the eta_T pairing over F_3[x]/(x^97 + x^12 + 2). Our architecture is based on a unified arithmetic operator which performs addition, multiplication, and cubing over F_3^9...
A common Misconception about the Categorical Arithmetic
Raguní, Giuseppe
2016-01-01
Although the categorical arithmetic is not effectively axiomatizable, the belief that the incompleteness Theorems can be apply to it is fairly common. Furthermore, the so-called "essential" (or "inherent") semantic incompleteness of the second-order Logic that can be deduced by these same Theorems does not imply the standard semantic incompleteness that can be derived using the Loewenheim-Skolem or the compactness Theorem. This state of affairs has its origins in an incorrect and misinterpret...
Arithmetic expressions optimisation using dual polarity property
Moraga Claudio; Stanković Radomir S.; Janković Dragan
2003-01-01
A method for optimisation of fixed polarity arithmetic expressions (FPAEs) based on dual polarity is proposed. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using the dual polarity route. Using one-bit check carries out conversion from one FPAE to another. Each term in an FPAE is processed by the proposed processing rule. Terms, which differ in a single position, can be subs...
Residues : The gateway to higher arithmetic I
Siebeneicher, Christian
2012-01-01
Residues to a given modulus have been introduced to mathematics by Carl Friedrich Gauss with the definition of congruence in the `Disquisitiones Arithmeticae'. Their extraordinary properties provide the basis for a change of paradigm in arithmetic. By restricting residues to remainders left over by divison Peter Gustav Lejeune Dirichlet - Gauss's successor in G\\"ottingen - eliminated in his `Lectures on number theory' the fertile concept of residues and attributed with the number-theoretic ap...
Arithmetic functions in torus and tree networks
Bhanot, Gyan; Blumrich, Matthias A.; Chen, Dong; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Philip; Steinmacher-Burow, Burkhard D.; Vranas, Pavlos M.
2007-12-25
Methods and systems for performing arithmetic functions. In accordance with a first aspect of the invention, methods and apparatus are provided, working in conjunction of software algorithms and hardware implementation of class network routing, to achieve a very significant reduction in the time required for global arithmetic operation on the torus. Therefore, it leads to greater scalability of applications running on large parallel machines. The invention involves three steps in improving the efficiency and accuracy of global operations: (1) Ensuring, when necessary, that all the nodes do the global operation on the data in the same order and so obtain a unique answer, independent of roundoff error; (2) Using the topology of the torus to minimize the number of hops and the bidirectional capabilities of the network to reduce the number of time steps in the data transfer operation to an absolute minimum; and (3) Using class function routing to reduce latency in the data transfer. With the method of this invention, every single element is injected into the network only once and it will be stored and forwarded without any further software overhead. In accordance with a second aspect of the invention, methods and systems are provided to efficiently implement global arithmetic operations on a network that supports the global combining operations. The latency of doing such global operations are greatly reduced by using these methods.
Duverne, Sandrine; Lemaire, Patrick; Michel, Bernard François
2003-08-01
Three groups of healthy younger adults, healthy older adults, and probable AD patients, performed an addition/number comparison task. They compared 128 couples of additions and numbers (e.g., 4 + 9 15) and had to identify the largest item for each problem by pressing one of two buttons located under each item. Manipulations of problem characteristics (i.e., problem difficulty and splits between correct sums and proposed numbers) enabled us to examine strategy selection and specific arithmetic fact retrieval processes. Results showed that arithmetic facts retrieval processes, which were spared with aging, were impaired in AD patients. However, AD patients were able to switch between strategies across trials according to problem characteristics as well as healthy older adults, and less systematically than healthy younger adults. We discuss implications of these findings for further understanding AD-related differences in arithmetic in particular, and problem solving in general. PMID:12907175
Sets of integers that do not contain long arithmetic progressions
O'Bryant, Kevin
2008-01-01
In 1946, Behrend gave a construction of dense finite sets of integers that do not contain 3-term arithmetic progressions. In 1961, Rankin generalized Behrend's construction to sets avoiding k-term arithmetic progressions, and in 2008 Elkin refined Behrend's 3-term construction. In this work, we combine Elkin's refinement and Rankin's generalization. Arithmetic progressions are handled as a special case of polynomial progressions. In 1946, Behrend gave a construction of dense finite sets of in...
Are individual differences in arithmetic fact retrieval related to inhibition?
Bellon, Elien
2016-01-01
Although it has been proposed that inhibition is related to individual differences in mathematical achievement, it is not clear how it is related to specific aspects of mathematical skills, such as arithmetic fact retrieval. The present study therefore investigated the association between inhibition and arithmetic fact retrieval and further examined the unique role of inhibition in individual differences in arithmetic fact retrieval, in addition to numerical magnitude processin...
Aztec arithmetic: positional notation and area calculation.
Harvey, H R; Williams, B J
1980-10-31
Texcocan-Aztec peoples in the Valley of Mexico used both picture symbols and lines and dots for numerical notation. Decipherment and analysis of mid-16th-century native pictorial land documents from the Texcocan region indicate that the line-and-dot system incorporated a symbol for zero and used position to ascribe values. Positional line-and-dot notation was used to record areas of agricultural fields, and analysis of the documentary data suggests that areas were calculated arithmetically. These findings demonstrate that neither positional notation nor the zero were unique to the Maya area, and they imply an equally sophisticated mathematical development among the Aztecs. PMID:17841389
A Geometric Characterization of Arithmetic Varieties
Indian Academy of Sciences (India)
Kapil Hari Paranjape
2002-08-01
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.
Arithmetic after School: How Do Adults' Mental Arithmetic Abilities Evolve with Age?
Charron, Camilo; Fischer, Jean-Paul; Meljac, Claire
2008-01-01
To date, few studies have investigated the evolution of problem solving and general numeracy abilities during adulthood: skills that have obvious social importance. In this research, evolutions in adults' mental arithmetic skills were investigated using data from the IVQ 2004 French national survey, which tested 9,185 adults aged between 18 and…
Iglesias-Sarmiento, Valentín; Deaño, Manuel
2016-01-01
This study analyzed the cognitive functioning underlying arithmetical difficulties and explored the predictors of arithmetic achievement in the last three grades of Spanish Primary Education. For this purpose, a group of 165 students was selected and divided into three groups of arithmetic competence: Mathematical Learning Disability group (MLD, n = 27), Low Achieving group (LA, n = 39), and Typical Achieving group (TA, n = 99). Students were assessed in domain-general abilities (working memory and PASS cognitive processes), and numerical competence (counting and number processing) during the last two months of the academic year. Performance of children from the MLD group was significantly poorer than that of the LA group in writing dictated Arabic numbers (d = -0.88), reading written verbal numbers (d = -0.84), transcoding written verbal numbers to Arabic numbers (-0.75) and comprehension of place value (d = -0.69), as well as in simultaneous (d = -0.62) and successive (d = -0.59) coding. In addition, a specific developmental sequence was observed in both groups, the implications of which are discussed. Hierarchical regression analysis revealed simultaneous coding (β = .47, t(155) = 6.18, p < .001) and number processing (β = .23, t(155) = 3.07, p < .01) as specific predictors of arithmetical performance. PMID:27320030
Marghetis, Tyler; Núñez, Rafael; Bergen, Benjamin K
2014-01-01
Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental "number-line", the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial-arithmetical bias, moreover, was distinct from-but correlated with-individuals' spatial-numerical biases (i.e., spatial-numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes. PMID:25051274
Outer Billiards, Arithmetic Graphs, and the Octagon
Schwartz, Richard Evan
2010-01-01
Outer Billiards is a geometrically inspired dynamical system based on a convex shape in the plane. When the shape is a polygon, the system has a combinatorial flavor. In the polygonal case, there is a natural acceleration of the map, a first return map to a certain strip in the plane. The arithmetic graph is a geometric encoding of the symbolic dynamics of this first return map. In the case of the regular octagon, the case we study, the arithmetic graphs associated to periodic orbits are polygonal paths in R^8. We are interested in the asymptotic shapes of these polygonal paths, as the period tends to infinity. We show that the rescaled limit of essentially any sequence of these graphs converges to a fractal curve that simultaneously projects one way onto a variant of the Koch snowflake and another way onto a variant of the Sierpinski carpet. In a sense, this gives a complete description of the asymptotic behavior of the symbolic dynamics of the first return map. What makes all our proofs work is an efficient...
FPGA Based Quadruple Precision Floating Point Arithmetic for Scientific Computations
Directory of Open Access Journals (Sweden)
Mamidi Nagaraju
2012-09-01
Full Text Available In this project we explore the capability and flexibility of FPGA solutions in a sense to accelerate scientific computing applications which require very high precision arithmetic, based on IEEE 754 standard 128-bit floating-point number representations. Field Programmable Gate Arrays (FPGA is increasingly being used to design high end computationally intense microprocessors capable of handling floating point mathematical operations. Quadruple Precision Floating-Point Arithmetic is important in computational fluid dynamics and physical modelling, which require accurate numerical computations. However, modern computers perform binary arithmetic, which has flaws in representing and rounding the numbers. As the demand for quadruple precision floating point arithmetic is predicted to grow, the IEEE 754 Standard for Floating-Point Arithmetic includes specifications for quadruple precision floating point arithmetic. We implement quadruple precision floating point arithmetic unit for all the common operations, i.e. addition, subtraction, multiplication and division. While previous work has considered circuits for low precision floating-point formats, we consider the implementation of 128-bit quadruple precision circuits. The project will provide arithmetic operation, simulation result, hardware design, Input via PS/2 Keyboard interface and results displayed on LCD using Xilinx virtex5 (XC5VLX110TFF1136 FPGA device.
Numeral Writing Skill and Elementary Arithmetic Mental Calculations
Johansson, Bo S.
2005-01-01
The paper reports three studies addressing the role of numeral writing for arithmetic performance. About 650 children in the age range 5-7 years participated in the studies. The results demonstrate a positive correlation between number of digits correctly written and number of arithmetic problems solved. The correlations between number of reversed…
The Arithmetic Tie Effect Is Mainly Encoding-based.
Blankenberger, Sven
2001-01-01
Examined two possible explanations for the arithmetic tie effect: faster encoding of tie problems versus faster access to arithmetic facts. Found that the tie effect vanished with heterogeneous addition problems, and for seven out of eight participants, the effect vanished with heterogeneous multiplication problems. Concludes that the tie effect…
Coinductive Formal Reasoning in Exact Real Arithmetic
Niqui, Milad
2008-01-01
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by coinductive streams. The algorithms work on coinductive stream of M\\"obius maps and form the basis of the Edalat--Potts exact real arithmetic. We use the machinery of the Coq proof assistant for the coinductive types to present the formalisation. The formalised algorithms are only partially productive, i.e., they do not output provably infinite streams for all possible inputs. We show how to deal with this partiality in the presence of syntactic restrictions posed by the constructive type theory of Coq. Furthermore we show that the type theoretic techniques that we develop are compatible with the semantics of the algorithms as continuous maps on real numbers. The resulting Coq formalisation is available for public download.
On the pullback of an arithmetic theta function
Kudla, Stephen
2011-01-01
In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space $\\Cal C$ of elliptic curves with CM by the ring of integers $\\OK$ in an imaginary quadratic field $\\kay$, on the one hand, and those associated to cycles on the arithmetic surface $\\M$ parametrizing 2-dimensional abelian varieties with an action of the maximal order $O_B$ in an indefinite quaternion algebra $B$ over $\\Q$, on the other. We show that the arithmetic degree of the pullback to $Cal C$ of the arithmetic theta function of weight 3/2 valued in $\\hat CH^1(\\M)$ can be expressed as a linear combination of arithmetic theta functions of weight 1 for $\\Cal C$ and unary theta series. This identity can be viewed as an arithmetic seesaw identity. In addition, we show that the arithmetic theta series of weight 1 coincide with the central derivative of certain incoherent Eisenstein series for SL(2)/Q, generalizing earlier joint work with M. Rapoport for the case of a ...
Similarity interference in learning and retrieving arithmetic facts.
De Visscher, A; Noël, M-P
2016-01-01
Storing the solution of simple calculations in long-term memory is an important learning in primary school that is subsequently essential in adult daily living. While most children succeed in storing arithmetic facts to which they have been trained at school, huge individual differences are reported, particularly in children with developmental dyscalculia, who show a severe and persistent deficit in arithmetic facts learning. This chapter reports important advances in the understanding of the development of an arithmetic facts network and focuses on the detrimental effect of similarity interference. First, at the retrieval stage, connectionist models highlighted that the similarity of the neighbor problems in the arithmetic facts network creates interference. More recently, the similarity interference during the learning stage was pointed out in arithmetic facts learning. The interference parameter, that captures the proactive interference that a problem receives from previously learned problems, was shown as a substantial determinant of the performance across multiplication problems. This proactive interference was found both in children and adults and showed that when a problem is highly similar to previously learned ones, it is more difficult to remember it. Furthermore, the sensitivity to this similarity interference determined individual differences in the learning and retrieving of arithmetic facts, giving new insights for interindividual differences. Regarding the atypical development, hypersensitivity-to-interference in memory was related to arithmetic facts deficit in a single case of developmental dyscalculia and in a group of fourth-grade children with low arithmetic facts knowledge. In sum, the impact of similarity interference is shown in the learning stage of arithmetic facts and concerns the typical and atypical development.
A novel operation associated with Gauss' arithmetic-geometric means
Tanimoto, Shinji
2007-01-01
The arithmetic mean is the mean for addition and the geometric mean is that for multiplication. Then what kind of binary operation is associated with the arithmetic-geometric mean (AGM) due to C. F. Gauss? If it is possible to construct an arithmetic operation such that AGM is the mean for this operation, it can be regarded as an intermediate operation between addition and multiplication in view of the meaning of AGM. In this paper such an operation is introduced and several of its algebraic ...
Frege, Dedekind, and Peano on the foundations of arithmetic
Gillies, Donald
2013-01-01
First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosop
Pricing Arithmetic Asian Options under the CEV Process
Directory of Open Access Journals (Sweden)
Bin Peng
2010-12-01
Full Text Available This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.
IBM system/360 assembly language interval arithmetic software
Phillips, E. J.
1972-01-01
Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.
Conference on Number Theory and Arithmetic Geometry
Silverman, Joseph; Stevens, Glenn; Modular forms and Fermat’s last theorem
1997-01-01
This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, ...
Development of Superconductive Arithmetic and Logic Devices
International Nuclear Information System (INIS)
Due to the very fast switching speed of Josephson junctions, superconductive digital circuit has been a very good candidate fur future electronic devices. High-speed and Low-power microprocessor can be developed with Josephson junctions. As a part of an effort to develop superconductive microprocessor, we have designed an RSFQ 4-bit ALU (Arithmetic Logic Unit) in a pipelined structure. To make the circuit work faster, we used a forward clocking scheme. This required a careful design of timing between clock and data pulses in ALU. The RSFQ 1-bit block of ALU used in this work consisted of three DC current driven SFQ switches and a half-adder. We successfully tested the half adder cell at clock frequency up to 20 GHz. The switches were commutating output ports of the half adder to produce AND, OR, XOR, or Add functions. For a high-speed test, we attached switches at the input ports to control the high-speed input data by low-frequency pattern generators. The output in this measurement was an eye-diagram. Using this setup, 1-bit block of Alum was successfully tested up to 40 GHz. An RSFQ 4-bit ALU was fabricated and tested. The circuit worked at 5 GHz. The circuit size of the 4-bit ALU was 3 mm X 1.5 mm, fitting in a 5 mm X 5 mm chip.
On the arithmetic of crossratios and generalised Mertens' formulas
Parkkonen, Jouni; Paulin, Frédéric
2013-01-01
We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension up to 5. We prove generalisations of Mertens' formula for quadratic imaginary number fields and definite quaternion algebras over the rational numbers, counting results of quadratic irrationals with respect to two different natural complexities, and counting results of representations of (algebraic) int...
Neurofunctional Differences Associated with Arithmetic Processing in Turner Syndrome
Kesler, Shelli R.; Menon, Vinod; Reiss, Allan L.
2005-01-01
Turner syndrome (TS) is a neurogenetic disorder characterized by the absence of one X chromosome in a phenotypic female. Individuals with TS are at risk for impairments in mathematics. We investigated the neural mechanisms underlying arithmetic processing in TS. Fifteen subjects with TS and 15 age-matched typically developing controls were scanned using functional MRI while they performed easy (two-operand) and difficult (three-operand) versions of an arithmetic processing task. Both groups a...
Finite and Infinite Arithmetic Progressions Related to Beta-Expansion
Directory of Open Access Journals (Sweden)
Bing Li
2014-01-01
Full Text Available Let 1<β<2 and ε(x,β be the β-expansion of x∈[0,1. Denote by Aβ(x the set of positions where the digit 1 appears in ε(x,β. We consider the sets of points x such that Aβ(x contains arbitrarily long arithmetic progressions and includes infinite arithmetic progressions, respectively. Their sizes are investigated from the topological, metric, and dimensional viewpoints.
Finite Field Arithmetic Architecture Based on Cellular Array
Directory of Open Access Journals (Sweden)
Kee-Won Kim
2015-05-01
Full Text Available Recently, various finite field arithmetic structures are introduced for VLSI circuit implementation on cryptosystems and error correcting codes. In this study, we present an efficient finite field arithmetic architecture based on cellular semi-systolic array for Montgomery multiplication by choosing a proper Montgomery factor which is highly suitable for the design on parallel structures. Therefore, our architecture has reduced a time complexity by 50% compared to typical architecture.
Guest Editors' Introduction: Special Section on Computer Arithmetic
DEFF Research Database (Denmark)
Nannarelli, Alberto; Seidel, Peter-Michael; Tang, Ping Tak Peter
2014-01-01
The articles in this special issue focus on current trends and developments in the field of computer arithmetic. This is a field that encompasses the definition and standardization of arithmetic system for computers. The field also deals with issues of hardware and software implementations and th...... engineering. Advances in this field span from being highly theoretical (for instance, new exotic number systems) to being highly practical (for instance, new floating-point units for microprocessors)....
Torsionfree Sheaves over a Nodal Curve of Arithmetic Genus One
Indian Academy of Sciences (India)
Usha N Bhosle; Indranil Biswas
2008-02-01
We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over $\\mathbb{C}$. Let be a nodal curve of arithmetic genus one defined over $\\mathbb{R}$, with exactly one node, such that does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsionfree sheaves over of even rank. We also classify all isomorphism classes of real algebraic torsionfree sheaves over of rank one.
Crystallization of space: Space-time fractals from fractal arithmetics
Aerts, Diederik; Kuna, Maciej
2016-01-01
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated with appropriate Lie groups. The construction is illustrated by explicit examples.
Adams operations on higher arithmetic K-theory
DEFF Research Database (Denmark)
Feliu, Elisenda
2010-01-01
We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The de¿nition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy ¿ber of the reg......We construct Adams operations on the rational higher arithmetic K-groups of a proper arithmetic variety. The de¿nition applies to the higher arithmetic K-groups given by Takeda as well as to the groups suggested by Deligne and Soulé, by means of the homotopy groups of the homotopy ¿ber...... of the regulator map. They are compatible with the Adams operations on algebraic K-theory. The de¿nition relies on the chain morphism representing Adams operations in higher algebraic K-theory given previously by the author. It is shown that this chain morphism commutes strictly with the representative...
Number processing and arithmetic skills in children with cochlear implants
Pixner, Silvia; Leyrer, Martin; Moeller, Korbinian
2014-01-01
Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties. PMID:25566152
A New Fast Modular Arithmetic Method in Public Key Cryptography
Institute of Scientific and Technical Information of China (English)
WANG Bangju; ZHANG Huanguo
2006-01-01
Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modulus algorithm is proposed to improve the speed of the modular arithmetic in the presented paper. For changeable modulus algorithm, when modular computation of modulo n is difficult, it can be realized by computation of modulo n-1 and n-2 on the perquisite of easy modular computations of modulo n-1 and modulo n-2. The conclusion is that the new method is better than the direct method by computing the modular arithmetic operation with large modulus. Especially, when computations of modulo n-1 and modulo n-2 are easy and computation of modulo n is difficult, this new method will be faster and has more advantages than other algorithms on modular arithmetic. Lastly, it is suggested that the proposed method be applied in public key cryptography based on modular multiplication and modular exponentiation with large integer modulus effectively
Optimization Approaches for Designing Quantum Reversible Arithmetic Logic Unit
Haghparast, Majid; Bolhassani, Ali
2016-03-01
Reversible logic is emerging as a promising alternative for applications in low-power design and quantum computation in recent years due to its ability to reduce power dissipation, which is an important research area in low power VLSI and ULSI designs. Many important contributions have been made in the literatures towards the reversible implementations of arithmetic and logical structures; however, there have not been many efforts directed towards efficient approaches for designing reversible Arithmetic Logic Unit (ALU). In this study, three efficient approaches are presented and their implementations in the design of reversible ALUs are demonstrated. Three new designs of reversible one-digit arithmetic logic unit for quantum arithmetic has been presented in this article. This paper provides explicit construction of reversible ALU effecting basic arithmetic operations with respect to the minimization of cost metrics. The architectures of the designs have been proposed in which each block is realized using elementary quantum logic gates. Then, reversible implementations of the proposed designs are analyzed and evaluated. The results demonstrate that the proposed designs are cost-effective compared with the existing counterparts. All the scales are in the NANO-metric area.
Training of Attention in Children With Low Arithmetical Achievement
Directory of Open Access Journals (Sweden)
Maria Guarnera
2014-05-01
Full Text Available This study focuses on the role of attentional processes in arithmetical skills and examines if training of basic attentive skills may improve also working memory abilities reducing arithmetic difficulties. In order to study the efficacy of attentional treatment in arithmetic achievement and in enhancing working memory abilities a test-treatment-retest quasi experimental design was adopted. The research involved 14 children, attending fourth and fifth grades, with Arithmetical Learning Disabilities (ALD assigned to experimental and control conditions. The numerical comprehension and calculation processes were assessed using the ABCA battery (Lucangeli, Tressoldi, & Fiore, 1998. Attentional abilities were evaluated using a multitask computerized assessment battery Attenzione e Concentrazione (Di Nuovo, 2000. WM abilities were evaluated by Listening span task, Digit span backward, Making verbal trails and Making colour trails. The results showed that intensive computerized attention training increased basic attentive skills and arithmetical performances with respect to numeric system in children with ALD. No effect on working memory abilities was found. Results are also important from a clinical perspective, since they may suggest strategies for planning individualized training programs.
Perceiving fingers in single-digit arithmetic problems
Directory of Open Access Journals (Sweden)
Ilaria eBerteletti
2015-03-01
Full Text Available In this study, we investigate in children the neural underpinnings of finger representation and finger movement involved in single-digit arithmetic problems. Evidence suggests that finger representation and finger-based strategies play an important role in learning and understanding arithmetic. Because different operations rely on different networks, we compared activation for subtraction and multiplication problems in independently localized finger somatosensory and motor areas and tested whether activation was related to skill. Brain activations from children between 8 and 13 years of age revealed that only subtraction problems significantly activated finger motor areas, suggesting reliance on finger-based strategies. In addition, larger subtraction problems yielded greater somatosensory activation than smaller problems, suggesting a greater reliance on finger representation for larger numerical values. Interestingly, better performance in subtraction problems was associated with lower activation in the finger somatosensory area. Our results support the importance of fine-grained finger representation in arithmetical skill and are the first neurological evidence for a functional role of the somatosensory finger area in proficient arithmetical problem solving, in particular for those problems requiring quantity manipulation. From an educational perspective, these results encourage investigating whether different finger-based strategies facilitate arithmetical understanding and encourage educational practices aiming at integrating finger representation and finger-based strategies as a tool for instilling stronger numerical sense.
Lossless Image Compression Based on Multiple-Tables Arithmetic Coding
Directory of Open Access Journals (Sweden)
Rung-Ching Chen
2009-01-01
Full Text Available This paper is intended to present a lossless image compression method based on multiple-tables arithmetic coding (MTAC method to encode a gray-level image f. First, the MTAC method employs a median edge detector (MED to reduce the entropy rate of f. The gray levels of two adjacent pixels in an image are usually similar. A base-switching transformation approach is then used to reduce the spatial redundancy of the image. The gray levels of some pixels in an image are more common than those of others. Finally, the arithmetic encoding method is applied to reduce the coding redundancy of the image. To promote high performance of the arithmetic encoding method, the MTAC method first classifies the data and then encodes each cluster of data using a distinct code table. The experimental results show that, in most cases, the MTAC method provides a higher efficiency in use of storage space than the lossless JPEG2000 does.
Design and Implementation of Fixed Point Arithmetic Unit
Directory of Open Access Journals (Sweden)
S Ramanathan
2016-06-01
Full Text Available This paper aims at Implementation of Fixed Point Arithmetic Unit. The real number is represented in Qn.m format where n is the number of bits to the left of the binary point and m is the number of bits to the right of the binary point. The Fixed Point Arithmetic Unit was designed using Verilog HDL. The Fixed Point Arithmetic Unit incorporates adder, multiplier and subtractor. We carried out the simulations in ModelSim and Cadence IUS, used Cadence RTL Compiler for synthesis and used Cadence SoC Encounter for physical design and targeted 180 nm Technology for ASIC implementation. From the synthesis result it is found that our design consumes 1.524 mW of power and requires area 20823.26 μm2 .
Age-related differences in arithmetic strategy sequential effects.
Lemaire, Patrick
2016-03-01
In this article, I review a series of new findings concerning how age-related changes in strategic variations are modulated by sequential effects. Sequential effects refer to how strategy selection and strategy execution on current problems are influenced by which strategy is used on immediately preceding problems. Two sequential effects during strategy selection (i.e., strategy revisions and strategy perseverations) and during strategy execution (i.e., strategy switch costs and modulations of poorer strategy effects) are presented. I also discuss how these effects change with age during adulthood. These phenomena are important, as they shed light on arithmetic processes and how these processes change with age during adulthood. In particular, they speak to the role of executive control while participants select and execute arithmetic strategies. Finally, I discuss the implications of sequential effects for theories of strategies and of arithmetic.
Relativity of arithmetics as a fundamental symmetry of physics
Czachor, Marek
2014-01-01
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters `plus' or `times' one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in natural sciences. A change of realization of arithmetics, without altering the remaining structures of a given equation, plays the same role as a symmetry transformation. An appropriate construction of arithmetics turns out to be particularly important for dynamical systems in fractal space-times. Simple examples from classical and quantum, relativistic and nonrelativistic physics are discussed.
Reason's Nearest Kin Philosophies of Arithmetic from Kant to Carnap
Potter, Michael
2000-01-01
How do we account for the truth of arithmetic? And if it does not depend for its truth on the way the world is, what constrains the world to conform to arithmetic? Reason's Nearest Kin is a critical examination of the astonishing progress made towards answering these questions from the late nineteenth to the mid-twentieth century. In the space of fifty years Frege, Dedekind, Russell, Wittgenstein, Ramsey, Hilbert, and Carnap developed accounts of the content of arithmeticthat were brilliantly original both technically and philosophically. Michael Potter's innovative study presents them all as
Algebraic and arithmetic area for $m$ planar Brownian paths
Desbois, Jean; Ouvry, Stephane
2011-01-01
The leading and next to leading terms of the average arithmetic area $$ enclosed by $m\\to\\infty$ independent closed Brownian planar paths, with a given length $t$ and starting from and ending at the same point, is calculated. The leading term is found to be $ \\sim {\\pi t\\over 2}\\ln m$ and the $0$-winding sector arithmetic area inside the $m$ paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed.
Algebraic and arithmetic area for m planar Brownian paths
International Nuclear Information System (INIS)
The leading and next to leading terms of the average arithmetic area (S(m)) enclosed by m→∞ independent closed Brownian planar paths, with a given length t and starting from and ending at the same point, are calculated. The leading term is found to be (S(m)) ∼ (πt/2)lnm and the 0-winding sector arithmetic area inside the m paths is subleading in the asymptotic regime. A closed form expression for the algebraic area distribution is also obtained and discussed
Computer arithmetic and validity theory, implementation, and applications
Kulisch, Ulrich
2013-01-01
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic capability of the computer can be enhanced. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties
24 CFR Appendix E to Part 3500 - Arithmetic Steps
2010-04-01
... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Arithmetic Steps E Appendix E to Part 3500 Housing and Urban Development Regulations Relating to Housing and Urban Development (Continued) OFFICE OF ASSISTANT SECRETARY FOR HOUSING-FEDERAL HOUSING COMMISSIONER, DEPARTMENT OF HOUSING...
Beginners' Progress in Early Arithmetic in the Swedish Compulsory School
Eriksson, Gota
2008-01-01
This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of "multiple clinical…
Toward a Student-Centred Process of Teaching Arithmetic
Eriksson, Gota
2011-01-01
This article describes a way toward a student-centred process of teaching arithmetic, where the content is harmonized with the students' conceptual levels. At school start, one classroom teacher is guided in recurrent teaching development meetings in order to develop teaching based on the students' prerequisites and to successively learn the…
Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions
Indian Academy of Sciences (India)
BISWAJYOTI SAHA
2016-08-01
For an arithmetical function $f$ with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the $\\sum_{n\\leq N}$ f(n)$ with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.
Optimal Inequalities for Generalized Logarithmic, Arithmetic, and Geometric Means
Chu Yu-Ming; Long Bo-Yong
2010-01-01
For , the generalized logarithmic mean , arithmetic mean , and geometric mean of two positive numbers and are defined by , for , , for , , and , , for , and , , for , and , , and , respectively. In this paper, we find the greatest value (or least value , resp.) such that the inequality (or , resp.) holds for (or , resp.) and all with .
Sex Differences in Arithmetical Performance Scores: Central Tendency and Variability
Martens, R.; Hurks, P. P. M.; Meijs, C.; Wassenberg, R.; Jolles, J.
2011-01-01
The present study aimed to analyze sex differences in arithmetical performance in a large-scale sample of 390 children (193 boys) frequenting grades 1-9. Past research in this field has focused primarily on average performance, implicitly assuming homogeneity of variance, for which support is scarce. This article examined sex differences in…
A Stock Pricing Model Based on Arithmetic Brown Motion
Institute of Scientific and Technical Information of China (English)
YAN Yong-xin; HAN Wen-xiu
2001-01-01
This paper presents a new stock pricing model based on arithmetic Brown motion. The model overcomes the shortcomings of Gordon model completely. With the model investors can estimate the stock value of surplus companies, deficit companies, zero increase companies and bankrupt companies in long term investment or in short term investment.
Effects of Numerical Surface Form in Arithmetic Word Problems
Orrantia, Josetxu; Múñez, David; San Romualdo, Sara; Verschaffel, Lieven
2015-01-01
Adults' simple arithmetic performance is more efficient when operands are presented in Arabic digit (3 + 5) than in number word (three + five) formats. An explanation provided is that visual familiarity with digits is higher respect to number words. However, most studies have been limited to single-digit addition and multiplication problems. In…
An arithmetic regularity lemma, an associated counting lemma, and applications
Green, Ben
2010-01-01
Szemer\\'edi's regularity lemma can be viewed as a rough structure theorem for arbitrary dense graphs, decomposing such graphs into a structured piece (a partition into cells with edge densities), a small error (corresponding to irregular cells), and a uniform piece (the pseudorandom deviations from the edge densities). We establish an \\emph{arithmetic regularity lemma} that similarly decomposes bounded functions $f : [N] \\to \\C$, into a (well-equidistributed, virtual) $s$-step nilsequence, an error which is small in $L^2$ and a further error which is miniscule in the Gowers $U^{s+1}$-norm, where $s \\geq 1$ is a parameter. We then establish a complementary \\emph{arithmetic counting lemma} that counts arithmetic patterns in the nilsequence component of $f$. We provide a number of applications of these lemmas: a proof of Szemer\\'edi's theorem on arithmetic progressions, a proof of a conjecture of Bergelson, Host and Kra, and a generalisation of certain results of Gowers and Wolf. Our result is dependent on the i...
Dark energy as a manifestation of nontrivial arithmetic
Czachor, Marek
2016-01-01
Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, $\\mathbb{R}_+^4$ and $(-L/2,L/2)^4$, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the `natural' Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the non-Diophantine formalism. When the `natural' formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating e...
Arithmetic procedural knowledge: a cortico-subcortical circuit.
Roşca, Elena Cecilia
2009-12-11
The disturbances of arithmetic procedural knowledge form a heterogeneous picture, in which we can distinguish "memory" impairments and "monitoring" problems. Patients with "memory" disturbances reported in the literature present left parietal lesions, while "monitoring" impairments have been assumed to be due to frontal damage. Procedural knowledge has been less investigated in basal ganglia lesions, in which there has been no analysis of procedural impairments. The present study investigates and compares the patterns of acalculia in two patients, one with a left parietal lesion and the other with a left basal ganglia lesion. The patients were tested on a broad range of neuropsychological abilities, with the main focus on number processing and calculation. The results show many similarities between their deficits, with some difficulties in simple arithmetic, arithmetical rules and mental and written complex calculations. The errors made in complex mental and written calculations were due to memory-based procedural impairments in both patients. These findings, corroborated with other studies reported in the literature, suggest the existence of a fronto-parieto-subcortical circuit responsible for arithmetic complex calculations and that procedural knowledge relies on a visuo-spatial sketchpad that contains a representation of each sub-step of the procedure. PMID:19765552
Nonsymbolic, Approximate Arithmetic in Children: Abstract Addition Prior to Instruction
Barth, Hilary; Beckmann, Lacey; Spelke, Elizabeth S.
2008-01-01
Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this…
Arithmetic Word-Problem-Solving in Huntington's Disease
Allain, P.; Verny, C.; Aubin, G.; Pinon, K.; Bonneau, D.; Dubas, F.; Gall, D.L.
2005-01-01
The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…
Neuroanthropological Understanding of Complex Cognition – Numerosity and Arithmetics
Directory of Open Access Journals (Sweden)
Zarja Mursic
2013-10-01
Full Text Available Humankind has a long evolutionary history. When we are trying to understand human complex cognition, it is as well important to look back to entire evolution. I will present the thesis that our biological predispositions and culture, together with natural and social environment, are tightly connected. During ontogenetically development we are shaped by various factors, and they enabled humans to develop some aspects of complex cognition, such as mathematics.In the beginning of the article I present the importance of natural and cultural evolution in other animals. In the following part, I briefly examine the field of mathematics – numerosity and arithmetic. Presentation of comparative animal studies, mainly made on primates, provides some interesting examples in animals’ abilities to separate between different quantities. From abilities for numerosity in animals I continue to neuroscientific studies of humans and our ability to solve simple arithmetic tasks. I also mention cross-cultural studies of arithmetic skills. In the final part of the text I present the field neuroanthropology as a possible new pillar of cognitive science. Finally, it is important to connect human evolution and development with animal cognition studies, but as well with cross-cultural studies in shaping of human ability for numerosity and arithmetic.
Park, Joonkoo; Brannon, Elizabeth M
2014-10-01
A nonverbal primitive number sense allows approximate estimation and mental manipulations on numerical quantities without the use of numerical symbols. In a recent randomized controlled intervention study in adults, we demonstrated that repeated training on a non-symbolic approximate arithmetic task resulted in improved exact symbolic arithmetic performance, suggesting a causal relationship between the primitive number sense and arithmetic competence. Here, we investigate the potential mechanisms underlying this causal relationship. We constructed multiple training conditions designed to isolate distinct cognitive components of the approximate arithmetic task. We then assessed the effectiveness of these training conditions in improving exact symbolic arithmetic in adults. We found that training on approximate arithmetic, but not on numerical comparison, numerical matching, or visuo-spatial short-term memory, improves symbolic arithmetic performance. In addition, a second experiment revealed that our approximate arithmetic task does not require verbal encoding of number, ruling out an alternative explanation that participants use exact symbolic strategies during approximate arithmetic training. Based on these results, we propose that nonverbal numerical quantity manipulation is one key factor that drives the link between the primitive number sense and symbolic arithmetic competence. Future work should investigate whether training young children on approximate arithmetic tasks even before they solidify their symbolic number understanding is fruitful for improving readiness for math education. PMID:25044247
Interval arithmetic operations for uncertainty analysis with correlated interval variables
Institute of Scientific and Technical Information of China (English)
Chao Jiang; Chun-Ming Fu; Bing-Yu Ni; Xu Han
2016-01-01
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analy-sis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional par-allelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addi-tion, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
Arithmetic Motivic Poincar\\'e series of toric varieties
Pablos, Helena Cobo
2010-01-01
The arithmetic motivic Poincar\\'e series of a variety $V$ defined over a field of characteristic zero, is an invariant of singularities which was introduced by Denef and Loeser by analogy with the Serre-Oesterl\\'e series in arithmetic geometry. They proved that this motivic series has a rational form which specializes to the Serre-Oesterl\\'e series when $V$ is defined over the integers. This invariant, which is known explicitly for a few classes of singularities, remains quite mysterious. In this paper we study this motivic series when $V$ is an affine toric variety. We obtain a formula for the rational form of this series in terms of the Newton polyhedra of the ideals of sums of combinations associated to the minimal system of generators of the semigroup of the toric variety. In particular, we deduce explicitly a finite set of candidate poles for this invariant.
INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
郭书祥; 吕震宙
2001-01-01
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters,median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
Executable Set Theory and Arithmetic Encodings in Prolog
Tarau, Paul
2008-01-01
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip . First, ranking and unranking functions for some "mathematically elegant" data types in the universe of Hereditarily Finite Sets with Urelements are provided, resulting in arithmetic encodings for powersets, hypergraphs, ordinals and choice functions. After implementing a digraph representation of Hereditarily Finite Sets we define {\\em decoration functions} that can recover well-founded sets from encodings of their associated acyclic digraphs. We conclude with an encoding of arbitrary digraphs and discuss a concept of duality induced by the set membership relation. In the process, we uncover the surprising possibility of internally sharing isomorphic objects, independently of their language level types and meanings.
Memristor-based Circuits for Performing Basic Arithmetic Operations
Merrikh-Bayat, Farnood
2010-01-01
In almost all of the currently working circuits, especially in analog circuits implementing signal processing applications, basic arithmetic operations such as multiplication, addition, subtraction and division are performed on values which are represented by voltages or currents. However, in this paper, we propose a new and simple method for performing analog arithmetic operations which in this scheme, signals are represented and stored through a memristance of the newly found circuit element, i.e. memristor, instead of voltage or current. Some of these operators such as divider and multiplier are much simpler and faster than their equivalent voltage-based circuits and they require less chip area. In addition, a new circuit is designed for programming the memristance of the memristor with predetermined analog value. Presented simulation results demonstrate the effectiveness and the accuracy of the proposed circuits.
Heights of varieties in multiprojective spaces and arithmetic Nullstellensatze
D'Andrea, Carlos; Sombra, Martin
2011-01-01
We present bounds for the degree and the height of the polynomials arising in some central problems in effective algebraic geometry including the implicitation of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed heights of multiprojective varieties. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz.
Interval arithmetic operations for uncertainty analysis with correlated interval variables
Jiang, Chao; Fu, Chun-Ming; Ni, Bing-Yu; Han, Xu
2016-08-01
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation, and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
SHORTCUTS TO SELECTING OPEN-ACUPOINTS VIA MENTAL ARITHMETIC
Institute of Scientific and Technical Information of China (English)
刘永锋
2004-01-01
There are many methods for calculating a certain time to select open-acupoints in applying Ziwuliuzhu (Midnight-Noon Ebb-Flow) method, but most of them are so complicated that it is inconvenient to apply Najia method (Stem-Prescription of Acupoints)in clinical practice.In comparison with other ways, the following one is so easy that the open-acupoints can be calculated directly in mental arithmetic, and helps us save time.
A study on arithmetical functions and the prime number theorem
Imm, Yeoh Saw
2014-06-01
In this paper, Leibniz triangle and suitable binomial coefficients were used to get the bounds of ψ (x) . Using the generalized convolution and the differentiation on generalized convolution of arithmetical functions, we get to prove Tatuzawa-Izeki identity. Selberg's asymptotic formula is included as a special case, which is the beginning of certain elementary proofs of the Prime Number Theorem. Integration is used on some related inequalities to provide a smoother elementary proof of the Prime Number Theorem.
Computing Integer Powers in Floating-Point Arithmetic
Kornerup, Peter; Muller, Jean-Michel
2007-01-01
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).
Self-Similarity in Geometry, Algebra and Arithmetic
Rastegar, Arash
2012-01-01
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced. Self-similar objects provide a framework in which, one can unite some results and conjectures in different mathematical frameworks. In some general situations, one can define a well-behaved notion of dimension for self-similar objects. Morphisms between self-similar o...
On Jacobian group arithmetic for typical divisors on curves
Khuri-Makdisi, Kamal
2013-01-01
In a previous joint article with F. Abu Salem, we gave efficient algorithms for Jacobian group arithmetic of "typical" divisor classes on C_{3,4} curves, improving on similar results by other authors. At that time, we could only state that a generic divisor was typical, and hence unlikely to be encountered if one implemented these algorithms over a very large finite field. This article pins down an explicit characterization of these typical divisors, for an arbitrary smooth projective curve o...
Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic
Cheng, Ka-Yue
2016-01-01
According to Chaitin, G\\"odel once told him "it doesn't matter which paradox you use [to prove the First Incompleteness Theorem]". In this paper I will present a few infinitary paradoxes and show how to "translate" them to some undecidable sentences in Peano arithmetic, like what G\\"odel did to the Liar paradox. The results partly verify G\\"odel's claim.
PRICING OF EXOTIC ENERGY DERIVATIVES BASED ON ARITHMETIC SPOT MODELS
FRED ESPEN BENTH; RODWELL KUFAKUNESU
2009-01-01
Based on a non-Gaussian Ornstein–Uhlenbeck model for energy spot, we derive prices for Asian and spread options using Fourier techniques. The option prices are expressed in terms of the Fourier transform of the payoff function and the characteristic functions of the driving noises, being independent increment processes. In many relevant situations, these functions are explicitly available, and fast Fourier transform can be used for efficient numerical valuation. The arithmetic nature of our m...
ARITHMETICAL OPERATIONS OF EXPONENTIAL FUZZY NUMBERS USING THE FUNCTION PRINCIPLE
SHAN-HUO CHEN; CHIEN-CHUNG WANG; SHU MAN CHANG
2006-01-01
Fuzzy numbers with exponential membership function are quite common in real world cases. In this paper, we applied Graded Mean Integration Representation Method to compute the representation of exponential fuzzy numbers. Then the Function Principle is applied to generate the arithmetical operations of exponential fuzzy numbers. By the way, some properties of operation under the Function Principle are proved. Finally, an application of the lifetime of the lamps of projectors is proposed.
Independence of basic arithmetic operations: evidence from cognitive neuropsychology
Directory of Open Access Journals (Sweden)
María P. Salguero-Alcañiz
2013-10-01
Full Text Available The cases described in literature evidence that arithmetical operations can function independently, which allows to infer that the cognitive processes involved in the different operations might be different. Objective of that work is to determine the different processes involved in the resolution of arithmetical operations: addition, subtraction and multiplication. Method: Instrument: Assesment of Numeric Processing and Calculation Battery (Salguero & Alameda, 2007, 2011. Subjects. Patients of acquired cerebral injury. Results and conclusions: The patient MNL preserves the addition and the multiplication but he presents altered the subtraction. On the contrary, the patient PP shows alterations in addition and multiplication but he conserves the skills for the subtraction. ISR presents a selective deficit for multiplication with intact addition and substraction. Finally, ACH preserves the addition but presents deficit for substraction and multiplication. This double dissociation confirms the postulates of the anatomical functional model of Dehaene and Cohen (1995, 1997 that consider a double route for the resolution of arithmetical simple operations: linguistic route, for numerical information learned automatically (of memory and would be used for the operations of addition and multiplication, on the other hand the semantic elaboration would be for substraction.
Electro-Photo-Sensitive Memristor for Neuromorphic and Arithmetic Computing
Maier, P.; Hartmann, F.; Emmerling, M.; Schneider, C.; Kamp, M.; Höfling, S.; Worschech, L.
2016-05-01
We present optically and electrically tunable conductance modifications of a site-controlled quantum-dot memristor. The conductance of the device is tuned by electron localization on a quantum dot. The control of the conductance with voltage and low-power light pulses enables applications in neuromorphic and arithmetic computing. As in neural networks, applying pre- and postsynaptic voltage pulses to the memristor allows us to increase (potentiation) or decrease (depression) the conductance by tuning the time difference between the electrical pulses. Exploiting state-dependent thresholds for potentiation and depression, we are able to demonstrate a memory-dependent induction of learning. The discharging of the quantum dot can further be induced by low-power light pulses in the nanowatt range. In combination with the state-dependent threshold voltage for discharging, this enables applications as generic building blocks to perform arithmetic operations in bases ranging from binary to decimal with low-power optical excitation. Our findings allow the realization of optoelectronic memristor-based synapses in artificial neural networks with a memory-dependent induction of learning and enhanced functionality by performing arithmetic operations.
Critical Path Reduction of Distributed Arithmetic Based FIR Filter
Directory of Open Access Journals (Sweden)
Sunita Badave
2016-03-01
Full Text Available Operating speed, which is reciprocal of critical path computation time, is one of the prominent design matrices of finite impulse response (FIR filters. It is largely affected by both, system architecture as well as technique used to design arithmetic modules. A large computation time of multipliers in conventionally designed multipliers, limits the speed of system architecture. Distributed arithmetic is one of the techniques, used to provide multiplier-free multiplication in the implementation of FIR filter. However suffers from a sever limitation of exponential growth of look up table (LUT with order of filter. An improved distributed arithmetic technique is addressed here to design for system architecture of FIR filter. In proposed technique, a single large LUT of conventional DA is replaced by number of smaller indexed LUT pages to restrict exponential growth and to reduce system access time. It also eliminates the use of adders. Selection module selects the desired value from desired page, which leads to reduce computational time of critical path. Trade off between access times of LUT pages and selection module helps to achieve minimum critical path so as to maximize the operating speed. Implementations are targeted to Xilinx ISE, Virtex IV devices. FIR filter with 8 bit data width of input sample results are presented here. It is observed that, proposed design perform significantly faster as compared to the conventional DA and existing DA based designs.
Berg, Derek H.; Hutchinson, Nancy L.
2010-01-01
This study investigated whether processing speed, short-term memory, and working memory accounted for the differential mental addition fluency between children typically achieving in arithmetic (TA) and children at-risk for failure in arithmetic (AR). Further, we drew attention to fluency differences in simple (e.g., 5 + 3) and complex (e.g., 16 +…
Study and realisation of the arithmetic unit of an information processing machine
International Nuclear Information System (INIS)
After having defined the arithmetic unit of an information processing machine, and its role, and described the main characteristics of two types of machine (fixed or varying word length), the author of this research thesis reports the study of a decimal adder, describes the operation of a synchronous arithmetic unit for a varying word length machine, reports the technological study of the arithmetic unit (electronic components and circuits, printed circuits), and finally presents multiplication and division subroutines
Are Individual Differences in Arithmetic Fact Retrieval in Children Related to Inhibition?
Bellen, Elien; Fias, Wim; De Smedt, Bert
2016-01-01
Although it has been proposed that inhibition is related to individual differences in mathematical achievement, it is not clear how it is related to specific aspects of mathematical skills, such as arithmetic fact retrieval. The present study therefore investigated the association between inhibition and arithmetic fact retrieval and further examined the unique role of inhibition in individual differences in arithmetic fact retrieval, in addition to numerical magnitude processing. We administe...
Profiles of children’s arithmetic fact development: A model-based clustering approach
Vanbinst, Kiran; Ceulemans, Eva; Ghesquière, Pol; De Smedt, Bert
2015-01-01
The current longitudinal study tried to capture profiles of individual differences in children’s arithmetic fact development. We used a model-based clustering approach (Banfield & Raftery, 1993) to delineate profiles of arithmetic fact development, based upon empirically derived differences in parameters of arithmetic fact mastery repeatedly assessed at the start of three subsequent school years, i.e. third, fourth and fifth grade. This cluster analysis revealed three profiles in a random sam...
Wang, Li-Qun; Saito, Masao
We used 1.5T functional magnetic resonance imaging (fMRI) to explore that which brain areas contribute uniquely to numeric computation. The BOLD effect activation pattern of metal arithmetic task (successive subtraction: actual calculation task) was compared with multiplication tables repetition task (rote verbal arithmetic memory task) response. The activation found in right parietal lobule during metal arithmetic task suggested that quantitative cognition or numeric computation may need the assistance of sensuous convert, such as spatial imagination and spatial sensuous convert. In addition, this mechanism may be an ’analog algorithm’ in the simple mental arithmetic processing.
Vedas and the Development of Arithmetic and Algebra
Directory of Open Access Journals (Sweden)
Gurudeo A. Tularam
2010-01-01
Full Text Available Problem statement: Algebra developed in three stages: rhetorical or prose algebra, syncopated or abbreviated algebra and symbolic algebra-known as school algebra. School algebra developed rather early in India and the literature now suggests that the first civilization to develop symbolic algebra was the Vedic Indians. Approach: Philosophical ideas of the time influenced the development of the decimal system and arithmetic and that in turn led to algebra. Indeed, symbolic algebraic ideas are deep rooted in Vedic philosophy. The Vedic arithmetic and mathematics were of a high level at an early period and the Hindus used algebraic ideas to generate formulas simplifying calculations. Results: In the main, they developed formulas to understand the physical world satisfying the needs of religion (apara and para vidya. While geometrical focus, logic and proof type are features of Greek mathematics, boldness of conception, abstraction, symbolism are essentially in Indian mathematics. From such a history study, a number of implications can be drawn regarding the learning of algebra. Real life, imaginative and creative problems that encourage risk should be the focus in student learning; allowing students freely move between numbers, magnitudes and symbols rather than taking separate static or unchanging view. A move from concrete to pictorial to symbolic modes was present in ancient learning. Real life practical needs motivated the progress to symbolic algebra. The use of rich context based problems that stimulate and motivate students to raise levels higher to transfer knowledge should be the focus of learning. Conclusion/Recommendations: The progress from arithmetic to algebra in India was achieved through different modes of learning, risk taking, problem solving and higher order thinking all in line with current emphasis in mathematics education but at rather early stage in human history.
Oscillatory EEG correlates of arithmetic strategies: A training study
Directory of Open Access Journals (Sweden)
Roland H. Grabner
2012-10-01
Full Text Available There has been a long tradition of research on mathematics education showing that children and adults use different strategies to solve arithmetic problems. Neurophysiological studies have recently begun to investigate the brain correlates of these strategies. The existing body of data, however, reflect static end points of the learning process and do not provide information on how brain activity changes in response to training or intervention. In this study, we explicitly address this issue by training participants in using fact retrieval strategies. We also investigate whether brain activity related to arithmetic fact learning is domain-specific or whether this generalizes to other learning materials, such as the solution of figural-spatial problems. Twenty adult students were trained on sets of two-digit multiplication problems and figural-spatial problems. After the training, they were presented with the trained and untrained problems while their brain activity was recorded by means of electroencephalography (EEG . In both problem types, the training resulted in accuracies over 90 % and significant decreases in solution times. Analyses of the oscillatory EEG data also revealed training effects across both problem types. Specifically, we observed training-related activity increases in the theta band (3-6 Hz and decreases in the lower alpha band (8-10 Hz, especially over parieto-occipital and parietal brain regions. These results provide the first evidence that a short term fact retrieval training results in significant changes in oscillatory EEG activity. These findings further corroborate the role of the theta band in the retrieval of semantic information from memory and suggest that theta activity is not only sensitive to fact retrieval in mental arithmetic but also in other domains.
Arithmetic progressions that consist only of reduced residues
Paul A. Tanner III
2001-01-01
This paper contains an elementary derivation of formulas for multiplicative functions of m which exactly yield the following numbers: the number of distinct arithmetic progressions of w reduced residues modulo m; the number of the same with first term n; the number of the same with mean n; the number of the same with common difference n. With m and odd w fixed, the values of the first two of the last three functions are fixed and equal for all n relatively prime to m; other similar relations ...
Arithmetic coding as a non-linear dynamical system
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
Strategy-Enhanced Interactive Proving and Arithmetic Simplification for PVS
diVito, Ben L.
2003-01-01
We describe an approach to strategy-based proving for improved interactive deduction in specialized domains. An experimental package of strategies (tactics) and support functions called Manip has been developed for PVS to reduce the tedium of arithmetic manipulation. Included are strategies aimed at algebraic simplification of real-valued expressions. A general deduction architecture is described in which domain-specific strategies, such as those for algebraic manipulation, are supported by more generic features, such as term-access techniques applicable in arbitrary settings. An extended expression language provides access to subterms within a sequent.
A Fast π/4-DQPSK Demodulation Arithmetic and Realization
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-yong; ZHONG Hong-sheng; WANG Jun-mei
2004-01-01
The modulated signals of π /4-DQPSK can be demodulated with the differenced method,and the technology has been used in the communication. The traditional demodulated method needs a lot of calculation. In this paper, a new method based on fast arithmetic digital demodulation of DQPSK is presented. The new method only uses the sign of the modulated signal instead of digital signal through the A/D in the traditional method. With the new method, the system has higher speed, and can save some hardware in the FPGA. An experiment of the new method with the DQPSK is given in this paper.
CIMPA Summer School on Arithmetic and Geometry Around Hypergeometric Functions
Uludağ, A; Yoshida, Masaaki; Arithmetic and Geometry Around Hypergeometric Functions
2007-01-01
This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.
Second grade students understanding of the arithmetic operations
Slapar, Ana
2012-01-01
People face Mathematics at a very early stage in their lives since it is a part of various everyday activities. M. Jurkovič (2009) came to a conclusion in her research that Mathematics in the first grades of elementary schools is one of the most popular subjects, despite of the fact that a lot of pupils have difficulties with it. In my diploma I tried to asses how the pupils who have difficulties with Mathematics understand arithmetic operations of adding and subtracting, which calculati...
On containment of conjunctive queries with arithmetic comparisons
Afrati, F; Li, Chen; Mitra, P.
2004-01-01
We study the following problem: how to test if Q(2) is contained in Q(1), where Q(1) and Q(2) are conjunctive queries with arithmetic comparisons? This problem is fundamental in a large variety of database applications. Existing algorithms first normalize the queries, then test a logical implication using multiple containment mappings from Q(1) to Q(2). We are interested in cases where the containment can be tested more efficiently. This work aims to (a) reduce the problem complexity from Pi(...
On consistency of the weighted arithmetical mean complex judgement matrix
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The weighted arithmetical mean complex judgement matrix(WAMCJM)is the most common method for aggregating group opinions,but it has a shortcoming,namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency.An upper bound of the WAMCJM's consistency is presented.Simultaneously,a compatibility index of judging the aggregating extent of group opinions is also introduced.The WAMCJM is of acceptable consistency and is proved provided the compatibilities of all judgement matrices given by experts are smaller than the threshold value of acceptable consistency.These conclusions are important to group decision making.
On the periodicity of some Farhi arithmetical functions
Ji, Qing-Zhong; Ji, Chun-Gang
2009-01-01
Let $k\\in\\mathbb{N}$. Let $f(x)\\in \\Bbb{Z}[x]$ be any polynomial such that $f(x)$ and $f(x+1)f(x+2)... f(x+k)$ are coprime in $\\mathbb{Q}[x]$. We call $$g_{k,f}(n):=\\frac{|f(n)f(n+1)... f(n+k)|}{\\text{lcm}(f(n),f(n+1),...,f(n+k))}$$ a Farhi arithmetic function. In this paper, we prove that $g_{k,f}$ is periodic. This generalizes the previous results of Farhi and Kane, and Hong and Yang.
Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility
Directory of Open Access Journals (Sweden)
Min-Ku Lee
2014-01-01
Full Text Available Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity of variance to understand the price structure of continuous arithmetic average Asian options. The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. In terms of the elasticity parameter governing the leverage effect, a correction to the stochastic volatility model is made for more efficient pricing and hedging of Asian options.
Prime polynomials in short intervals and in arithmetic progressions
Bank, Efrat; Bary-Soroker, Lior; Rosenzweig, Lior
2013-01-01
In this paper we establish function field versions of two classical conjectures on prime numbers. The first says that the number of primes in intervals $(x,x+x^{\\epsilon}]$ is about $x^{\\epsilon}/\\log x$ . The second says that the number of primes $p\\lt x$ in the arithmetic progression $p\\equiv a\\ (\\mathrm{mod}\\ d)$ , for $d\\lt x^{1-\\delta}$ , is about $\\frac{\\pi(x)}{\\phi(d)}$ , where $\\phi$ is the Euler totient function. ¶ More precisely, for short intervals we prove: Let $k$ be a fixe...
Arguments and elements of realistic interpretation of mathematics: arithmetical component
Directory of Open Access Journals (Sweden)
Arepiev E. I.
2015-01-01
Full Text Available The prospects for realistic interpretation of the nature of initial mathematical truths and objects are considered in the article. The arguments of realism, reasons impeding its recognition among philosophers of mathematics as well as the ways to eliminate these reasons are discussed. It is proven that the absence of acceptable ontological interpretation of mathematical realism is the main obstacle to its recognition. This paper explicates the introductory positions of this interpretation and presents a realistic interpretation of the arithmetical component of mathematics. In summary, we should like to note that such constructions, as it is shown to us, ought to bring the direct use not only for the philosophical foundation of mathematics but for mathematics itself. In the justification of the author's conclusions based on the works of famous mathematicians of the twentieth century, interpreting their findings in a broad historical and philosophical context. To illustrate his point, the author gives examples of arithmetic and geometry - both Euclidean and non-Euclidean.
Working memory failures in children with arithmetical difficulties.
Passolunghi, Maria Chiara; Cornoldi, Cesare
2008-09-01
A large body of literature has examined the relationship between working memory and arithmetic achievement, but results are still ambiguous. To examine this relationship, we compared the performance of third and fifth graders with arithmetic difficulties (AD) and controls of the same age, grade, and verbal intelligence on a battery of working memory tasks, differentiating between different aspects of working memory. Children with AD scored significantly lower on active working memory tasks requiring manipulation of the to-be-recalled information (Listening Completion task, Corsi Span Backwards, Digit Backwards), but not in passive working memory tasks, requiring the recall of information in the same format in which it had been presented (Digit, Word, and Corsi Forwards Span tasks), nor in tasks involving word processing (word articulation rate, forwards and backwards word spans). A regression analysis showed that the best predictors of differences between AD children and the control group were the Corsi Span Backwards, the Listening Completion task, and the rate of articulation of pseudowords. The analysis of strategies used by children in mental calculation revealed the greater tendency of children with AD to rely on more primitive strategies: finger use never appeared as the most frequent strategy in skilled children, whereas it was the most used strategy in children with AD. Verbal and visual strategies appeared associated with successful performance in third graders, but in fifth grade, the most successful strategy was verbalization. PMID:18608224
Design of arithmetic circuits in quantum dot cellular automata nanotechnology
Sridharan, K
2015-01-01
This research monograph focuses on the design of arithmetic circuits in Quantum Dot Cellular Automata (QCA). Using the fact that the 3-input majority gate is a primitive in QCA, the book sets out to discover hitherto unknown properties of majority logic in the context of arithmetic circuit designs. The pursuit for efficient adders in QCA takes two forms. One involves application of the new results in majority logic to existing adders. The second involves development of a custom adder for QCA technology. A QCA adder named as hybrid adder is proposed and it is shown that it outperforms existing multi-bit adders with respect to area and delay. The work is extended to the design of a low-complexity multiplier for signed numbers in QCA. Furthermore the book explores two aspects unique to QCA technology, namely thermal robustness and the role of interconnects. In addition, the book introduces the reader to QCA layout design and simulation using QCADesigner. Features & Benefits: This research-based book: · �...
Cardiorespiratory Information Dynamics during Mental Arithmetic and Sustained Attention.
Directory of Open Access Journals (Sweden)
Devy Widjaja
Full Text Available An analysis of cardiorespiratory dynamics during mental arithmetic, which induces stress, and sustained attention was conducted using information theory. The information storage and internal information of heart rate variability (HRV were determined respectively as the self-entropy of the tachogram, and the self-entropy of the tachogram conditioned to the knowledge of respiration. The information transfer and cross information from respiration to HRV were assessed as the transfer and cross-entropy, both measures of cardiorespiratory coupling. These information-theoretic measures identified significant nonlinearities in the cardiorespiratory time series. Additionally, it was shown that, although mental stress is related to a reduction in vagal activity, no difference in cardiorespiratory coupling was found when several mental states (rest, mental stress, sustained attention are compared. However, the self-entropy of HRV conditioned to respiration was very informative to study the predictability of RR interval series during mental tasks, and showed higher predictability during mental arithmetic compared to sustained attention or rest.
An Efficient Image Compression Technique Based on Arithmetic Coding
Directory of Open Access Journals (Sweden)
Prof. Rajendra Kumar Patel
2012-12-01
Full Text Available The rapid growth of digital imaging applications, including desktop publishing, multimedia, teleconferencing, and high visual definition has increased the need for effective and standardized image compression techniques. Digital Images play a very important role for describing the detailed information. The key obstacle for many applications is the vast amount of data required to represent a digital image directly. The various processes of digitizing the images to obtain it in the best quality for the more clear and accurate information leads to the requirement of more storage space and better storage and accessing mechanism in the form of hardware or software. In this paper we concentrate mainly on the above flaw so that we reduce the space with best quality image compression. State-ofthe-art techniques can compress typical images from 1/10 to 1/50 their uncompressed size without visibly affecting image quality. From our study I observe that there is a need of good image compression technique which provides better reduction technique in terms of storage and quality. Arithmetic coding is the best way to reducing encoding data. So in this paper we propose arithmetic coding with walsh transformation based image compression technique which is an efficient way of reduction
Relationship of Bender Memory to Achievement in Arithmetic by First Graders.
Snyder, Robert T.; And Others
1980-01-01
Arithmetic and reading achievement scores of 84 children were correlated with power and precision of Bender Memory using the Bender Visual Memory Technique (BVMT). Of the 20 correlations, 16 were significant. Support for recommended use of the BVMT as a screening instrument for early assessment of arithmetic skill is provided. (Author/SJL)
Statistics of the zeros of $L$-functions and arithmetic correlations
Smith, D.J.
2016-01-01
This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the expected number of prime numbers over short intervals are generalised by associating these concepts to $L$-functions arising from number theoretic objects.
Arithmetic Achievement in Children with Cerebral Palsy or Spina Bifida Meningomyelocele
Jenks, Kathleen M.; van Lieshout, Ernest C. D. M.; de Moor, Jan
2009-01-01
The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic instruction time. Twenty-two children with CNSd…
Arithmetic achievement in children with cerebral palsy or spina bifida meningomyelocele
Jenks, K.M.; Lieshout, E.C.D.M. van; Moor, J.M.H. de
2009-01-01
The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic
Sabrewing: a lightweight architecture for combined floating-point and integer arithmetic
Bruintjes, Tom M.; Walters, Karel H.G.; Gerez, Sabih H.; Molenkamp, Bert; Smit, Gerard J.M.
2012-01-01
In spite of the fact that floating-point arithmetic is costly in terms of silicon area, the joint design of hardware for floating-point and integer arithmetic is seldom considered. While components like multipliers and adders can potentially be shared, floating-point and integer units in contemporar
Simplification of integrity constraints with aggregates and arithmetic built-ins
DEFF Research Database (Denmark)
Martinenghi, Davide
2004-01-01
Both aggregates and arithmetic built-ins are widely used in current database query languages: Aggregates are second-order constructs such as CNT and SUM of SQL; arithmetic built-ins include relational and other mathematical operators that apply to numbers, such as
Early Number and Arithmetic Performance of Ecuadorian 4-5-Year-Olds
Bojorque, Gina; Torbeyns, Joke; Moscoso, Jheni; Van Nijlen, Daniël; Verschaffel, Lieven
2015-01-01
This study aimed at (a) constructing a reliable and valid test to assess Ecuadorian 4-5-year olds' number and arithmetic skills; (b) providing empirical data on Ecuadorian 4-5-year olds' number and arithmetic skills; and (c) confronting these children's actual performances with the performances expected by national experts in this domain. We…
How Is Phonological Processing Related to Individual Differences in Children's Arithmetic Skills?
De Smedt, Bert; Taylor, Jessica; Archibald, Lisa; Ansari, Daniel
2010-01-01
While there is evidence for an association between the development of reading and arithmetic, the precise locus of this relationship remains to be determined. Findings from cognitive neuroscience research that point to shared neural correlates for phonological processing and arithmetic as well as recent behavioral evidence led to the present…
Jenks, Kathleen M.; de Moor, Jan; van Lieshout, Ernest C. D. M.
2009-01-01
Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and…
Grothendieck's trace map for arithmetic surfaces via residues and higher adeles
Morrow, Matthew
2011-01-01
We establish the reciprocity law along a vertical curve for residues of differential forms on arithmetic surfaces, and describe Grothendieck's trace map of the surface as a sum of residues. Points at infinity are then incorporated into the theory and the reciprocity law is extended to all curves on the surface. Applications to adelic duality for the arithmetic surface are discussed.
Arithmetic performance of children with cerebral palsy: The influence of cognitive and motor factors
Rooijen, M. van; Verhoeven, L.T.W.; Smits, D.W.; Ketelaar, M.; Steenbergen, B.
2012-01-01
Children diagnosed with cerebral palsy (CP) often show difficulties in arithmetic compared to their typically developing peers. The present study explores whether cognitive and motor variables are related to arithmetic performance of a large group of primary school children with CP. More specificall
Teachers’ Beliefs and Practices Regarding the Role of Executive Functions in Reading and Arithmetic
Rapoport, Shirley; Rubinsten, Orly; Katzir, Tami
2016-01-01
The current study investigated early elementary school teachers’ beliefs and practices regarding the role of Executive Functions (EFs) in reading and arithmetic. A new research questionnaire was developed and judged by professionals in the academia and the field. Reponses were obtained from 144 teachers from Israel. Factor analysis divided the questionnaire into three valid and reliable subscales, reflecting (1) beliefs regarding the contribution of EFs to reading and arithmetic, (2) pedagogical practices, and (3) a connection between the cognitive mechanisms of reading and arithmetic. Findings indicate that teachers believe EFs affect students’ performance in reading and arithmetic. These beliefs were also correlated with pedagogical practices. Additionally, special education teachers’ scored higher on the different subscales compared to general education teachers. These findings shed light on the way teachers perceive the cognitive foundations of reading and arithmetic and indicate to which extent these perceptions guide their teaching practices. PMID:27799917
International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
DEVELOPMENTS IN RELIABLE COMPUTING
1999-01-01
The SCAN conference, the International Symposium on Scientific Com puting, Computer Arithmetic and Validated Numerics, takes place bian nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation). SCAN-98 attracted more than 100 participants from 21 countries all over the world. During the four days from September 22 to 25, nine highlighted, plenary lectures and over 70 contributed talks were given. These figures indicate a large participation, which was partly caused by the attraction of the organizing country, Hungary, but also the effec tive support system have contributed to the success. The conference was substantially supported by the Hungarian Research Fund OTKA, GAMM, the National Technology Development Board OMFB and by the J6zsef Attila University. Due to this funding, it was possible to subsidize the participation of over 20 scientists, mainly from Eastern European countries. I...
GDI based full adders for energy efficient arithmetic applications
Directory of Open Access Journals (Sweden)
Mohan Shoba
2016-03-01
Full Text Available Addition is a vital arithmetic operation and acts as a building block for synthesizing all other operations. A high-performance adder is one of the key components in the design of application specific integrated circuits. In this paper, three low power full adders are designed with full swing AND, OR and XOR gates to alleviate threshold voltage problem which is commonly encountered in Gate Diffusion Input (GDI logic. This problem usually does not allow the full adder circuits to operate without additional inverters. However, the three full adders are successfully realized using full swing gates with the significant improvement in their performance. The performance of the proposed designs is compared with the other full adder designs, namely CMOS, CPL, hybrid and GDI through SPICE simulations using 45 nm technology models. Simulation results reveal that proposed designs have lower energy consumption among all the conventional designs taken for comparison.
Conference on Arithmetic and Ideal Theory of Rings and Semigroups
Fontana, Marco; Geroldinger, Alfred; Olberding, Bruce
2016-01-01
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
Degrading Precision Arithmetics for Low-power FIR Implementation
DEFF Research Database (Denmark)
Albicocco, Pietro; Cardarilli, Gian Carlo; Nannarelli, Alberto;
2011-01-01
In this paper a review of different techniques used to implement highly optimized DSP systems is presented. The case of study is the implementation of parallel FIR filters aimed to applications characterized by high speed and high selectivity in frequency where at the same time low power dissipat......In this paper a review of different techniques used to implement highly optimized DSP systems is presented. The case of study is the implementation of parallel FIR filters aimed to applications characterized by high speed and high selectivity in frequency where at the same time low power...... on selective bit freezing, DPA-II, based on VDD voltage scaling, and DPA-III, based on power gating. Some theoreticaVsimuiative analysis of the introduced arithmetic errors and some implementation results are shown. A discussion on the suitability of these methodologies on standard cell technologies and FPGAs...
HIGH SPEED POINT ARITHMETIC ARCHITECTURE FOR ECC ON FPGA
Directory of Open Access Journals (Sweden)
Rahila Bilal,
2010-09-01
Full Text Available Elliptic curve cryptography plays a crucial role in networking and communication security. ECC have evolved in the recent past as an important alternative to established systems like RSA. This paper describes the implementation of an elliptic curve coprocessor based on the FPGA , which can provide a significant speedup for these cryptosystems. The FPGA configuration file is synthesized from VHDL code applying different hardware synthesis products. The implementation of ECC lies in three levels: scalar multiplication, point addition/doubling and finite field modular arithmetic. In this paper, we present a novel fast architecture for the point addition/doubling level in the projective coordinate. The proposed Architecture is based on Binary Field. The Design performs multiplication using Polynomial Basis. Analysis shows that, with reasonable hardware overhead, our architecture can achieve a high speedup for the point addition operation and point Doubling operation.Furthermore, the architecture is parameterized for different data widths to evaluate the optimal resource utilization.
Arithmetic and local circuitry underlying dopamine prediction errors.
Eshel, Neir; Bukwich, Michael; Rao, Vinod; Hemmelder, Vivian; Tian, Ju; Uchida, Naoshige
2015-09-10
Dopamine neurons are thought to facilitate learning by comparing actual and expected reward. Despite two decades of investigation, little is known about how this comparison is made. To determine how dopamine neurons calculate prediction error, we combined optogenetic manipulations with extracellular recordings in the ventral tegmental area while mice engaged in classical conditioning. Here we demonstrate, by manipulating the temporal expectation of reward, that dopamine neurons perform subtraction, a computation that is ideal for reinforcement learning but rarely observed in the brain. Furthermore, selectively exciting and inhibiting neighbouring GABA (γ-aminobutyric acid) neurons in the ventral tegmental area reveals that these neurons are a source of subtraction: they inhibit dopamine neurons when reward is expected, causally contributing to prediction-error calculations. Finally, bilaterally stimulating ventral tegmental area GABA neurons dramatically reduces anticipatory licking to conditioned odours, consistent with an important role for these neurons in reinforcement learning. Together, our results uncover the arithmetic and local circuitry underlying dopamine prediction errors.
Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence
Directory of Open Access Journals (Sweden)
Verguts Tom
2007-12-01
Full Text Available Abstract Background Recent cognitive and computational models (e.g. the Interacting Neighbors Model state that in simple multiplication decade and unit digits of the candidate answers (including the correct result are represented separately. Thus, these models challenge holistic views of number representation as well as traditional accounts of the classical problem size effect in simple arithmetic (i.e. the finding that large problems are answered slower and less accurate than small problems. Empirical data supporting this view are still scarce. Methods Data of 24 participants who performed a multiplication verification task with Arabic digits (e.g. 8 × 4 = 36 - true or false? are reported. Behavioral (i.e. RT and errors and EEG (i.e. ERP measures were recorded in parallel. Results We provide evidence for neighborhood-consistency effects in the verification of simple multiplication problems (e.g. 8 × 4. Behaviorally, we find that decade-consistent lures, which share their decade digit with the correct result (e.g. 36, are harder to reject than matched inconsistent lures, which differ in both digits from the correct result (e.g. 28. This neighborhood consistency effect in product verification is similar to recent observations in the production of multiplication results. With respect to event-related potentials we find significant differences for consistent compared to inconsistent lures in the N400 (increased negativity and Late Positive Component (reduced positivity. In this respect consistency effects in our paradigm resemble lexico-semantic effects earlier found in simple arithmetic and in orthographic input processing. Conclusion Our data suggest that neighborhood consistency effects in simple multiplication stem at least partly from central (lexico-semantic' stages of processing. These results are compatible with current models on the representation of simple multiplication facts – in particular with the Interacting Neighbors Model
Directory of Open Access Journals (Sweden)
Yongxin eLi
2013-12-01
Full Text Available Arithmetic skill is of critical importance for academic achievement, professional success and everyday life, and childhood is the key period to acquire this skill. Neuroimaging studies have identified that left parietal regions are a key neural substrate for representing arithmetic skill. Although the relationship between functional brain activity in left parietal regions and arithmetic skill has been studied in detail, it remains unclear about the relationship between arithmetic achievement and structural properties in left inferior parietal area in schoolchildren. The current study employed a combination of voxel-based morphometry (VBM for high-resolution T1-weighted images and fiber tracking on diffusion tensor imaging (DTI to examine the relationship between structural properties in the inferior parietal area and arithmetic achievement in 10-year-old schoolchildren. VBM of the T1-weighted images revealed that individual differences in arithmetic scores were significantly and positively correlated with the grey matter (GM volume in the left intraparietal sulcus (IPS. Fiber tracking analysis revealed that the forceps major, left superior longitudinal fasciculus (SLF, bilateral inferior longitudinal fasciculus (ILF and inferior fronto-occipital fasciculus (IFOF were the primary pathways connecting the left IPS with other brain areas. Furthermore, the regression analysis of the probabilistic pathways revealed a significant and positive correlation between the fractional anisotropy (FA values in the left SLF, ILF and bilateral IFOF and arithmetic scores. The brain structure-behavior correlation analyses indicated that the GM volumes in the left IPS and the FA values in the tract pathways connecting left IPS were both related to children’s arithmetic achievement. The present findings provide evidence that individual structural differences in the left IPS are associated with arithmetic scores in schoolchildren.
Teitler, Zach; Torrance, Douglas A.
2012-01-01
We give the Castelnuovo-Mumford regularity of arrangements of (n-2)-planes in P^n whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen-Macaulay.
Directory of Open Access Journals (Sweden)
Kiran Vanbinst
Full Text Available In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children's numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties.
Vanbinst, Kiran; Ansari, Daniel; Ghesquière, Pol; De Smedt, Bert
2016-01-01
In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children's numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties. PMID:26942935
Directory of Open Access Journals (Sweden)
Urszula eMihulowicz
2014-05-01
Full Text Available Different specific mechanisms have been suggested for solving single-digit arithmetic operations. However, the neural correlates underlying basic arithmetic (multiplication, addition, subtraction are still under debate. In the present study, we systematically assessed single-digit arithmetic in a group of acute stroke patients (n=45 with circumscribed left- or right-hemispheric brain lesions. Lesion sites significantly related to impaired performance were found only in the left-hemisphere damaged group. Deficits in multiplication and addition were related to subcortical/white matter brain regions differing from those for subtraction tasks, corroborating the notion of distinct processing pathways for different arithmetic tasks. Additionally, our results further point to the importance of investigating fiber pathways in numerical cognition.
Small Solutions of Quadratic Equations with Prime Variables in Arithmetic Progressions
Institute of Scientific and Technical Information of China (English)
Tian Ze WANG
2009-01-01
A necessary and sufficient solvable condition for diagonal quadratic equation with prime variables in arithmetic progressions is given, and the best qualitative bound for small solutions of the equation is obtained.
Husserl, Edmund
2003-01-01
In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The "appendices" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. "Completeness" is integrated into Husserl's own problematic of the "imaginary", and allows him to move beyond the analysis of "representations" in his understanding of the logic of mathematics. Husserl's work here provides an alternative model of...
Advanced topics in the arithmetic of elliptic curves
Silverman, Joseph H
1994-01-01
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of can...
Circular Interval Arithmetic Applied on LDMT for Linear Interval System
Directory of Open Access Journals (Sweden)
Stephen Ehidiamhen Uwamusi
2014-07-01
Full Text Available The paper considers the LDMT Factorization of a general nxn matrix arising from system of interval linear equations. We paid special emphasis on Interval Cholesky Factorization. The basic computational tool used is the square root method of circular interval arithmetic in a sense analogous to Gargantini and Henrici as well as the generalized square root method due to Petkovic which enables the construction of the square root of the resulting diagonal matrix. We also made use of Rump’s method for multiplying two intervals expressed in the form of midpoint-radius respectively. Numerical example of matrix factorization in this regard is given which forms the basis of discussion. It is shown that LDMT even though is a numerically stable method for any diagonally dominant matrix it also can lead to excess width of the solution set. It is also pointed out that in spite of the above mentioned objection to interval LDMT it has in addition , the advantage that in the presence of several solution sets sharing the same interval matrix the LDMT Factorization requires to be computed only once which helps in saving substantial computational time. This may be found applicable in the development of military hard ware which requires shooting at a single point but produces multiple broadcast at all other points
Arithmetic Properties of Mirror Map and Quantum Coupling
International Nuclear Information System (INIS)
We study some arithmetic properties of the mirror maps and the quantum Yukawa couplings for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equations, which we derived previously, to characterize the mirror map in each case. For algebraic K3 surfaces, we solve the equation in terms of the J-function. By deriving explicit modular relations we prove that some K3 mirror maps are algebraic over the genus zero function field Q(J). This leads to a uniform proof that those mirror maps have integral Fourier coefficients. Regarding the maps as Riemann mappings, we prove that they are genus zero functions. By virtue of the Conway-Norton conjecture (proved by Borcherds using Frenkel-Lepowsky-Meurman's Moonshine module), we find that these maps are actually the reciprocals of the Thompson series for certain conjugacy classes in the Griess-Fischer group. This also gives, as an immediate consequence, a second proof that those mirror maps are integral. We thus conjecture a surprising connection between K3 mirror maps and the Thompson series. For threefolds, we construct a formal nonlinear ODE for the quantum coupling reduced mod p. Under the mirror hypothesis and an integrality assumption, we derive mod p congruences for the Fourier coefficients. For the quintics, we deduce, that the degree d instanton numbers nd are divisible by 53 - a fact first conjectured by Clemens. (orig.)
Arithmetic properties of mirror map and quantum coupling
Lian, Bong H.; Yau, Shing-Tung
1996-02-01
We study some arithmetic properties of the mirror maps and the quantum Yukawa couplings for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to characterize the mirror map in each case. For algebraic K3 surfaces, we solve the equation in terms of the J-function. By deriving explicit modular relations we prove that some K3 mirror maps are algebraic over the genus zero function field Q( J). This leads to a uniform proof that those mirror maps have integral Fourier coefficients. Regarding the maps as Riemann mappings, we prove that they are genus zero functions. By virtue of the Conway-Norton conjecture (proved by Borcherds using Frenkel-Lepowsky-Meurman's Moonshine module), we find that these maps are actually the reciprocals of the Thompson series for certain conjugacy classes in the Griess-Fischer group. This also gives, as an immediate consequence, a second proof that those mirror maps are integral. We thus conjecture a surprising connection between K3 mirror maps and the Thompson series. For threefolds, we construct a formal nonlinear ODE for the quantum coupling reduced mod p. Under the mirror hypothesis and an integrality assumption, we derive mod p congurences for the Fourier coefficients. For the quintics, we deduce, (at least for 5× d) that the degree d instanton numbers n d are divisible by 53 — a fact first conjectured by Clemens.
Arithmetic properties of mirror map and quantum coupling
Lian Bong H; Lian, Bong H; Yau, Shing Tung
1994-01-01
Abstract: We study some arithmetic properties of the mirror maps and the quantum Yukawa coupling for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to characterize the mirror map in each case. For algebraic K3 surfaces, we solve the equation in terms of the J-function. By deriving explicit modular relations we prove that some K3 mirror maps are algebraic over the genus zero function field {\\bf Q}(J). This leads to a uniform proof that those mirror maps have integral Fourier coefficients. Regarding the maps as Riemann mappings, we prove that they are genus zero functions. By virtue of the Conway-Norton conjecture (proved by Borcherds using Frenkel-Lepowsky-Meurman's Moonshine module), we find that these maps are actually the reciprocals of the Thompson series for certain conjugacy classes in the Griess-Fischer group. This also gives, as an immediate consequence, a second proof that those mirror maps are integral. We thus co...
Numeral words and arithmetic operations in the Alor-Pantar languages
Corbett, GG; Klamer, M; Schapper, A; Holton, G.; Kratochvil, F.; Robinson, L.
2014-01-01
The indigenous numerals of the AP languages, as well as the indigenous structures for arithmetic operations are currently under pressure from Indonesian, and will inevitably be replaced with Indonesian forms and structures. This chapter presents a documentary record of the forms and patterns currently in use to express numerals and arithmetic operations in the Alor-Pantar languages. We describe the structure of cardinal, ordinal and distributive numerals, and how operations of ...
Karin eLanderl
2013-01-01
Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a two-year period from beginning of Grade 2, when children were 7;6 years old, to beginning of Grade 4. A battery of nume...
A precise result on the arithmetic of non-principal orders in algebraic number fields
Philipp, Andreas
2011-01-01
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.
Asymptotic free probability for arithmetic functions and factorization of Dirichlet series
Cho, Ilwoo; Gillespie, Timothy; Jorgensen, Palle E. T.
2015-11-01
In this paper, we study a free-probabilistic model on the algebra of arithmetic functions by considering their asymptotic behavior. As an application, we concentrate on arithmetic functions arising from certain representations attached to the general linear group GL_n . We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness.
Stoianov, Ivilin P.
2014-01-01
Number skills are popularly bound to arithmetic knowledge in its symbolic form, such as " five + nine = fourteen, " but mounting evidence suggests that these symbolic relations are actually grounded, i.e., computed (see Harnad, 1990) on noisy internal magnitude representations that bear our general understanding of numbers and further improve with math experience (Figure 1). Multiple lines of evidence support the idea of semantics-based arithmetic, including behavioral research on humans (Gal...
Nondigital implementation of the arithmetic of real numbers by means of quantum computer media
Litvinov, Grigori; Maslov, Viktor; Shpiz, Grigori
1999-01-01
In the framework of a model for quantum computer media, a nondigital implementation of the arithmetic of the real numbers is described. For this model, an elementary storage "cell" is an ensemble of qubits (quantum bits). It is found that to store an arbitrary real number it is sufficient to use four of these ensembles and the arithmetic operations can be implemented by fixed quantum circuits.
Good and bad at numbers: typical and atypical development of number processing and arithmetic
Iuculano, T.
2012-01-01
This thesis elucidates the heterogeneous nature of mathematical skills by examining numerical and arithmetical abilities in typical, atypical and exceptional populations. Moreover, it looks at the benefits of intervention for remediating and improving mathematical skills. First, we establish the nature of the ‘number sense’ and assess its contribution to typical and atypical arithmetical development. We confirmed that representing and manipulating numerosities approximately is fundamentally d...
Profiles of children's arithmetic fact development: a model-based clustering approach.
Vanbinst, Kiran; Ceulemans, Eva; Ghesquière, Pol; De Smedt, Bert
2015-05-01
The current longitudinal study tried to capture profiles of individual differences in children's arithmetic fact development. We used a model-based clustering approach to delineate profiles of arithmetic fact development based on empirically derived differences in parameters of arithmetic fact mastery repeatedly assessed at the start of three subsequent school years: third, fourth, and fifth grades. This cluster analysis revealed three profiles in a random sample-slow and variable (n = 8), average (n = 24), and efficient (n = 20)-that were marked by differences in children's development in arithmetic fact mastery from third grade to fifth grade. These profiles did not differ in terms of age, sex, socioeconomic status, or intellectual ability. In addition, we explored whether these profiles varied in cognitive skills that have been associated with individual differences in single-digit arithmetic. The three profiles differed in nonsymbolic and symbolic numerical magnitude processing as well as phonological processing, but not in digit naming or working memory. After also controlling for cluster differences in general mathematics achievement and reading ability, only differences in symbolic numerical magnitude processing remained significant. Taken together, our longitudinal data reveal that symbolic numerical magnitude processing represents an important variable that contributes to individual variability in children's acquisition of arithmetic facts. PMID:25731679
Arithmetic Operations and Factorization using Asynchronous P Systems
Directory of Open Access Journals (Sweden)
Takayuki Murakawa
2012-07-01
Full Text Available
In the present paper, we consider the asynchronous parallelism in membrane computing, and propose asynchronous P systems that perform two basic arithmetic operations and factorization. Since there is no restrictive assumption for application of rules, sequential and maximal parallel executions are allowed on the asynchronous P system.
We first propose a P system that computes addition of two binary numbers of m bits. The P system works in O(m sequential and parallel steps using O(m types of objects. We next propose a P system for multiplication of the two binary numbers of m bits, and show that the P system works in O(m log m parallel steps or O(m^{3} sequential steps using O(m^{2} types of objects. Finally, we propose a P system for factorization of a positive integer of $m$ bits using the above P system as a sub-system. The P system computes the factorization in O(m log m parallel steps or O(4^{m}
Lonnemann, Jan; Linkersdörfer, Janosch; Hasselhorn, Marcus; Lindberg, Sven
2016-01-01
Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge.
Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.
Chen, Yalin; Yanke, Jill; Campbell, Jamie I D
2016-04-01
The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems. Each operation was trained in one language or the other. The subsequent test phase included all problems with addition and multiplication alternating across trials in two blocks, one in each language. Averaging over training language, the response time (RT) gains for trained problems relative to untrained problems were greater in the trained language than in the untrained language. Subsequent analysis showed that English training produced larger RT gains for trained problems relative to untrained problems in English at test relative to the untrained Chinese language. In contrast, there was no evidence with Chinese training that problem-specific RT gains differed between Chinese and the untrained English language. We propose that training in Chinese promoted a translation strategy for English arithmetic (particularly multiplication) that produced strong cross-language generalization of practice, whereas training in English strengthened relatively weak, English-language arithmetic memories and produced little generalization to Chinese (i.e., English training did not induce an English translation strategy for Chinese language trials). The results support the existence of language-specific strengthening of memory for everyday arithmetic facts.
Metcalfe, Arron W S; Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Menon, Vinod
2013-10-01
Baddeley and Hitch's multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7-9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development.
Rivera, S M; Reiss, A L; Eckert, M A; Menon, V
2005-11-01
Arithmetic reasoning is arguably one of the most important cognitive skills a child must master. Here we examine neurodevelopmental changes in mental arithmetic. Subjects (ages 8-19 years) viewed arithmetic equations and were asked to judge whether the results were correct or incorrect. During two-operand addition or subtraction trials, for which accuracy was comparable across age, older subjects showed greater activation in the left parietal cortex, along the supramarginal gyrus and adjoining anterior intra-parietal sulcus as well as the left lateral occipital temporal cortex. These age-related changes were not associated with alterations in gray matter density, and provide novel evidence for increased functional maturation with age. By contrast, younger subjects showed greater activation in the prefrontal cortex, including the dorsolateral and ventrolateral prefrontal cortex and the anterior cingulate cortex, suggesting that they require comparatively more working memory and attentional resources to achieve similar levels of mental arithmetic performance. Younger subjects also showed greater activation of the hippocampus and dorsal basal ganglia, reflecting the greater demands placed on both declarative and procedural memory systems. Our findings provide evidence for a process of increased functional specialization of the left inferior parietal cortex in mental arithmetic, a process that is accompanied by decreased dependence on memory and attentional resources with development. PMID:15716474
Palchaudhuri, Ayan
2016-01-01
This book describes the optimized implementations of several arithmetic datapath, controlpath and pseudorandom sequence generator circuits for realization of high performance arithmetic circuits targeted towards a specific family of the high-end Field Programmable Gate Arrays (FPGAs). It explores regular, modular, cascadable, and bit-sliced architectures of these circuits, by directly instantiating the target FPGA-specific primitives in the HDL. Every proposed architecture is justified with detailed mathematical analyses. Simultaneously, constrained placement of the circuit building blocks is performed, by placing the logically related hardware primitives in close proximity to one another by supplying relevant placement constraints in the Xilinx proprietary “User Constraints File”. The book covers the implementation of a GUI-based CAD tool named FlexiCore integrated with the Xilinx Integrated Software Environment (ISE) for design automation of platform-specific high-performance arithmetic circuits from us...
Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm.
Thevenot, Catherine; Fanget, Muriel; Fayol, Michel
2007-09-01
According to LeFevre, Sadesky, and Bisanz, averaging solution latencies in order to study individuals' arithmetic strategies can result in misleading conclusions. Therefore, in addition to classical chronometric data, they collected verbal reports and challenged the assumption that adults rely systematically on retrieval of arithmetic facts from memory to solve simple addition problems. However, Kirk and Ashcraft questioned the validity of such a methodology and concluded that a more appropriate method has to be found. Thus, we developed an operand recognition paradigm that does not rely on verbal reports or on solution latencies. In accordance with LeFevre et al., we show in a first experiment that adults resort to nonretrieval strategies to solve addition problems involving medium numbers. However, in a second experiment, we show that high-skilled individuals can solve the same problems using a retrieval strategy. The benefits of our paradigm to the study of arithmetic strategies are discussed. PMID:18035632
A VHDL Implementation of Direct, Pipelined and Distributed Arithmetic FIR Filters
Directory of Open Access Journals (Sweden)
Sucharitha. L
2013-03-01
Full Text Available Digital filters are typically used to modify or alter the attributes of a signal in the time or frequency domain. In this project, various FIR filter structures will be studied and implemented in VHDL. Basic arithmetic blocks to carry out DSP on FPGAs will be discussed. The very popular LUT based approach for arithmetic circuit implementation will be presented. The conventional PDSP MAC and Distributed arithmetic MAC units will be implemented and their performance will be compared. Usage of Pipelining in multipliers for improving the speed will also be discussed. The ModelSim XE simulator will be used to simulate the design at various stages. Xilinx synthesis tool (XST will be used to synthesize the design for spartan3E family FPGA (XC3S500E. Xilinx Placement {&} Routing tools will be used for backend, design optimization and I/O routing
Design of Parity Preserving Logic Based Fault Tolerant Reversible Arithmetic Logic Unit
Directory of Open Access Journals (Sweden)
Rakshith Saligram
2013-07-01
Full Text Available Reversible Logic is gaining significant consideration as the potential logic design style for implementationin modern nanotechnology and quantum computing with minimal impact on physical entropy .FaultTolerant reversible logic is one class of reversible logic that maintain the parity of the input and theoutputs. Significant contributions have been made in the literature towards the design of fault tolerantreversible logic gate structures and arithmetic units, however, there are not many efforts directed towardsthe design of fault tolerant reversible ALUs. Arithmetic Logic Unit (ALU is the prime performing unit inany computing device and it has to be made fault tolerant. In this paper we aim to design one such faulttolerant reversible ALU that is constructed using parity preserving reversible logic gates. The designedALU can generate up to seven Arithmetic operations and four logical operations.
Design of Parity Preserving Logic Based Fault Tolerant Reversible Arithmetic Logic Unit
Directory of Open Access Journals (Sweden)
Rakshith Saligram1
2013-06-01
Full Text Available Reversible Logic is gaining significant consideration as the potential logic design style for implementation in modern nanotechnology and quantum computing with minimal impact on physical entropy .Fault Tolerant reversible logic is one class of reversible logic that maintain the parity of the input and the outputs. Significant contributions have been made in the literature towards the design of fault tolerant reversible logic gate structures and arithmetic units, however, there are not many efforts directed towards the design of fault tolerant reversible ALUs. Arithmetic Logic Unit (ALU is the prime performing unit in any computing device and it has to be made fault tolerant. In this paper we aim to design one such fault tolerant reversible ALU that is constructed using parity preserving reversible logic gates. The designed ALU can generate up to seven Arithmetic operations and four logical operations
The functional anatomy of single-digit arithmetic in children with developmental dyslexia.
Evans, Tanya M; Flowers, D Lynn; Napoliello, Eileen M; Olulade, Olumide A; Eden, Guinevere F
2014-11-01
Some arithmetic procedures, such as addition of small numbers, rely on fact retrieval mechanisms supported by left hemisphere perisylvian language areas, while others, such as subtraction, rely on procedural-based mechanisms subserved by bilateral parietal cortices. Previous work suggests that developmental dyslexia, a reading disability, is accompanied by subtle deficits in retrieval-based arithmetic, possibly because of compromised left hemisphere function. To test this prediction, we compared brain activity underlying arithmetic problem solving in children with and without dyslexia during addition and subtraction operations using a factorial design. The main effect of arithmetic operation (addition versus subtraction) for both groups combined revealed activity during addition in the left superior temporal gyrus and activity during subtraction in the bilateral intraparietal sulcus, the right supramarginal gyrus and the anterior cingulate, consistent with prior studies. For the main effect of diagnostic group (dyslexics versus controls), we found less activity in dyslexic children in the left supramarginal gyrus. Finally, the interaction analysis revealed that while the control group showed a strong response in the right supramarginal gyrus for subtraction but not for addition, the dyslexic group engaged this region for both operations. This provides physiological evidence in support of the theory that children with dyslexia, because of disruption to left hemisphere language areas, use a less optimal route for retrieval-based arithmetic, engaging right hemisphere parietal regions typically used by good readers for procedural-based arithmetic. Our results highlight the importance of language processing for mathematical processing and illustrate that children with dyslexia have impairments that extend beyond reading.
Directory of Open Access Journals (Sweden)
Amandine eVan Rinsveld
2015-03-01
Full Text Available Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g. greater difficulties, error types, etc. in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German-French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g. unit-ten vs. ten-unit also induced significant modulations of bilinguals’ arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals.
Van Rinsveld, Amandine; Brunner, Martin; Landerl, Karin; Schiltz, Christine; Ugen, Sonja
2015-01-01
Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German-French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals. PMID:25821442
Van Rinsveld, Amandine; Brunner, Martin; Landerl, Karin; Schiltz, Christine; Ugen, Sonja
2015-01-01
Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German-French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals.
Contribution to the design of a micro-programmed floating point arithmetical operator
International Nuclear Information System (INIS)
This report is intended for a presentation of the implementation of an arithmetical operator. Fast microprocessor together with microprogramming techniques were used for development. For clarity, this report is shared in three parts following the different steps of design and development. The first part relates the preliminary study stage, setting down the outlines of the project: tentative data, choice of components and architecture of operator. The second part is devoted to the development step. It deals with implementation aid systems and computation algorithms for arithmetical functions. Results and conclusions are the subject of the third part. (author)
Munir, Kusnendar, Jajang; Rahmadhani
2016-02-01
This research aims to develop and test the effectiveness of multimedia in education for special education (MESE) of students with cognitive disabilities in introducing Arithmetic. Students with cognitive disabilities are those who have a level of intelligence under the normal ones. They think concretely and tend to have a very limited memory, switched concentration and forgot easily. The mastery of words is minimal, and also requires a long time to learn. These limitations will interfere in introduction learning to Arithmetic, with the material of numbers 1 to 10. The study resulted that MESE is worth to be used and enhanced the ability of the students.
On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds
Marshall, Simon
2011-01-01
In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomology grows exponentially as the local system grows. We also consider the twisted Ruelle zeta function of a closed arithmetic hyperbolic 3-manifold and we express the leading coefficient of its Laurent expansion at the origin in terms of the orders of the torsion subgroups of the cohomology.
Applications of interval arithmetic in solving polynomial equations by Wu's elimination method
Institute of Scientific and Technical Information of China (English)
CHEN Falai; YANG Wu
2005-01-01
Wu's elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach are two-folds: First, the problem of the numerical instability arisen from floating-point arithmetic is largely overcome. Second,the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved. Some examples are provided to illustrate the effectiveness of the proposed algorithm.
Andersson, Ulf
2008-01-01
Background: The study was conducted in an attempt to further our understanding of how working memory contributes to written arithmetical skills in children. Aim: The aim was to pinpoint the contribution of different central executive functions and to examine the contribution of the two subcomponents of children's written arithmetical skills.…
Alcoholado, Cristián; Diaz, Anita; Tagle, Arturo; Nussbaum, Miguel; Infante, Cristián
2016-01-01
This study aims to understand the differences in student learning outcomes and classroom behaviour when using the interpersonal computer, personal computer and pen-and-paper to solve arithmetic exercises. In this multi-session experiment, third grade students working on arithmetic exercises from various curricular units were divided into three…
Deaño, Manuel Deaño; Alfonso, Sonia; Das, Jagannath Prasad
2015-03-01
This study reports the cognitive and arithmetic improvement of a mathematical model based on the program PASS Remedial Program (PREP), which aims to improve specific cognitive processes underlying academic skills such as arithmetic. For this purpose, a group of 20 students from the last four grades of Primary Education was divided into two groups. One group (n=10) received training in the program and the other served as control. Students were assessed at pre and post intervention in the PASS cognitive processes (planning, attention, simultaneous and successive processing), general level of intelligence, and arithmetic performance in calculus and solving problems. Performance of children from the experimental group was significantly higher than that of the control group in cognitive process and arithmetic. This joint enhancement of cognitive and arithmetic processes was a result of the operationalization of training that promotes the encoding task, attention and planning, and learning by induction, mediation and verbalization. The implications of this are discussed. PMID:25594486
Numeral words and arithmetic operations in the Alor-Pantar languages
Schapper, Antoinette; Holton, Gary; Klamer, Marian; Kratochvíl, František; Robinson, Laura; Klamer, Marian
2014-01-01
The indigenous numerals of the AP languages, as well as the indigenous structures for arithmetic operations are currently under pressure from Indonesian, and will inevitably be replaced with Indonesian forms and structures. This chapter presents a documentary record of the forms and patterns current
Fehr, Thorsten; Weber, Jochen; Willmes, Klaus; Herrmann, Manfred
2010-01-01
Prodigies are individuals with exceptional mental abilities. How is it possible that some of these people mentally calculate exponentiations with high accuracy and speed? We examined CP, a mental calculation prodigy, and a control group of 11 normal calculators for moderate mental arithmetic tasks. CP has additionally been tested for exceptionally…
Arithmetic Facts Storage Deficit: The Hypersensitivity-to-Interference in Memory Hypothesis
De Visscher, Alice; Noël, Marie-Pascale
2014-01-01
Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, 2007). While various profiles of dyscalculia coexist, a general and persistent hallmark of this math learning disability is the difficulty in memorizing arithmetic facts (Geary, Hoard & Hamson, 1999; Jordan & Montani, 1997; Slade…
Working Memory in Nonsymbolic Approximate Arithmetic Processing: A Dual-Task Study with Preschoolers
Xenidou-Dervou, Iro; van Lieshout, Ernest C. D. M.; van der Schoot, Menno
2014-01-01
Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an…
Arithmetical Thinking in Children Attending Special Schools for the Intellectually Disabled
Eriksson, Gota
2008-01-01
This article focuses on spontaneous and progressive knowledge building in ''the arithmetic of the child.'' The aim is to investigate variations in the behavior patterns of eight pupils attending a school for the intellectually disabled. The study is based on the epistemology of radical constructivism and the methodology of multiple clinical…
Supervision of Teachers Based on Adjusted Arithmetic Learning in Special Education
Eriksson, Gota
2008-01-01
This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…
Evaluation of AnimalWatch: An Intelligent Tutoring System for Arithmetic and Fractions
Beal, Carole R.; Arroyo, Ivon M.; Cohen, Paul R.; Woolf, Beverly P.
2010-01-01
Three studies were conducted with middle school students to evaluate a web-based intelligent tutoring system (ITS) for arithmetic and fractions. The studies involved pre and post test comparisons, as well as group comparisons to assess the impact of the ITS on students' math problem solving. Results indicated that students improved from pre to…
A Teachable Agent Game Engaging Primary School Children to Learn Arithmetic Concepts and Reasoning
Pareto, Lena
2014-01-01
In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…
Abikoff, H; Courtney, M E; Szeibel, P J; Koplewicz, H S
1996-05-01
This study evaluated the impact of extra-task stimulation on the academic task performance of children with attention-deficit/hyperactivity disorder (ADHD). Twenty boys with ADHD and 20 nondisabled boys worked on an arithmetic task during high stimulation (music), low stimulation (speech), and no stimulation (silence). The music "distractors" were individualized for each child, and the arithmetic problems were at each child's ability level. A significant Group x Condition interaction was found for number of correct answers. Specifically, the nondisabled youngsters performed similarly under all three auditory conditions. In contrast, the children with ADHD did significantly better under the music condition than speech or silence conditions. However, a significant Group x Order interaction indicated that arithmetic performance was enhanced only for those children with ADHD who received music as the first condition. The facilitative effects of salient auditory stimulation on the arithmetic performance of the children with ADHD provide some support for the underarousal/optimal stimulation theory of ADHD. PMID:8732885
A practical approach to model checking Duration Calculus using Presburger Arithmetic
DEFF Research Database (Denmark)
Hansen, Michael Reichhardt; Dung, Phan Anh; Brekling, Aske Wiid
2014-01-01
This paper investigates the feasibility of reducing a model-checking problem K ⊧ ϕ for discrete time Duration Calculus to the decision problem for Presburger Arithmetic. Theoretical results point at severe limitations of this approach: (1) the reduction in Fränzle and Hansen (Int J Softw Inform 3...... limits of the approach are illustrated by a family of examples....
Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca
2015-01-01
Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…
Predicting arithmetical achievement from neuro-psychological performance: a longitudinal study.
Fayol, M; Barrouillet, P; Marinthe, C
1998-08-01
In this article, we show that the performances of 5- to 6-year-old children in arithmetic tests can be predicted from their performances in neuro-psychological tests administered a number of months in advance, independently of their level of development. PMID:9818514
Identifying Strategies in Arithmetic with the Operand Recognition Paradigm: A Matter of Switch Cost?
Thevenot, Catherine; Castel, Caroline; Danjon, Juliette; Fayol, Michel
2015-01-01
Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we…
Arithmetic memory networks established in childhood are changed by experience in adulthood.
Martinez-Lincoln, Amanda; Cortinas, Christina; Wicha, Nicole Y Y
2015-01-01
Adult bilinguals show stronger access to multiplication tables when using the language in which they learned arithmetic during childhood (LA+) than the other language (LA-), implying language-specific encoding of math facts. However, most bilinguals use LA+ throughout their life, confounding the impact of encoding and use. We tested if using arithmetic facts in LA- could reduce this LA- disadvantage. We measured event related brain potentials while bilingual teachers judged the correctness of multiplication problems in each of their languages. Critically, each teacher taught arithmetic in either LA+ or LA-. Earlier N400 peak latency was observed in both groups for the teaching than non-teaching language, showing more efficient access to these facts with use. LA+ teachers maintained an LA+ advantage, while LA- teachers showed equivalent N400 congruency effects (for incorrect versus correct solutions) in both languages. LA- teachers also showed a late positive component that may reflect conflict monitoring between their LA+ and a strong LA-. Thus, the LA- disadvantage for exact arithmetic established in early bilingual education can be mitigated by later use of LA-. PMID:25445361
On the history of van der Waerden's theorem on arithmetic progressions
Directory of Open Access Journals (Sweden)
Tom C. Brown
2001-12-01
Full Text Available In this expository note, we discuss the celebrated theorem known as ``van der Waerden's theorem on arithmetic progressions", the history of work on upper and lower bounds for the function associated with this theorem, a number of generalizations, and some open problems.
Development of Working Memory and Performance in Arithmetic: A Longitudinal Study with Children
López, Magdalena
2014-01-01
Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…
On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups
Sengun, Mehmet Haluk
2010-01-01
Numerical data concerning the growth of torsion in the first homology of non-arithmetic hyperbolic tetrahedral groups are collected. The data provide support the speculations of Bergeron and Venkatesh on the growth of torsion homology and the regulators for lattices in SL(2,C).
Eye Gaze Reveals a Fast, Parallel Extraction of the Syntax of Arithmetic Formulas
Schneider, Elisa; Maruyama, Masaki; Dehaene, Stanislas; Sigman, Mariano
2012-01-01
Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols. We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the…
The foundations of arithmetic a logico-mathematical enquiry into the concept of number
Frege, Gottlob
1986-01-01
The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics, general ontology, and mathematics.
International Nuclear Information System (INIS)
The structure and software of the arithmetical module for the multi-microprocessor intelligent graphics terminal designed for realization of the world coordinate two-dimensional transformation are described. The module performs the operations like coordinate system displacement, scaling and rotation as well as transformations for window/viewport separation
Reinvention of early algebra : developmental research on the transition from arithmetic to algebra
Amerom, B.A. van
2002-01-01
In chapter 1 we give our reasons for carrying out this developmental research project on the transition from arithmetic to algebra, which includes the design of an experimental learning strand on solving equations. Chapter 2 describes the theoretical background of the book: current views on the teac
A simplified proof of arithmetical completeness theorem for provability logic GLP
Beklemishev, L.D.
2011-01-01
We present a simplified proof of Japaridze’s arithmetical completeness theorem for the well-known polymodal provability logic GLP. The simplification is achieved by employing a fragment J of GLP that enjoys a more convenient Kripke-style semantics than the logic considered in the papers by Ignatiev
Kamii, Constance
This book describes and develops an innovative program of teaching arithmetic in the early elementary grades. The educational strategies employed are based on Jean Piaget's constructivist scientific ideas of how children develop logico-mathematical thinking. The book is written in collaboration with a classroom teacher and premised on the…
Hardware realizations of arithmetic with complex integer numbers on PLD-base
Directory of Open Access Journals (Sweden)
Opanasenko V. N.
2008-10-01
Full Text Available Hardware realizations of arithmetic with complex integer numbers were proposed. The generators of sine and cosine with different frequency were used to make behavior stand. Real verification was made by block Spartan–3–400 Evaluation Kit, which connect up PCI of personal computer.
Do Birth Order, Family Size and Gender Affect Arithmetic Achievement in Elementary School?
Desoete, Annemie
2008-01-01
Introduction: For decades birth order and gender differences have attracted research attention. Method: Birth order, family size and gender, and the relationship with arithmetic achievement is studied among 1152 elementary school children (540 girls, 612 boys) in Flanders. Children were matched on socioeconomic status of the parents and…
An image joint compression-encryption algorithm based on adaptive arithmetic coding
International Nuclear Information System (INIS)
Through a series of studies on arithmetic coding and arithmetic encryption, a novel image joint compression-encryption algorithm based on adaptive arithmetic coding is proposed. The contexts produced in the process of image compression are modified by keys in order to achieve image joint compression encryption. Combined with the bit-plane coding technique, the discrete wavelet transform coefficients in different resolutions can be encrypted respectively with different keys, so that the resolution selective encryption is realized to meet different application needs. Zero-tree coding is improved, and adaptive arithmetic coding is introduced. Then, the proposed joint compression-encryption algorithm is simulated. The simulation results show that as long as the parameters are selected appropriately, the compression efficiency of proposed image joint compression-encryption algorithm is basically identical to that of the original image compression algorithm, and the security of the proposed algorithm is better than the joint encryption algorithm based on interval splitting. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Bragman, Ruth; Hardy, Robert C.
1982-01-01
Results from testing 20 first graders in a remedial class in Maryland indicated that: same pattern recognition was significantly higher than reverse pattern recognition; identical pattern recognition did not affect performance on reading and arithmetic achievement; reverse pattern recognition significantly affected performance on reading and…
Maschietto, Michela
2015-01-01
This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero + 1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory…
Hui, Sheldon; Suganthan, Ponnuthurai N
2016-01-01
Multimodal optimization problems consists of multiple equal or comparable spatially distributed solutions. Niching and clustering differential evolution (DE) techniques have been demonstrated to be highly effective for solving such problems. The key challenge in the speciation niching technique is to balance between local solution exploitation and global exploration. Our proposal enhances exploration by applying arithmetic recombination with speciation and improves exploitation of individual peaks by applying neighborhood mutation with ensemble strategies. Our novel algorithm, called ensemble and arithmetic recombination-based speciation DE, is shown to either outperform or perform comparably to the state-of-the-art algorithms on 29 common multimodal benchmark problems. Comparable performance is observed only when some problems are solved perfectly by the algorithms in the literature. PMID:25781971
Directory of Open Access Journals (Sweden)
Erich Selder
2015-01-01
Full Text Available The correspondence between right triangles with rational sides, triplets of rational squares in arithmetic succession and integral solutions of certain quadratic forms is well-known. We show how this correspondence can be extended to the generalized notions of rational θ-triangles, rational squares occurring in arithmetic progressions and concordant forms. In our approach we establish one-to-one mappings to rational points on certain elliptic curves and examine in detail the role of solutions of the θ-congruent number problem and the concordant form problem associated with nontrivial torsion points on the corresponding elliptic curves. This approach allows us to combine and extend some disjoint results obtained by a number of authors, to clarify some statements in the literature and to answer some hitherto open questions.
DEBT AMORTIZATION AND SIMPLE INTEREST: THE CASE OF PAYMENTS IN AN ARITHMETIC PROGRESSION
Directory of Open Access Journals (Sweden)
Clovis José Daudt Lyra Darrigue Faro
2014-12-01
Full Text Available With the argument that, necessarily, compound interest implies anatocism, the Brazilian Judiciary has been determining that, specially for the case of debt amortization in accordance with the so called Tabela Price, when we have constant payments, the use of simple interest. With the same determination occurring in the case of the Constant Amortization Scheme, when the payments follow arithmetic progressions. However, as simple interest lacks the property of time subdivision, it is shown that as in the case of constant payments, the adoption of simple interest in the case of payments following an arithmetic progression results in amortization schemes that are financially inconsistent. In the sense that the determination of the outstanding principal in accordance with the prospective, retrospective and of recurrence methods lead to conflicting results. To this end, four different variations of the use of simple interest are numerically analyzed.
Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model.
Gallas, Marcia R; Gallas, Jason A C
2015-06-01
We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.
Lightweight Floating-Point Arithmetic: Case Study of Inverse Discrete Cosine Transform
Fang, Fang; Chen, Tsuhan; Rutenbar, Rob A.
2002-12-01
To enable floating-point (FP) signal processing applications in low-power mobile devices, we propose lightweight floating-point arithmetic. It offers a wider range of precision/power/speed/area trade-offs, but is wrapped in forms that hide the complexity of the underlying implementations from both multimedia software designers and hardware designers. Libraries implemented in C++ and Verilog provide flexible and robust floating-point units with variable bit-width formats, multiple rounding modes and other features. This solution bridges the design gap between software and hardware, and accelerates the design cycle from algorithm to chip by avoiding the translation to fixed-point arithmetic. We demonstrate the effectiveness of the proposed scheme using the inverse discrete cosine transform (IDCT), in the context of video coding, as an example. Further, we implement lightweight floating-point IDCT into hardware and demonstrate the power and area reduction.
Arithmetic gravity and Yang-Mills theory: An approach to adelic physics via algebraic spaces
Schmidt, Rene
2008-01-01
This work is a dissertation thesis written at the WWU Muenster (Germany), supervised by Prof. Dr. Raimar Wulkenhaar. We present an approach to adelic physics based on the language of algebraic spaces. Relative algebraic spaces X over a base S are considered as fundamental objects which describe space-time. This yields a formulation of general relativity which is covariant with respect to changes of the chosen domain of numbers S. With regard to adelic physics the choice of S as an excellent Dedekind scheme is of interest (because this way also the finite prime spots, i.e. the p-adic degrees of freedom are taken into account). In this arithmetic case, it turns out that X is a Neron model. This enables us to make concrete statements concerning the structure of the space-time described by X. Furthermore, some solutions of the arithmetic Einstein equations are presented. In a next step, Yang-Mills gauge fields are incorporated.
A New Arithmetic Coding System Combining Source Channel Coding and MAP Decoding
Institute of Scientific and Technical Information of China (English)
PANG Yu-ye; SUN Jun; WANG Jia
2007-01-01
A new arithmetic coding system combining source channel coding and maximum a posteriori decoding were proposed.It combines source coding and error correction tasks into one unified process by introducing an adaptive forbidden symbol.The proposed system achieves fixed length code words by adaptively adjusting the probability of the forbidden symbol and adding tail digits of variable length.The corresponding improved MAP decoding metric was derived.The proposed system can improve the performance.Simulations were performed on AWGN channels with various noise levels by using both hard and soft decision with BPSK modulation.The results show its performance is slightly better than that of our adaptive arithmetic error correcting coding system using a forbidden symbol.
Fleeting footsteps tracing the conception of arithmetic and algebra in ancient China
Yong, Lam Lay
2004-01-01
The Hindu-Arabic numeral system (1, 2, 3,...) is one of mankind''sgreatest achievements and one of its most commonly usedinventions. How did it originate? Those who have written about thenumeral system have hypothesized that it originated in India; however,there is little evidence to support this claim. This book provides considerable evidence to show that theHindu-Arabic numeral system, despite its commonly accepted name,has its origins in the Chinese rod numeral system. This system waswidely used in China from antiquity till the 16th century. It was usedby officials, astronomers, traders and others to perform addition,subtraction, multiplication, division and other arithmetic operations,and also used by mathematicians to develop arithmetic andalgebra. Based on this system, numerous mathematical treatises werewritten.
DNA based arithmetic function: a half adder based on DNA strand displacement.
Li, Wei; Zhang, Fei; Yan, Hao; Liu, Yan
2016-02-14
Biomolecular programming utilizes the reactions and information stored in biological molecules, such as proteins and nucleic acids, for computational purposes. DNA has proven itself an excellent candidate for building logic operating systems due to its highly predictable molecular behavior. In this work we designed and realized an XOR logic gate and an AND logic gate based on DNA strand displacement reactions. These logic gates utilize ssDNA as input and output signals. The XOR gate and the AND gate were used as building blocks for constructing a half adder logic circuit, which is a primary step in constructing a full adder, a basic arithmetic unit in computing. This work provides the field of DNA molecular programming with a potential universal arithmetic tool. PMID:26814628
Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.
Buelow, Melissa T; Frakey, Laura L
2013-06-01
Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.
DNA based arithmetic function: a half adder based on DNA strand displacement
Li, Wei; Zhang, Fei; Yan, Hao; Liu, Yan
2016-02-01
Biomolecular programming utilizes the reactions and information stored in biological molecules, such as proteins and nucleic acids, for computational purposes. DNA has proven itself an excellent candidate for building logic operating systems due to its highly predictable molecular behavior. In this work we designed and realized an XOR logic gate and an AND logic gate based on DNA strand displacement reactions. These logic gates utilize ssDNA as input and output signals. The XOR gate and the AND gate were used as building blocks for constructing a half adder logic circuit, which is a primary step in constructing a full adder, a basic arithmetic unit in computing. This work provides the field of DNA molecular programming with a potential universal arithmetic tool.Biomolecular programming utilizes the reactions and information stored in biological molecules, such as proteins and nucleic acids, for computational purposes. DNA has proven itself an excellent candidate for building logic operating systems due to its highly predictable molecular behavior. In this work we designed and realized an XOR logic gate and an AND logic gate based on DNA strand displacement reactions. These logic gates utilize ssDNA as input and output signals. The XOR gate and the AND gate were used as building blocks for constructing a half adder logic circuit, which is a primary step in constructing a full adder, a basic arithmetic unit in computing. This work provides the field of DNA molecular programming with a potential universal arithmetic tool. Electronic supplementary information (ESI) available: Detailed descriptions of DNA logic gate design, materials and methods, and additional data analysis. See DOI: 10.1039/c5nr08497k
Institute of Scientific and Technical Information of China (English)
ZHANG Yun-ting; ZHANG Quan; ZHANG Jing; LI Wei
2005-01-01
Background Asymmetry of bilateral cerebral function, i.e. laterality, is an important phenomenon in many brain actions: arithmetic calculation may be one of these phenomena. In this study, first, laterality of brain areas associated with arithmetic calculations was revealed by functional magnetic resonance imaging (fMRI). Second, the relationship among laterality, handedness, and types of arithmetic task was assessed. Third, we postulate possible reasons for laterality.Methods Using a block-designed experiment, twenty-five right-handed and seven left-handed healthy volunteers carried out simple calculations, complex calculations and proximity judgments. T1WI and GRE-EPI fMRI were performed with a GE 1.5T whole body MRI scanner. Statistical parametric mapping (SPM99) was used to process data and localize functional areas. Numbers of activated voxels were recorded to calculate laterality index for evaluating the laterality of functional brain areas.Results For both groups, the activation of functional areas in the frontal lobe showed a tendency towards the nonpredominant hand side, but the functional areas in the inferior parietal lobule had left laterality. During simple and complex calculations, the laterality indices of the prefrontal cortex and premotor area were higher in the right-handed group than that in the left-handed group, whereas the laterality of the inferior parietal lobule had no such significant difference. In both groups, when the difficulty of the task increased, the laterality of the prefrontal cortex, premotor area, and inferior parietal lobule decreased, but the laterality of posterior part of the inferior frontal gyrus increased.Conclusions The laterality of the functional brain areas associated with arithmetic calculations can be detected with fMRI. The laterality of the functional areas was related to handedness and task difficulty.
Separators of Arithmetically Cohen-Macaulay fat points in P^1 x P^1
Guardo, Elena
2010-01-01
Let Z be a set of fat points in P^1 x P^1 that is also arithmetically Cohen-Macaulay (ACM). We describe how to compute the degree of a separator of a fat point of multiplicity m for each point in the support of Z using only a numerical description of Z. Our formula extends the case of reduced points which was previously known.
Arithmetic properties of the first secant variety to a projective variety
Vermeire, Peter
2010-01-01
Under an explicit positivity condition, we show the first secant variety of a linearly normal smooth variety is projectively normal, give results on the regularity of the ideal of the secant variety, and give conditions on the variety that are equivalent to the secant variety being arithmetically Cohen-Macaulay. Under this same condition, we then show that if $X$ satisfies $N_{p+2\\dim(X)}$, then the secant variety satisfies $N_{3,p}$.
Computer Arithmetic Algorithms for Mega-Digit Floating Point Numbers' Precision
Musbah J. Aqel; Mohammed H. Saleh
2007-01-01
IEEE standard 754 floating point is the most common representation used for floating point numbers, and many computer arithmetic algorithms are developed for basic operations on this standard. In this study, new computer algorithms are proposed to increase the precision range and to solve some problems that are available while using these algorithms. However, these algorithms provide an optional range of required accuracy (Mega-Digit precision) to meet new computer's applications.
Bogdanov, Alexander; Khramushin, Vasily
2016-02-01
The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
Mei, T.
2009-01-01
Based on the MRDP theorem, we introduce the ideas of the proof equation of a formula and universal proof equation of Peano Arithmetic (PA); and then, combining universal proof equation and G\\"odel's Second Incompleteness Theorem, it is proved that, if PA is consistent, then for every axiom and every theorem of PA, we can construct a corresponding undecidable proposition with Diophantine form. Finally, we present an approach that transforms seeking a proof of a mathematical (set theoretical, n...
Interactivity And Mental Arithmetic: Coupling Mind And World Transforms And Enhances Performance
Directory of Open Access Journals (Sweden)
Guthrie Lisa G.
2015-06-01
Full Text Available Interactivity has been linked to better performance in problem solving, due in part to a more efficient allocation of attentional resources, a better distribution of cognitive load, but perhaps more important by enabling the reasoner to shape and reshape the physical problem presentation to promote the development of the problem solution. Interactivity in solving quotidian arithmetic problems involves gestures, pointing, and the recruitment of artefacts to facilitate computation and augment efficiency. In the experiment reported here, different types of interactivity were examined with a series of mental arithmetic problems. Using a repeated-measures design, participants solved series of five 11-digit sums in four conditions that varied in the type of interactivity: (i no interactivity (participants solved the problems with their hands on the table top, (ii pointing (participants could point at the numbers, (iii pen and paper (participants could note interim totals with a pen, and (iv tokens (the sums were presented as 11 numbered tokens the arrangement of which participants were free to modify as they proceeded to the solution. Performance in the four conditions was measured in terms of accuracy, calculation error, and efficiency (a ratio composed of the proportion correct over the proportion of time invested in working on the sums. These quantitative analyses were supplemented by a detailed qualitative examination of a participant’s actions in the different conditions. The integration of artefacts, such as tokens or a pen, offered reasoners the opportunity to reconfigure the physical presentation of the problem, enacting different arithmetic strategies: the affordance landscape shifts as the problem trajectory is enacted through interactivity, and this generally produced better “mental” arithmetic performance. Participants also felt more positive about and better engaged with the task when they could reconfigure the problem presentation
Campbell, Jamie I. D.
2005-01-01
Meuter and Allport (1999) demonstrated greater RT (response time) costs for bilinguals to switch to their first language (L1) from their second language (L2) relative to switching to L2 from L1. Here, analyses of digit naming and simple arithmetic (from 2+2 to 9+9 and from 2x2 to 9x9) by Chinese-English bilinguals demonstrated that these…
Schlimm, Dirk; Neth, Hansjörg
2008-01-01
To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar - a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate trade-offs between problem representation, algorithm, and interactive resources....
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
Aerts, Diederik; Czachor, Marek; Kuna, Maciej
2016-10-01
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the expected basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
Zhang, Shaohua
2009-01-01
The problem of the least prime number in an arithmetic progression is one of the most important topics in Number Theory. In [11], we are the first to study the relations between this problem and Goldbach's conjecture. In this paper, we further consider its applications to Goldbach's conjecture and refine the result in [11]. Moreover, we also try to generalize the problem of the least prime number in an arithmetic progression and give an analogy of Goldbach's conjecture.
Willard, Dan E.
2006-01-01
Gödel’s Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show that axiomatizations for a computer’s floating point arithmetic can recognize their cut-free consistency in a stronger respect than is feasible under integer arithmetics. This paper will include both new generalizations of the Second Incompleteness Theorem and techniques for evading it.
Potential Infinity, Abstraction Principles and Arithmetic (Leśniewski Style
Directory of Open Access Journals (Sweden)
Rafal Urbaniak
2016-06-01
Full Text Available This paper starts with an explanation of how the logicist research program can be approached within the framework of Leśniewski’s systems. One nice feature of the system is that Hume’s Principle is derivable in it from an explicit definition of natural numbers. I generalize this result to show that all predicative abstraction principles corresponding to second-level relations, which are provably equivalence relations, are provable. However, the system fails, despite being much neater than the construction of Principia Mathematica (PM. One of the key reasons is that, just as in the case of the system of PM, without the assumption that infinitely many objects exist, (renderings of most of the standard axioms of Peano Arithmetic are not derivable in the system. I prove that introducing modal quantifiers meant to capture the intuitions behind potential infinity results in the (renderings of axioms of Peano Arithmetic (PA being valid in all relational models (i.e. Kripke-style models, to be defined later on of the extended language. The second, historical part of the paper contains a user-friendly description of Leśniewski’s own arithmetic and a brief investigation into its properties.
Heuristics and representational change in two-move matchstick arithmetic tasks
Directory of Open Access Journals (Sweden)
Michael Öllinger
2006-01-01
Full Text Available Insight problems are problems where the problem solver struggles to find a solution until * aha! * the solution suddenly appears. Two contemporary theories suggest that insight problems are difficult either because problem solvers begin with an incorrect representation of the problem, or that problem solvers apply inappropriate heuristics to the problem. The relative contributions of representational change and inappropriate heuristics on the process of insight problem solving was studied with a task that required the problem solver to move two matchsticks in order to transform an incorrect arithmetic statement into a correct one. Problem solvers (N = 120 worked on two different types of two-move matchstick arithmetic problems that both varied with respect to the effectiveness of heuristics and to the degree of a necessary representational change of the problem representation. A strong influence of representational change on solution rates was found whereas the influence of heuristics hadminimal effects on solution rates. That is, the difficulty of insight problems within the two-move matchstick arithmetic domain is governed by the degree of representational change required. A model is presented that details representational change as the necessary condition for ensuring that appropriate heuristics can be applied on the proper problem representation.
PaCAL: A Python Package for Arithmetic Computations with Random Variables
Directory of Open Access Journals (Sweden)
Marcin Korze?
2014-05-01
Full Text Available In this paper we present PaCAL, a Python package for arithmetical computations on random variables. The package is capable of performing the four arithmetic operations: addition, subtraction, multiplication and division, as well as computing many standard functions of random variables. Summary statistics, random number generation, plots, and histograms of the resulting distributions can easily be obtained and distribution parameter ?tting is also available. The operations are performed numerically and their results interpolated allowing for arbitrary arithmetic operations on random variables following practically any probability distribution encountered in practice. The package is easy to use, as operations on random variables are performed just as they are on standard Python variables. Independence of random variables is, by default, assumed on each step but some computations on dependent random variables are also possible. We demonstrate on several examples that the results are very accurate, often close to machine precision. Practical applications include statistics, physical measurements or estimation of error distributions in scienti?c computations.
Directory of Open Access Journals (Sweden)
R Kalpana
2013-08-01
Full Text Available To localize the brain dynamics for cognitive processes from EEG signature has been a challenging taskfrom last two decades. In this paper we explore the spatial-temporal correlations of brain electricalneuronal activity for cognitive task such as Arithmetic and Motor Task using 3D cortical distributionmethod. Ten healthy right handed volunteers participated in the experiment. EEG signal was acquiredduring resting state with eyes open and eyes closed; performing motor task and arithmetic calculations.The signal was then computed for three dimensional cortical distributions on realistic head model withMNI152 template using standardized low resolution brain electromagnetic tomography (sLORETA. Thiswas followed by an appropriate standardization of the current density, producing images of electricneuronal activity without localization bias. Neuronal generators responsible for cognitive state such asArithmetic Task and Motor Task were localized. The result was correlated with the previous neuroimaging(fMRI study investigation. Hence our result directed that the neuronal activity from EEG signal can bedemonstrated in cortical level with good spatial resolution. 3D cortical distribution method, thus, may beused to obtain both spatial and temporal information from EEG signal and may prove to be a significanttechnique to investigate the cognitive functions in mental health and brain dysfunctions. Also, it may behelpful for brain/human computer interfacing.
The Effect Of Peer Collaboration On Children’s Arithmetic And Self-Regulated Learning Skills
Directory of Open Access Journals (Sweden)
Joakim Samuelsson
2010-12-01
Full Text Available The present study examines the effect of peer collaboration, teaching children arithmetic in the beginning of 7th grade, age 13 years. Peer collaboration groups are compared to two different structured teaching methods, traditional and independent teaching. Progress made by these students are related to measures of their arithmetic ability, calculation and quantitative concept, as well as their self-regulated learning skills in mathematics, characterised as internal and instrumental motivation, self-concept and anxiety. The results will be discussed with reference to Piaget´s theory of the relation between social interaction and cognitive development. This study has a split-plot factorial design with time as within-subject and type of intervention as a between-subject factor. Students’ progress in quantitative concepts is significantly better if teachers teach traditionally or with peer collaboration. The results show that there are no significant differences between teaching methods when assessing arithmetic in total and calculation. Peer collaboration is more effective than traditional and independent work for students’ internal motivation. Traditional work and peer collaboration are more effective than independent work for students’ self-concept.
Switching Arithmetic for DC to DC Converters Using Delta Sigma Modulator Based Control Circuit
Directory of Open Access Journals (Sweden)
K.Diwakar
2016-02-01
Full Text Available In the proposed arithmetic unit for dc to dc converters using delta sigma modulator, a new technique is proposed for addition and multiplication of sampled analog signals. The output is in digital form to drive the converters. The conventional method has input signal limitation whereas in the proposed method the inputs can vary to full-scale. The addition of two discrete signals is done by sampling the two signals at a period called update period and feeding each signal to the input of signal dependant delta sigma modulator for half of the update period and combining the outputs for the update period. The extension of three discrete data addition can be carried out by using the same technique. For the multiplication of two discrete signals different method is adopted. One analog signal is fed to the input of first delta-sigma modulator (DSM1 after sampling. The sampled output of the second analog signal is negated or not negated depending on the bit state at the output of DSM1 and is fed to the input of second DSM(DSM2. The resulting bit stream at the output of DSM2 is the digital representation of the product of the sampled data of the two analog signals. In order to multiply three discrete data, the sampled output of third data is negated or not negated depending on the bit state at the output of DSM2 and is fed to the input of third DSM(DSM3. The resulting bit stream at the output of DSM3 is the digital representation of the product of the sampled data of the three analog signals. Using the proposed adder and multiplier circuits any expressions can be evaluated such that the average value of the digital output of the arithmetic unit over the update period gives the value of expressions during that period. The digital output of the arithmetic unit is used to drive the dc-dc converters.
The Influence of verbalization on the pattern of cortical activation during mental arithmetic
Directory of Open Access Journals (Sweden)
Zarnhofer Sabrina
2012-03-01
Full Text Available Abstract Background The aim of the present functional magnetic resonance imaging (fMRI study at 3 T was to investigate the influence of the verbal-visual cognitive style on cerebral activation patterns during mental arithmetic. In the domain of arithmetic, a visual style might for example mean to visualize numbers and (intermediate results, and a verbal style might mean, that numbers and (intermediate results are verbally repeated. In this study, we investigated, first, whether verbalizers show activations in areas for language processing, and whether visualizers show activations in areas for visual processing during mental arithmetic. Some researchers have proposed that the left and right intraparietal sulcus (IPS, and the left angular gyrus (AG, two areas involved in number processing, show some domain or modality specificity. That is, verbal for the left AG, and visual for the left and right IPS. We investigated, second, whether the activation in these areas implied in number processing depended on an individual's cognitive style. Methods 42 young healthy adults participated in the fMRI study. The study comprised two functional sessions. In the first session, subtraction and multiplication problems were presented in an event-related design, and in the second functional session, multiplications were presented in two formats, as Arabic numerals and as written number words, in an event-related design. The individual's habitual use of visualization and verbalization during mental arithmetic was assessed by a short self-report assessment. Results We observed in both functional sessions that the use of verbalization predicts activation in brain areas associated with language (supramarginal gyrus and auditory processing (Heschl's gyrus, Rolandic operculum. However, we found no modulation of activation in the left AG as a function of verbalization. Conclusions Our results confirm that strong verbalizers use mental speech as a form of mental
A motif extraction algorithm based on hashing and modulo-4 arithmetic.
Sheng, Huitao; Mehrotra, Kishan; Mohan, Chilukuri; Raina, Ramesh
2008-01-01
We develop an algorithm to identify cis-elements in promoter regions of coregulated genes. This algorithm searches for subsequences of desired length whose frequency of occurrence is relatively high, while accounting for slightly perturbed variants using hash table and modulo arithmetic. Motifs are evaluated using profile matrices and higher-order Markov background model. Simulation results show that our algorithm discovers more motifs present in the test sequences, when compared with two well-known motif-discovery tools (MDScan and AlignACE). The algorithm produces very promising results on real data set; the output of the algorithm contained many known motifs.
Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory
Schimmrigk, R
2003-01-01
It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and the underlying conformal field theory. Specifically it is pointed out how the algebraic number field determined by the fusion rules of the conformal field theory can be derived from the number theoretic structure of the cohomological Hasse-Weil L-function determined by Artin's congruent zeta function of the algebraic variety. In this context a natural number theoretic characterization arises for the quantum dimensions in this geometrically determined algebraic number field.
A Pixel Domain Video Coding based on Turbo code and Arithmetic code
Directory of Open Access Journals (Sweden)
Cyrine Lahsini
2012-05-01
Full Text Available In recent years, with emerging applications such as multimedia sensors networks, wirelesslow-power surveillance and mobile camera phones, the traditional video coding architecture in beingchallenged. In fact, these applications have different requirements than those of the broadcast videodelivery systems: a low power consumption at the encoder side is essential.In this context, we propose a pixel-domain video coding scheme which fits well in these senarios.In this system, both the arithmetic and turbo codes are used to encode the video sequence's frames.Simulations results show significant gains over Pixel-domain Wyner-Ziv video codeingr.
Algorithmic solution of arithmetic problems and operands-answer associations in long-term memory.
Thevenot, C; Barrouillet, P; Fayol, M
2001-05-01
Many developmental models of arithmetic problem solving assume that any algorithmic solution of a given problem results in an association of the two operands and the answer in memory (Logan & Klapp, 1991; Siegler, 1996). In this experiment, adults had to perform either an operation or a comparison on the same pairs of two-digit numbers and then a recognition task. It is shown that unlike comparisons, the algorithmic solution of operations impairs the recognition of operands in adults. Thus, the postulate of a necessary and automatic storage of operands-answer associations in memory when young children solve additions by algorithmic strategies needs to be qualified. PMID:11394064
Saniga, M
2001-01-01
It is shown that the two sequences of characteristic dimensions of transfinite heterotic string space-time found by El Naschie can be remarkably well accounted for in terms of the arithmetic of self-conjugate homaloidal nets of plane algebraic curves of orders 3 to 20. A firm algebraic geometrical justification is thus given not only for all the relevant dimensions of the classical theory, but also for other two dimensions proposed by El Naschie, viz. the inverse of quantum gravity coupling constant (~42.36067977) and that of (one half of) fine structure constant (~68.54101967). A non-trivial coupling between the two El Naschie sequences is also revealed.
Constant-coefficient FIR filters based on residue number system arithmetic
Directory of Open Access Journals (Sweden)
Stamenković Negovan
2012-01-01
Full Text Available In this paper, the design of a Finite Impulse Response (FIR filter based on the residue number system (RNS is presented. We chose to implement it in the (RNS, because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC unit. The three moduli set {2n+1,2n,2n-1}, which avoids 2n+1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.
Goldbach Conjecture and the least prime number in an arithmetic progression
Zhang, Shaohua
2008-01-01
In this Note, we try to study the relations between the Goldbach Conjecture and the least prime number in an arithmetic progression. We give a new weakened form of the Goldbach Conjecture. We prove that this weakened form and a weakened form of the Chowla Hypothesis imply that every sufficiently large even integer may be written as the sum of two distinct primes. R\\'{e}sum\\'{e} La conjecture de Goldbach et le plus petit nombre premier dans une progression arithm\\'{e}tique Dans ce document, no...
Directory of Open Access Journals (Sweden)
Bogdanov Alexander
2016-01-01
Full Text Available The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
Transcranial random noise stimulation mitigates increased difficulty in an arithmetic learning task.
Popescu, Tudor; Krause, Beatrix; Terhune, Devin B; Twose, Olivia; Page, Thomas; Humphreys, Glyn; Cohen Kadosh, Roi
2016-01-29
Proficiency in arithmetic learning can be achieved by using a multitude of strategies, the most salient of which are procedural learning (applying a certain set of computations) and rote learning (direct retrieval from long-term memory). Here we investigated the effect of transcranial random noise stimulation (tRNS), a non-invasive brain stimulation method previously shown to enhance cognitive training, on both types of learning in a 5-day sham-controlled training study, under two conditions of task difficulty, defined in terms of item repetition. On the basis of previous research implicating the prefrontal and posterior parietal cortex in early and late stages of arithmetic learning, respectively, sham-controlled tRNS was applied to bilateral prefrontal cortex for the first 3 days and to the posterior parietal cortex for the last 2 days of a 5-day training phase. The training involved learning to solve arithmetic problems by applying a calculation algorithm; both trained and untrained problems were used in a brief testing phase at the end of the training phase. Task difficulty was manipulated between subjects by using either a large ("easy" condition) or a small ("difficult" condition) number of repetition of problems during training. Measures of attention and working memory were acquired before and after the training phase. As compared to sham, participants in the tRNS condition displayed faster reaction times and increased learning rate during the training phase; as well as faster reaction times for both trained and untrained (new) problems, which indicated a transfer effect after the end of training. All stimulation effects reached significance only in the "difficult" condition when number of repetition was lower. There were no transfer effects of tRNS on attention or working memory. The results support the view that tRNS can produce specific facilitative effects on numerical cognition--specifically, on arithmetic learning. They also highlight the importance of
An Arithmetical Hierarchy of the Law of Excluded Middle and Related Principles
DEFF Research Database (Denmark)
Akama, Yohji; Berardi, Stefano; Hayashi, Susumu;
2004-01-01
The topic of this paper is Relative Constructivism. We are concerned with classifying non-constructive principles from the constructive viewpoint.We compare, up to provability in Intuitionistic Arithmetic, sub-classical principles like Markov's Principle, (a function-free version of) Weak König......'s Lemma, Post's Theorem, Excluded Middle for simply Existential and simply Universal statements, and many others.Our motivations are rooted in the experience of one of the authors with an extended program extraction and of another author with bound extraction from classical proofs....
Watermarking Capable of Identifying Embedding Order Based on an Arithmetic Mechanism
Institute of Scientific and Technical Information of China (English)
张新鹏; 王朔中; 张开文
2003-01-01
A digital watermark as a means for copyright protection may be crippled when a fake mark is embedded on top of it since both watermarks are detectable. In dealing with this problem, a watermarking scheme that does not satisfy the law of commutation is proposed. In this scheme, an order function based on an arithmetic mechanism is employed to identify the embedding order without affecting detection of the regular watermark. An earlier watermark corresponds to a larger value of the order function. In this way, the embedding order or watermarks can be identified according to the order function.
Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic
Hjermstad, Chris
1986-01-01
Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation.
Masson, Nicolas; Pesenti, Mauro
2016-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation. PMID:25991551
Masson, Nicolas; Pesenti, Mauro
2016-07-01
Solving arithmetic problems has been shown to induce shifts of spatial attention in simple probe-detection tasks, subtractions orienting attention to the left side and additions to the right side of space. Whether these attentional shifts constitute epiphenomena or are critically linked to the calculation process is still unknown. In the present study, we investigate participants' performance on addition and subtraction solving while they have to detect central or lateralized targets. The results show that lateralized distractors presented in the hemifield congruent to the operation to be solved interfere with arithmetical solving: participants are slower to solve subtractions or additions when distractors are located on the left or on the right, respectively. These results converge with previous data to show that attentional shifts underlie not only number processing but also mental arithmetic. They extend them as they reveal the reverse effect of the one previously reported by showing that inducing attention shifts interferes with the solving of arithmetic problems. They also demonstrate that spatial attentional shifts are part of the calculation procedure of solving mentally arithmetic problems. Their functional role is to access, from the first operand, the representation of the result in a direction congruent to the operation.
J.A. Bergstra; C.A. Middelburg
2009-01-01
An inversive meadow is a commutative ring with identity equipped with a multiplicative inverse operation made total by choosing 0 as its value at 0. Previously, inversive meadows were shortly called meadows. A divisive meadow is an inversive meadows with the multiplicative inverse operation replaced
Oyama, Katsunori; Sakatani, Kaoru
2016-01-01
Simultaneous monitoring of brain activity with near-infrared spectroscopy and electroencephalography allows spatiotemporal reconstruction of the hemodynamic response regarding the concentration changes in oxyhemoglobin and deoxyhemoglobin that are associated with recorded brain activity such as cognitive functions. However, the accuracy of state estimation during mental arithmetic tasks is often different depending on the length of the segment for sampling of NIRS and EEG signals. This study compared the results of a self-organizing map and ANOVA, which were both used to assess the accuracy of state estimation. We conducted an experiment with a mental arithmetic task performed by 10 participants. The lengths of the segment in each time frame for observation of NIRS and EEG signals were compared with the 30-s, 1-min, and 2-min segment lengths. The optimal segment lengths were different for NIRS and EEG signals in the case of classification of feature vectors into the states of performing a mental arithmetic task and being at rest.
Zhang, Shaohua
2009-01-01
The problem of the least prime number in an arithmetic progression is one of most important topics in Number Theory. In [11], we are the first to study the relations between this problem and Goldbach's conjecture. In this paper, we further consider its applications to Goldbach's conjecture and refine the result in [11]. From our work, one will see that the problem of the least prime number in an arithmetic progression is more significative than Goldbach's conjecture, more precisely, the weakened form of Chowla's hypothesis will implies Goldbach's conjecture. By the aforementioned results, undoubtedly, our real interest is the problem of the least prime number in an arithmetic progression. Naturally, what do the general forms of this problem look like? In this paper, we also try to consider this problem and further generalize Goldbach's conjecture.
Klein, Elise; Suchan, Julia; Moeller, Korbinian; Karnath, Hans-Otto; Knops, André; Wood, Guilherme; Nuerk, Hans-Christoph; Willmes, Klaus
2016-03-01
The current study provides a generalizable account of the anatomo-functional associations as well as the connectivity of representational codes underlying numerical processing as suggested by the triple code model (TCM) of numerical cognition. By evaluating the neural networks subserving numerical cognition in two specific and substantially different numerical tasks with regard to both grey matter localizations as well as white matter tracts we (1) considered the possibility of additional memory-related cortex areas crucial for arithmetic fact retrieval (e.g., the hippocampus); (2) specified the functional involvement of prefrontal areas in number magnitude processing, and, finally; (3) identified the connections between these anatomo-functional instantiations of the representations involved in number magnitude processing and arithmetic fact retrieval employing probabilistic fiber tracking. The resulting amendments to the TCM are summarized in a schematic update, and ideas concerning the possible functional interplay between number magnitude processing and arithmetic fact retrieval are discussed.
Directory of Open Access Journals (Sweden)
Megremi Athanasia
2015-01-01
Full Text Available The voluminous Treatise of the four mathematical sciences of Georgios Pachymeres is the most renowned quadrivium produced in Byzantium. Among its specific features, historians of mathematics have pointed out, is the inclusion of Diophantus, besides Nicomachus and Euclid, in the sources for the arithmetical section and, accordingly, the incorporation of series of problems and problem-solving in its contents. The present paper investigates the “Diophantine portion” of Pachymeres' treatise and it shows that it is structured according to two criteria intrinsically characterized by seriality: on one hand, the arrangement in which the problems are presented in book I of Diophantus' Arithmetica; on the other hand, for those problems of which the enunciation involves ratio, the order in which Nicomachus discusses the kinds of ratios in his Arithmetical introduction. Furthermore, it analyses the solutions that Pachymeres offers and argues that Nicomachus' Arithmetical introduction provides the necessary tools for pursuing them.
Knops, André; Willmes, Klaus
2014-01-01
A prominent proposal in numerical cognition states that our mental calculation abilities are grounded in the approximate number system (ANS). Recently, it was proposed that this association is mediated by numerical ordering abilities. As a first step in elucidating the neural correlates of this link this study tested which areas in the human brain carry information common to both calculation and numerical ordering. While lying in an MR scanner 17 healthy participants (a) decided whether or not a given number triplet was presented in numerically ascending order, and (b) solved simple addition and subtraction problems. Standard general linear model analyses revealed a largely overlapping network in fronto-parietal regions for both tasks. By analyzing the spatial information over voxels using a whole-brain searchlight algorithm we identified a right hemispheric network comprising areas along the intraparietal sulcus and in the inferior frontal cortex which was similarly involved in order judgments and symbolic arithmetic. Functional and anatomical characteristics of this network make it a candidate for linking the ANS to mental arithmetic. PMID:24064069
A Survey on the Permanence of Finnish Students’ Arithmetical Skills and the Role of Motivation
Directory of Open Access Journals (Sweden)
Timo Tossavainen
2015-01-01
Full Text Available This study concerns the permanence of the basic arithmetical skills of Finnish students by investigating how a group (N=463 of the eighth and eleventh year students and the university students of humanities perform in problems that are slightly modified versions of certain PISA 2003 mathematics test items. The investigation also aimed at finding out what the impact of motivation-related constructs, for example, students’ achievement goal orientations, is and what their perceived competence beliefs and task value on their performance in mathematics are. According to our findings, the younger students’ arithmetical skills have declined through the course of ten years but the older students’ skills have become generic to a greater extent. Further, three motivational clusters could be identified accounting for 7.5 per cent of students’ performance in the given assignments. These results are compatible with the outcomes of the recent assessments of the Finnish students’ mathematical skills and support the previous research on the benefits of learning orientation combined with the high expectation of success and the valuing of mathematics learning.
Minimal Graded Free Resolutions for Monomial Curves Defined by Arithmetic Sequences
Gimenez, Philippe; Srinivasan, Hema
2011-01-01
Let $\\mm=(m_0,...,m_n)$ be an arithmetic sequence, i.e., a sequence of integers $m_0<...
Non-Archimedean L-functions and arithmetical Siegel modular forms
1991-01-01
This book is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good supersingular reduction of ellptic curves and abelian varieties). The given construction of these p-adic L-functions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for non-experts giving a quick access to a rapidly developping domain of algebraic number theory: ...
The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
Grimm, Thomas W; Klevers, Denis
2016-01-01
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional ...
Landerl, Karin
2013-01-01
Numerical processing has been demonstrated to be closely associated with arithmetic skills, however, our knowledge on the development of the relevant cognitive mechanisms is limited. The present longitudinal study investigated the developmental trajectories of numerical processing in 42 children with age-adequate arithmetic development and 41 children with dyscalculia over a 2-year period from beginning of Grade 2, when children were 7; 6 years old, to beginning of Grade 4. A battery of numerical processing tasks (dot enumeration, non-symbolic and symbolic comparison of one- and two-digit numbers, physical comparison, number line estimation) was given five times during the study (beginning and middle of each school year). Efficiency of numerical processing was a very good indicator of development in numerical processing while within-task effects remained largely constant and showed low long-term stability before middle of Grade 3. Children with dyscalculia showed less efficient numerical processing reflected in specifically prolonged response times. Importantly, they showed consistently larger slopes for dot enumeration in the subitizing range, an untypically large compatibility effect when processing two-digit numbers, and they were consistently less accurate in placing numbers on a number line. Thus, we were able to identify parameters that can be used in future research to characterize numerical processing in typical and dyscalculic development. These parameters can also be helpful for identification of children who struggle in their numerical development. PMID:23898310
The arithmetic problem size effect in children: an event-related potential study
Directory of Open Access Journals (Sweden)
Leen eVan Beek
2014-09-01
Full Text Available This study used for the first time event-related potentials (ERPs to examine the well-known arithmetic problem size effect in children. The electrophysiological correlates of this problem size effect have been well documented in adults, but such information in children is lacking. In the present study, 22 typically developing 12-year-olds were asked to solve single-digit addition problems of small (sum ≤ 10 and large problem size (sum > 10 and to speak the solution into a voice key while ERPs were recorded. Children displayed similar early and late components compared to previous adult studies on the problem size effect. There was no effect of problem size on the early components P1, N1 and P2. The peak amplitude of the N2 component showed more negative potentials on left and right anterior electrodes for large additions compared to small additions, which might reflect differences in attentional and working memory resources between large and small problems. The mean amplitude of the late positivity component (LPC, which follows the N2, was significantly larger for large than for small additions at right parieto-occipital electrodes, in line with previous adult data. The ERPs of the problem size effect during arithmetic might be a useful neural marker for future studies on fact retrieval impairments in children with mathematical difficulties.
Barrouillet, P; Fayol, M
1998-03-01
A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of letters for the adult subjects. This suggests the use of an algorithmic strategy for both types of material in the case of the children and for the letters only in the case of the adults, who retrieved numerical results directly from memory. PMID:9584442
Xiang, Yanhui; Jiang, Yiqi; Chao, Xiaomei; Wu, Qihan; Mo, Lei
2016-01-01
Approximate strategies are crucial in daily human life. The studies on the "difficulty effect" seen in approximate complex arithmetic have long been neglected. Here, we aimed to explore the brain mechanisms related to this difficulty effect in the case of complex addition, using event-related potential-based methods. Following previous path-finding studies, we used the inequality paradigm and different split sizes to induce the use of two approximate strategies for different difficulty levels. By comparing dependent variables from the medium- and large-split conditions, we anticipated being able to dissociate the effects of task difficulty based on approximate strategy in electrical components. In the fronto-central region, early P2 (150-250 ms) and an N400-like wave (250-700 ms) were significantly different between different difficulty levels. Differences in P2 correlated with the difficulty of separation of the approximate strategy from the early physical stimulus discrimination process, which is dominant before 200 ms, and differences in the putative N400 correlated with different difficulties of approximate strategy execution. Moreover, this difference may be linked to speech processing. In addition, differences were found in the fronto-central region, which may reflect the regulatory role of this part of the cortex in approximate strategy execution when solving complex arithmetic problems. PMID:27072753
Rauh, Andreas; Kletting, Marco; Aschemann, Harald; Hofer, Eberhard P.
2007-02-01
A novel interval arithmetic simulation approach is introduced in order to evaluate the performance of biological wastewater treatment processes. Such processes are typically modeled as dynamical systems where the reaction kinetics appears as additive nonlinearity in state. In the calculation of guaranteed bounds of state variables uncertain parameters and uncertain initial conditions are considered. The recursive evaluation of such systems of nonlinear state equations yields overestimation of the state variables that is accumulating over the simulation time. To cope with this wrapping effect, innovative splitting and merging criteria based on a recursive uncertain linear transformation of the state variables are discussed. Additionally, re-approximation strategies for regions in the state space calculated by interval arithmetic techniques using disjoint subintervals improve the simulation quality significantly if these regions are described by several overlapping subintervals. This simulation approach is used to find a practical compromise between computational effort and simulation quality. It is pointed out how these splitting and merging algorithms can be combined with other methods that aim at the reduction of overestimation by applying consistency techniques. Simulation results are presented for a simplified reduced-order model of the reduction of organic matter in the activated sludge process of biological wastewater treatment.
Implementation of an Arithmetic Logic Using Area Efficient Carry Lookahead Adder
Directory of Open Access Journals (Sweden)
Navneet Dubey
2014-12-01
Full Text Available An arithmetic logic unit acts as the basic building blocks or cell of a central processing unit of a c omputer. And it is a digital circuit comprised of the basic electronics components, which is used to perform va rious function of arithmetic and logic and integral opera tions further the purpose of this work is to propos e the design of an 8-bit ALU which supports 4-bit multipl ication. Thus, the functionalities of the ALU in th is study consist of following main functions like addi tion also subtraction, increment, decrement, AND, O R, NOT, XOR, NOR also two complement generation Multip lication. And the functions with the adder in the airthemetic logic unit are implemented using a Carr y Look Ahead adder joined by a ripple carry approac h. The design of the following multiplier is achieved using the Booths Algorithm therefore the proposed A LU can be designed by using verilog or VHDL and can al so be designed on Cadence Virtuoso platform
Non-formal mechanisms in mathematical cognitive development: The case of arithmetic.
Braithwaite, David W; Goldstone, Robert L; van der Maas, Han L J; Landy, David H
2016-04-01
The idea that cognitive development involves a shift towards abstraction has a long history in psychology. One incarnation of this idea holds that development in the domain of mathematics involves a shift from non-formal mechanisms to formal rules and axioms. Contrary to this view, the present study provides evidence that reliance on non-formal mechanisms may actually increase with age. Participants - Dutch primary school children - evaluated three-term arithmetic expressions in which violation of formally correct order of evaluation led to errors, termed foil errors. Participants solved the problems as part of their regular mathematics practice through an online study platform, and data were collected from over 50,000 children representing approximately 10% of all primary schools in the Netherlands, suggesting that the results have high external validity. Foil errors were more common for problems in which formally lower-priority sub-expressions were spaced close together, and also for problems in which such sub-expressions were relatively easy to calculate. We interpret these effects as resulting from reliance on two non-formal mechanisms, perceptual grouping and opportunistic selection, to determine order of evaluation. Critically, these effects reliably increased with participants' grade level, suggesting that these mechanisms are not phased out but actually become more important over development, even when they cause systematic violations of formal rules. This conclusion presents a challenge for the shift towards abstraction view as a description of cognitive development in arithmetic. Implications of this result for educational practice are discussed. PMID:26795071
Guberman, Raisa
2016-01-01
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of "number" and the development thereof, calculation methods and…
Changa, M. E.
2005-04-01
The method of complex integration is used to derive asymptotic formulae for sums of multiplicative functions over numbers all of whose prime divisors belong to given arithmetic progressions. Generally, the principal term in such a formula takes the form of a sum with an increasing number of terms. However, under certain condition on the parameters of the problem, it becomes a finite sum.
International Nuclear Information System (INIS)
The method of complex integration is used to derive asymptotic formulae for sums of multiplicative functions over numbers all of whose prime divisors belong to given arithmetic progressions. Generally, the principal term in such a formula takes the form of a sum with an increasing number of terms. However, under certain condition on the parameters of the problem, it becomes a finite sum
Institute of Scientific and Technical Information of China (English)
Prabhu E; Mangalam H; Karthick S
2016-01-01
In this work, power efficient butterfly unit based FFT architecture is presented. The butterfly unit is designed using floating-point fused arithmetic units. The fused arithmetic units include two-term dot product unit and add-subtract unit. In these arithmetic units, operations are performed over complex data values. A modified fused floating-point two-term dot product and an enhanced model for the Radix-4 FFT butterfly unit are proposed. The modified fused two-term dot product is designed using Radix-16 booth multiplier. Radix-16 booth multiplier will reduce the switching activities compared to Radix-8 booth multiplier in existing system and also will reduce the area required. The proposed architecture is implemented efficiently for Radix-4 decimation in time (DIT) FFT butterfly with the two floating-point fused arithmetic units. The proposed enhanced architecture is synthesized, implemented, placed and routed on a FPGA device using Xilinx ISE tool. It is observed that the Radix-4 DIT fused floating-point FFT butterfly requires 50.17% less space and 12.16% reduced power compared to the existing methods and the proposed enhanced model requires 49.82% less space on the FPGA device compared to the proposed design. Also, reduced power consumption is addressed by utilizing the reusability technique, which results in 11.42% of power reduction of the enhanced model compared to the proposed design.
Gallardo, Aurora
2002-01-01
Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…
Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit
2016-01-01
In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…
Directory of Open Access Journals (Sweden)
Hatim Zaini
2004-12-01
Full Text Available paper introduces a novel method for complex number representation. The proposed Redundant Complex Binary Number System (RCBNS is developed by combining a Redundant Binary Number and a complex number in base (-1+j. Donald [1] and Walter Penny [2,3] represented complex numbers using base –j and (-1+j in the classified algorithmic models. A Redundant Complex Binary Number System consists of both real and imaginary-radix number systems that form a redundant integer digit set. This system is formed by using complex radix of (-1+j and a digit set of á= 3, where á assumes a value of -3, -2, -1, 0, 1, 2, 3. The arithmetic operations of complex numbers with this system treat the real and imaginary parts as one unit. The carry-free addition has the advantage of Redundancy in number representation in the arithmetic operations. Results of the arithmetic operations are in the RCBNS form. The two methods for conversion from the RCBNS form to the standard binary number form have been presented. In this paper the RCBNS reduces the number of steps required to perform complex number arithmetic operations, thus enhancing the speed.
Leinbach, L. Carl
2015-01-01
This paper illustrates a TI N-Spire .tns file created by the author for generating continued fraction representations of real numbers and doing arithmetic with them. The continued fraction representation provides an alternative to the decimal representation. The .tns file can be used as tool for studying continued fractions and their properties as…
High-Precision Floating-Point Arithmetic in ScientificComputation
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.
2004-12-31
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required: some of these applications require roughly twice this level; others require four times; while still others require hundreds or more digits to obtain numerically meaningful results. Such calculations have been facilitated by new high-precision software packages that include high-level language translation modules to minimize the conversion effort. These activities have yielded a number of interesting new scientific results in fields as diverse as quantum theory, climate modeling and experimental mathematics, a few of which are described in this article. Such developments suggest that in the future, the numeric precision used for a scientific computation may be as important to the program design as are the algorithms and data structures.
Pricing bounds for discrete arithmetic Asian options under Lévy models
Lemmens, D.; Liang, L. Z. J.; Tempere, J.; De Schepper, A.
2010-11-01
Analytical bounds for Asian options are almost exclusively available in the Black-Scholes framework. In this paper we derive bounds for the price of a discretely monitored arithmetic Asian option when the underlying asset follows an arbitrary Lévy process. Explicit formulas are given for Kou’s model, Merton’s model, the normal inverse Gaussian model, the CGMY model and the variance gamma model. The results are compared with the comonotonic upper bound, existing numerical results, Monte carlo simulations and in the case of the variance gamma model with an existing lower bound. The method outlined here provides lower and upper bounds that are quick to evaluate, and more accurate than existing bounds.
Power system transient stability simulation under uncertainty based on Taylor model arithmetic
Institute of Scientific and Technical Information of China (English)
Shouxiang WANG; Zhijie ZHENG; Chengshan WANG
2009-01-01
The Taylor model arithmetic is introduced to deal with uncertainty. The uncertainty of model parameters is described by Taylor models and each variable in functions is replaced with the Taylor model (TM). Thus,time domain simulation under uncertainty is transformed to the integration of TM-based differential equations. In this paper, the Taylor series method is employed to compute differential equations; moreover, power system time domain simulation under uncertainty based on Taylor model method is presented. This method allows a rigorous estimation of the influence of either form of uncertainty and only needs one simulation. It is computationally fast compared with the Monte Carlo method, which is another technique for uncertainty analysis. The proposed method has been tested on the 39-bus New England system. The test results illustrate the effectiveness and practical value of the approach by comparing with the results of Monte Carlo simulation and traditional time domain simulation.
An Adaptive Joint Source/Channel Coding Using Error Correcting Arithmetic Codes
Institute of Scientific and Technical Information of China (English)
LIU Jun-qing; PANG Yu-ye; SUN Jun
2007-01-01
An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques.The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy.In addition,an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed.The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity.Both hard and soft decoding were taken into account.
A novel architecture of non-volatile magnetic arithmetic logic unit using magnetic tunnel junctions
International Nuclear Information System (INIS)
Complementary metal–oxide–semiconductor (CMOS) technology is facing increasingly difficult obstacles such as power consumption and interconnection delay. Novel hybrid technologies and architectures are being investigated with the aim to circumvent some of these limits. In particular, hybrid CMOS/magnetic technology based on magnetic tunnel junctions (MTJs) is considered as a very promising approach thanks to the full compatibility of MTJs with CMOS technology. By tightly merging the conventional electronics with magnetism, both logic and memory functions can be implemented in the same device. As a result, non-volatility is directly brought into logic circuits, yielding significant improvement of device performances and new functionalities as well. We have conceived an innovative methodology to construct non-volatile magnetic arithmetic logic units (MALUs) combining spin-transfer torque MTJs with MOS transistors. The present 4-bit MALU utilizes 4 MTJ pairs to store its operation code (opcode). Its operations and performances have been confirmed and evaluated through electrical simulations. (paper)
Daud, Shahidah Md; Ramli, Razamin; Kasim, Maznah Mat; Kayat, Kalsom; Razak, Rafidah Abd
2015-12-01
Malaysian Homestay is very unique. It is classified as Community Based Tourism (CBT). Homestay Programme which is a community events where a tourist stays together with a host family for a period of time and enjoying cultural exchange besides having new experiences. Homestay programme has booming the tourism industry since there is over 100 Homestay Programme currently being registered with the Ministry of Culture and Tourism Malaysia. However, only few Homestay Programme enjoying the benefits of success Homestay Programme. Hence, this article seeks to identify the critical success factors for a Homestay Programme in Malaysia. An Arithmetic Average method is utilized to further evaluate the identified success factors in a more meaningful way. The findings will help Homestay Programme function as a community development tool that manages tourism resources. Thus, help the community in improving local economy and creating job opportunities.
The impact of arithmetic representation on implementing MLP-BP on FPGAs: a study.
Savich, Antony W; Moussa, Medhat; Areibi, Shawki
2007-01-01
In this paper, arithmetic representations for implementing multilayer perceptrons trained using the error backpropagation algorithm (MLP-BP) neural networks on field-programmable gate arrays (FPGAs) are examined in detail. Both floating-point (FLP) and fixed-point (FXP) formats are studied and the effect of precision of representation and FPGA area requirements are considered. A generic very high-speed integrated circuit hardware description language (VHDL) program was developed to help experiment with a large number of formats and designs. The results show that an MLP-BP network uses less clock cycles and consumes less real estate when compiled in an FXP format, compared with a larger and slower functioning compilation in an FLP format with similar data representation width, in bits, or a similar precision and range. PMID:17278475
Localized Model and Arithmetic System Based on Two Image Sensors Under Complex Circumstance
Institute of Scientific and Technical Information of China (English)
HE Guang-lin; YUAN Ben-sheng
2009-01-01
Two image sensors simulate directly the way of disposing images with the human's two eyes,so it has important value to apply in many domains,such as object identification,small unmaned aerial vehicle (UAV),workpiece localization,robot navigation and so on.The object localization based on two image sensors is studied in this paper.It concentrates on how to apply two charge coupled device (CCD) image sensors to object localization of sphere in complex environments.At first a space model of the two image sensors is set up,then Hough transformation is adopted to get localizated model and arithmetic system.An experiment platform is built in order to prove the correctness and feasibility of that localization algorithm.
Arithmetic and Frequency Filtering Methods of Pixel-Based Image Fusion Techniques
Al-Wassai, Firouz Abdullah; Al-Zuky, Ali A
2011-01-01
In remote sensing, image fusion technique is a useful tool used to fuse high spatial resolution panchromatic images (PAN) with lower spatial resolution multispectral images (MS) to create a high spatial resolution multispectral of image fusion (F) while preserving the spectral information in the multispectral image (MS).There are many PAN sharpening techniques or Pixel-Based image fusion techniques that have been developed to try to enhance the spatial resolution and the spectral property preservation of the MS. This paper attempts to undertake the study of image fusion, by using two types of pixel-based image fusion techniques i.e. Arithmetic Combination and Frequency Filtering Methods of Pixel-Based Image Fusion Techniques. The first type includes Brovey Transform (BT), Color Normalized Transformation (CN) and Multiplicative Method (MLT). The second type include High-Pass Filter Additive Method (HPFA), High-Frequency-Addition Method (HFA) High Frequency Modulation Method (HFM) and The Wavelet transform-base...
Thevenot, Catherine; Devidal, Michel; Barrouillet, Pierre; Fayol, Michel
2007-01-01
The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. In addition, this effect was more marked in the case of children who had poorer mathematical skills and in the case of more difficult problems. We argue that this pattern of results is compatible only with the situation or mental model theory, and not with the schema theory. PMID:17162507
Directory of Open Access Journals (Sweden)
György Bárdossy
2005-06-01
Full Text Available The completeness of an exploration project is of crutial importance for makingdecision to start or to give up a mining investment, or to continue the exploration to getcomplementary information. The authors discuss this problem on the example of theHalimba bauxite deposit, Hungary. Resource calculations were carried out in 12subsequent stages by fuzzy arithmetic with the aim to quantify the uncertainties of oretonnage and grade. Prior information and prior probabilities were applied to complete theexploration data. Ranges of influence for the main variables were calculated byvariograms. Spatial variability and spatial continuity of the ore bodies weremathematically evaluated. The authors found that the main geological, mining andeconomic factors must be evaluated separately and ranked according to their importance.
Schütt, Matthias; Yui, Noriko
2015-01-01
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.
Arithmetic computation using self-assembly of DNA tiles:subtraction and division
Institute of Scientific and Technical Information of China (English)
Xuncai Zhang; Yanfeng Wang; Zhihua Chen; Jin Xu; Guangzhao Cui
2009-01-01
Recently,experiments have demonstrated that simple binary arithmetic and logical operations can be computed by the process of selfassembly of DNA tiles.In this paper,we show how the tile assembly process can be used for subtraction and division.In order to achieve this aim,four systems,including the comparator system,the duplicator system,the subtraction system,and the division system,are proposed to compute the difference and quotient of two input numbers using the tile assembly model.This work indicates that these systems can be carried out in polynomial time with optimal O(1)distinct tile types in parallel and at very low cost.Furthermore,we provide a scheme to factor the product of two prime numbers,and it is a breakthrough in basic biological operations using a molecular computer by self-assembly.
Pre-Optimization of Brushless PM Motor Design using Interval Arithmetic
Directory of Open Access Journals (Sweden)
GautamMoni Patro*, Venkata R Basam ,S. Sashidhar , , P. Mallikarjuna Rao
Full Text Available These days, the desperate need for energy, provoked the requirement of energy efficient and ergonomic electrical machines suitable for propulsion, wind power applications, etc. This forces a machine designer to their extreme limits in designing their customized machine suitable for their application. Thus, in this quest for energy efficient electrical machines, there came into existence many new design based theories. In this research work the authors sincerely attempt to identifyand segregate the Brushless PM motor design parametersfrom CAD point of view and apply the concept of Interval Arithmetic; so that a valid range(bounds of the design parameter(s can be determined and acknowledged before going into a suitable optimization technique for optimizing them. With the help of MATLAB®CLI the bounds for the motor design parameters can be determined in which the optimal design solution lies.
Joint Distortion Model for Progressive Image Transmission Using Error Correcting Arithmetic Codes
Institute of Scientific and Technical Information of China (English)
LIU Jun-qing; SUN Jun; LONG Hu-qiang
2008-01-01
A novel joint source channel distortion model was proposed, which can essentially estimate the average distortion in progressive image transmission. To improve the precision of the model, the redundancy generated by a forbidden symbol in the arithmetic codes is used to distinguish the quantization distortion and the channel distortion, all the coefficients from the first error one to the end of the sequence are set to be a value within the variance range of the coefficients instead of zero, then the error propagation coming from the entropy coding can be essentially estimated, which is disregarded in the most conventional joint source channel coding (JSCC) systems. The precision of the model in terms of average peak-signal-to-noise has been improved about 0.5 dB compared to classical works. An efficient unequal error protection system based on the model is developed, and can be used in the wireless communication systems.
A novel VLSI architecture of arithmetic encoder with reduced memory in SPIHT
Liu, Kai; Li, YunSong; Belyaev, Eugeniy
2010-08-01
The paper presents a context-based arithmetic coder's VLSI architecture used in SPIHT with reduced memory, which is used for high speed real-time applications. For hardware implementation, a dedicated context model is proposed for the coder. Each context can be processed in parallel and high speed operators are used for interval calculations. An embedded register array is used for cumulative frequency update. As a result, the coder can consume one symbol at each clock cycle. After FPGA synthesis and simulation, the throughput of our coder is comparable with those of similar hardware architectures used in ASIC technology. Especially, the memory capacity of the coder is smaller than those of corresponding systems.
Ntsama, Eloundou Pascal; Colince, Welba; Ele, Pierre
2016-01-01
In this article, we make a comparative study for a new approach compression between discrete cosine transform (DCT) and discrete wavelet transform (DWT). We seek the transform proper to vector quantization to compress the EMG signals. To do this, we initially associated vector quantization and DCT, then vector quantization and DWT. The coding phase is made by the SPIHT coding (set partitioning in hierarchical trees coding) associated with the arithmetic coding. The method is demonstrated and evaluated on actual EMG data. Objective performance evaluations metrics are presented: compression factor, percentage root mean square difference and signal to noise ratio. The results show that method based on the DWT is more efficient than the method based on the DCT.
From functional programming to multicore parallelism: A case study based on Presburger Arithmetic
DEFF Research Database (Denmark)
Dung, Phan Anh; Hansen, Michael Reichhardt
2011-01-01
The overall goal of this work is studying parallelization of functional programs with the specific case study of decision procedures for Presburger Arithmetic (PA). PA is a first order theory of integers accepting addition as its only operation. Whereas it has wide applications in different areas......, we are interested in using PA in connection with the Duration Calculus Model Checker (DCMC) [5]. There are effective decision procedures for PA including Cooper’s algorithm and the Omega Test; however, their complexity is extremely high with doubly exponential lower bound and triply exponential upper...... in the SMT-solver Z3 [8] which has the capability of solving Presburger formulas. Functional programming is well-suited for the domain of decision procedures, and its immutability feature helps to reduce parallelization effort. While Haskell has progressed with a lot of parallelismrelated research [6], we...
Optimal Combinations Bounds of Root-Square and Arithmetic Means for Toader Mean
Indian Academy of Sciences (India)
Yu-Ming Chu; Miao-Kun Wang; Song-Liang Qiu
2012-02-01
We find the greatest values 1 and 2, and the least values 1 and 2, such that the double inequalities $_1S(a,b)+(1-_1)A(a,b) < T(a,b) < _1S(a,b)+(1-_1)A(a,b)$ and $S^{_2}(a,b)A^{1-_2}(a,b) < T(a,b) < S^{_2}(a,b)A^{1-_2}(a,b)$ hold for all ,>0 with ≠ . As applications, we get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, $S(a,b)=[(a^2+b^2)/2]^{1/2},A(a,b)=(a+b)/2$, and $T(a,b)=\\frac{2}{}\\int^{/2}_{0}\\sqrt{a^2\\cos^2+b^2\\sin^2}d$ denote the root-square, arithmetic, and Toader means of two positive numbers and , respectively.
de Zeeuw, Eveline L.; van Beijsterveldt, Catharina E.M.; Glasner, Tina J.; de Geus, Eco J.C.; Boomsma, Dorret I.
2016-01-01
Even children attending the same primary school and taught by the same teacher differ greatly in their performance. In the Netherlands, performance at the end of primary school determines the enrollment in a particular level of secondary education. Identifying the impact of genes and the environment on individual differences in educational achievement between children is important. The Netherlands Twin Register has collected data on scores of tests used in primary school (ages 6 to 12) to monitor a child’s educational progress in four domains, i.e. arithmetic, word reading, reading comprehension and spelling (1058 MZ and 1734 DZ twin pairs), and of a final test (2451 MZ and 4569 DZ twin pairs) in a large Dutch cohort. In general, individual differences in educational achievement were to a large extent due to genes and the influence of the family environment was negligible. Moreover, there is no evidence for gender differences in the underlying etiology. PMID:27182184
A hardware architecture for a context-adaptive binary arithmetic coder
Sudharsanan, Subramania; Cohen, Adam
2005-03-01
The H.264 video compression standard uses a context-adaptive binary arithmetic coder (CABAC) as an entropy coding mechanism. While the coder provides excellent compression efficiency, it is computationally demanding. On typical general-purpose processors, it can take up to hundreds of cycles to encode a single bit. In this paper, we propose an architecture for a CABAC encoder that can easily be incorporated into system-on-chip designs for H.264 compression. The CABAC is inherently serial and we divide the problem into several stages to derive a design that can provide a throughput of two cycles per encoded bit. The engine proposed is capable of handling binarization of the syntactical elements and provides the coded bit-stream via a first-in first-out buffer. The design is implemented on an Altera FPGA platform that can run at 50 MHz enabling a 25 Mbps encoding rate.
Context-Adaptive Arithmetic Coding Scheme for Lossless Bit Rate Reduction of MPEG Surround in USAC
Yoon, Sungyong; Pang, Hee-Suk; Sung, Koeng-Mo
We propose a new coding scheme for lossless bit rate reduction of the MPEG Surround module in unified speech and audio coding (USAC). The proposed scheme is based on context-adaptive arithmetic coding for efficient bit stream composition of spatial parameters. Experiments show that it achieves the significant lossless bit reduction of 9.93% to 12.14% for spatial parameters and 8.64% to 8.96% for the overall MPEG Surround bit streams compared to the original scheme. The proposed scheme, which is not currently included in USAC, can be used for the improved coding efficiency of MPEG Surround in USAC, where the saved bits can be utilized by the other modules in USAC.
Directory of Open Access Journals (Sweden)
Prabha Umapathy
2009-01-01
Full Text Available Total transfer capability (TTC is an important index in a power system with large volume of inter-area power exchanges. This paper proposes a novel technique to determine the TTC and its confidence intervals in the system by considering the uncertainties in the load and line parameters. The optimal power flow (OPF method is used to obtain the TTC. Variations in the load and line parameters are incorporated using the interval arithmetic (IA method. The IEEE 30 bus test system is used to illustrate the proposed methodology. Various uncertainties in the line, load and both line and load are incorporated in the evaluation of total transfer capability. From the results, it is observed that the solutions obtained through the proposed method provide much wider information in terms of closed interval form which is more useful in ensuring secured operation of the interconnected system in the presence of uncertainties in load and line parameters.
Modeling and Implementation of Reliable Ternary Arithmetic and Logic Unit Design Using Vhdl
Directory of Open Access Journals (Sweden)
Meruva Kumar Raja
2014-06-01
Full Text Available Multivalve logic is a reliable method for defining, analyzing, testing and implementing the basic combinational circuitry with VHDL simulator. It offers better utilization of transmission channels because of its high speed for higher information carried out and it gives more efficient performance. One of the main realizing of the MVL (ternary logic is that reduces the number of required computation steps, simplicity and energy efficiency in digital logic design. This paper using reliable method is brought out for implementing the basic combinational, sequential and TALU (Ternary Arithmetic and Logic Unit circuitry with minimum number of ternary switching circuits (Multiplexers. In this the potential of VHDL modelling and simulation that can be applied to ternary switching circuits to verify its functionality and timing specifications. An intention is to show how proposed simulator can be used to simulate MVL circuits and to evaluate system performance.
Directory of Open Access Journals (Sweden)
Dr.E.N.Ganesh
2010-08-01
Full Text Available Quantum cellular automata (QCA is a new technology in the nanometer scale and has been considered as one of the alternative to CMOS technology. QCA have a large potential in the development of circuits with high space density and low heat dissipation and allow the development of faster computers with lower power consumption. This paper discusses the design and construction of simple two bit arithmetic logic unit , four bit shifter and carry save in multiplier circuits. The advantage of this type of ALU is to construct functional unit all around the input lines and thereby reducing circuit complexity. Four bit shifter are constructed using serial AND and OR QCA circuits. QCA multiplier designed and constructed here has advantage of carry save in by delaying one clock cycle and no of bits can also be increased by adding the full adder stages. These circuits are the building block of nanoprocessors and provide us to understand the nanodevices of the future.
Deficient arithmetic fact retrieval--storage or access problem? A case study.
Kaufmann, Liane; Lochy, Aliette; Drexler, Arthur; Semenza, Carlo
2004-01-01
This paper aims at clarifying the nature of fact retrieval difficulties in an 18-year-old young man (MO) who exhibited a puzzling pattern of developmental dyscalculia. Contrasting performance on explicit (production and verification tasks) and implicit (priming) tasks we observed poor overt retrieval of addition and multiplication facts, classical interference effects in verification tasks and inconsistency of error patterns. Hence, MO's performance pattern is suggestive of the existence of a partly stored network of facts (reflecting imperfect storage), but is also compatible with an access deficit according to Warrington and Cipolotti's [Brain 119 (1996) 611] criteria for distinguishing access and storage deficits in dysphasic patients. Furthermore, while MO displayed interference effects in verification tasks, he did not show automatic access to arithmetic facts in implicit tasks. Finally, similar to the findings of Roussel, Fayol, and Barrouillet [European Journal of Cognitive Psychology 14(1) (2002) 61] on normal subjects, MO's performance pattern is suggestive of the existence of differential processing mechanisms for addition and multiplication facts. We propose a unifying mechanism, namely a deficit of the central executive of working memory (WM), that accounts both for the constitution of a fuzzy network of fact representations, and for an access deficit modulated by attentional demands as required in explicit/implicit task paradigms. Overall, our results clearly provide evidence that even in (a developmental) case of a non-perfect network of memory representations (e.g. [Journal of Experimental Psychology: General 117 (1988) 258]), interference effects might be observed. Future studies thus need to be cautious before concluding that interference effects prove the existence of a well-established associative memory network of arithmetic facts. PMID:14728921
Number word structure in first and second language influences arithmetic skills
Directory of Open Access Journals (Sweden)
Anat ePrior
2015-03-01
Full Text Available Languages differ in how they represent numerical information, and specifically whether the verbal notation of numbers follows the same order as the symbolic notation (in non-inverted languages, e.g. Hebrew, 25, twenty-five or whether the two notations diverge (in inverted languages, e.g. Arabic, 25, five-and-twenty. We examined how the structure of number-words affects how arithmetic operations are processed by bilingual speakers of an inverted and a non-inverted language. We examined Arabic-Hebrew bilinguals' performance in the first language, L1 (inverted and in the second language, L2 (non-inverted. Their performance was compared to that of Hebrew L1 speakers, who do not speak an inverted language. Participants judged the accuracy of addition problems presented aurally in L1, aurally in L2 or in visual symbolic notation. Problems were presented such that they matched or did not match the structure of number words in the language. Arabic-Hebrew bilinguals demonstrated both flexibility in processing and adaptation to the language of aural-verbal presentation – they were more accurate for the inverted order of presentation in Arabic, but more accurate for non-inverted order of presentation in Hebrew, thus exhibiting the same pattern found for native Hebrew speakers. In addition, whereas native Hebrew speakers preferred the non-inverted order in visual symbolic presentation as well, the Arabic-Hebrew bilinguals showed enhanced flexibility, without a significant preference for one order over the other, in either speed or accuracy. These findings suggest that arithmetic processing is sensitive to the linguistic representations of number words. Moreover, bilinguals exposed to inverted and non-inverted languages showed influence of both systems, and enhanced flexibility in processing. Thus, the L1 does not seem to have exclusive power in shaping numerical mental representations, but rather the system remains open to influences from a later learned
Algebra Structure of RSA Arithmetic%RSA算法中的代数结构
Institute of Scientific and Technical Information of China (English)
司光东; 杨加喜; 谭示崇; 肖国镇
2011-01-01
本文首次应用二次剩余理论对RSA中的代数结构进行了研究.计算出了Zn中模n的二次剩余和二次非剩余的个数,对它们之间的关系进行了分析,并用所有二次剩余构成的群对Zn进行了分割,证明了所有陪集构成的商群是一个Klein四元群.对强RSA的结构进行了研究,证明了强RSA中存在阶为φ(n)/2的元素,并且强RSA中Zn可由三个二次非剩余的元素生成.确定了Zn中任意元素的阶,证明了Zn中所有元素阶的最大值是lcm(p-1,q-1),并且给出了如何寻找Zn中最大阶元素方法.从而解决了RSA中的代数结构.%Based on the theory of quadratic residues, the algebra structure of RSA arithmetic is researched in this paper. This work calculates numbers of quadratic residues and non-residues in the group Zn* and investigates their relationship. Z*n is divided up by the group made up with all quadratic residues in Z*n and all cosets form a quotient group of order 4 which is a Klein group.Studyed the structure of strong RSA further,it shows that the element of order φ( n)/2 exists and the group Z*n can be generated by three elements of quadratic non-residues. Let the facterization n = p · q, the order of each element can be calculated, and the biggest order of all element is lcn ( p - 1, q - 1 ) in Z*n. It also shows how to find the element of the biggest order. So the algebra structure of RSA arithmetic is solved.
Reconfigurable and resettable arithmetic logic units based on magnetic beads and DNA
Zhang, Siqi; Wang, Kun; Huang, Congcong; Sun, Ting
2015-12-01
Based on the characteristics of magnetic beads and DNA, a simple and universal platform was developed for the integration of multiple logic gates to achieve resettable half adder and half subtractor functions. The signal reporter was composed of a split G-quadruplex DNAzyme and AuNP-surface immobilized molecular beacon molecule. The novel feature of the designed system is that the inputs (split G-quadruplexes) can interact with hairpin-modified Au NPs linked to magnetic particles. Another novel feature is that the logic operations can be reset by heating the output system and by using the magnetic separation of the computing modules. Moreover, the developed half adder and half subtractor are realized on a simple DNA/magnetic bead platform in an enzyme-free system and share a constant threshold setpoint. Due to the diversity and design flexibility of DNA, these investigations may provide a new method for the development of resettable DNA-based arithmetic operations.Based on the characteristics of magnetic beads and DNA, a simple and universal platform was developed for the integration of multiple logic gates to achieve resettable half adder and half subtractor functions. The signal reporter was composed of a split G-quadruplex DNAzyme and AuNP-surface immobilized molecular beacon molecule. The novel feature of the designed system is that the inputs (split G-quadruplexes) can interact with hairpin-modified Au NPs linked to magnetic particles. Another novel feature is that the logic operations can be reset by heating the output system and by using the magnetic separation of the computing modules. Moreover, the developed half adder and half subtractor are realized on a simple DNA/magnetic bead platform in an enzyme-free system and share a constant threshold setpoint. Due to the diversity and design flexibility of DNA, these investigations may provide a new method for the development of resettable DNA-based arithmetic operations. Electronic supplementary information
Directory of Open Access Journals (Sweden)
Sabyasachi Samanta
2011-03-01
Full Text Available In this paper, we have encrypted a text to an array of data bits through arithmetic coding technique. Forthis, we have assigned a unique range for both, a number of characters and groups using those. Usingunique range we may assign range only 10 characters. If we want to encrypt a large number ofcharacters, then every character has to assign a range with their group range of hundred, thousand andso on. Long textual message which have to encrypt, is subdivided into a number of groups with fewcharacters. Then the group of characters is encrypted into floating point numbers concurrently to theirgroup range by using arithmetic coding, where they are automatically compressed. Depending on key,the data bits from text are placed to some suitable nonlinear pixel and bit positions about the image. Inthe proposed technique, the key length and the number of characters for any encryption process is bothvariable.
Rauscher, Larissa; Kohn, Juliane; Käser, Tanja; Mayer, Verena; Kucian, Karin; McCaskey, Ursina; Esser, Günter; von Aster, Michael
2016-01-01
Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6–8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation. PMID:27445889
Rauscher, Larissa; Kohn, Juliane; Käser, Tanja; Mayer, Verena; Kucian, Karin; McCaskey, Ursina; Esser, Günter; von Aster, Michael
2016-01-01
Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation. PMID:27445889
van der Ven, Frauke; Takashima, Atsuko; Segers, Eliane; Fernández, Guillén; Verhoeven, Ludo
2016-07-15
Addition problems can be solved by mentally manipulating quantities for which the bilateral intraparietal sulcus (IPS) is likely recruited, or by retrieving the answer directly from fact memory in which the left angular gyrus (AG) and perisylvian areas may play a role. Mental addition is usually studied with problems presented in the Arabic notation (4+2), and less so with number words (four+two) or dots (:: +·.). In the present study, we investigated how the notation of numbers influences processing during simple mental arithmetic. Twenty-five highly educated participants performed simple arithmetic while their brain activity was recorded with functional magnetic resonance imaging. To reveal the effect of number notation, arithmetic problems were presented in a non-symbolic (Dots) or symbolic (Arabic; Words) notation. Furthermore, we asked whether IPS processing during mental arithmetic is magnitude specific or of a more general, visuospatial nature. To this end, we included perception and manipulation of non-magnitude formats (Colors; unfamiliar Japanese Characters). Increased IPS activity was observed, suggesting magnitude calculations during addition of non-symbolic numbers. In contrast, there was greater activity in the AG and perisylvian areas for symbolic compared to non-symbolic addition, suggesting increased verbal fact retrieval. Furthermore, IPS activity was not specific to processing of numerical magnitude but also present for non-magnitude stimuli that required mental visuospatial processing (Color-mixing; Character-memory measured by a delayed match-to-sample task). Together, our data suggest that simple non-symbolic sums are calculated using visual imagery, whereas answers for simple symbolic sums are retrieved from verbal memory. PMID:27117869
Kumar, Pranesh; Taneja, Inder Jeet
2005-01-01
In this paper we shall consider one parametric generalization of some non-symmetric divergence measures. The \\textit{non-symmetric divergence measures} are such as: Kullback-Leibler \\textit{relative information}, $\\chi ^2-$\\textit{divergence}, \\textit{relative J -- divergence}, \\textit{relative Jensen -- Shannon divergence} and \\textit{relative Arithmetic -- Geometric divergence}. All the generalizations considered can be written as particular cases of Csisz\\'{a}r's \\textit{f-divergence}. By ...
An Eﬃcient Approach for Solving Optimization over Linear Arithmetic Constraints
Institute of Scientific and Technical Information of China (English)
Li Chen; Jing-Zheng Wu; Yin-Run Lv; Yong-Ji Wang
2016-01-01
Satisfiability Modulo Theories (SMT) have been widely investigated over the last decade. Recently researchers have extended SMT to the optimization problem over linear arithmetic constraints. To the best of our knowledge, Symba and OPT-MathSAT are two most eﬃcient solvers available for this problem. The key algorithms used by Symba and OPT-MathSAT consist of the loop of two procedures: 1) critical finding for detecting a critical point, which is very likely to be globally optimal, and 2) global checking for confirming the critical point is really globally optimal. In this paper, we propose a new approach based on the Simplex method widely used in operation research. Our fundamental idea is to find several critical points by constructing and solving a series of linear problems with the Simplex method. Our approach replaces the algorithms of critical finding in Symba and OPT-MathSAT, and reduces the runtime of critical finding and decreases the number of executions of global checking. The correctness of our approach is proved. The experiment evaluates our implementation against Symba and OPT-MathSAT on a critical class of problems in real-time systems. Our approach outperforms Symba on 99.6% of benchmarks and is superior to OPT-MathSAT in large-scale cases where the number of tasks is more than 24. The experimental results demonstrate that our approach has great potential and competitiveness for the optimization problem.
A comparison of the effects of preferred music, arithmetic and humour on cold pressor pain.
Mitchell, Laura A; MacDonald, Raymond A R; Brodie, Eric E
2006-05-01
Research studies of 'audioanalgesia', the ability of music to affect pain perception, have significantly increased in number during the past two decades. Listening to preferred music in particular may provide an emotionally engaging distraction capable of reducing both the sensation of pain itself and the accompanying negative affective experience. The current study uses experimentally induced cold pressor pain to compare the effects of preferred music to two types of distracting stimuli found effective within the previous studies; mental arithmetic, a cognitive distraction, and humour, which may emotionally engage us in a similar manner to music. Forty-four participants (24 females, 20 males) underwent three cold pressor trials in counterbalanced order. The Paced Auditory Serial Addition Task provided the cognitive distraction and a choice was given from three types of audiotaped stand-up comedy. Participants provided their own preferred music. A circulating and cooling water bath administered cold pressor stimulation. Tolerance time, pain intensity on visual analogue scale and the pain rating index and perceived control were measured. Preferred music listening was found to significantly increase tolerance in comparison to the cognitive task, and significantly increase perceived control in comparison to humour. Ratings of pain intensity did not significantly differ. The results suggest preferred music listening to offer effective distraction and enhancement of control as a pain intervention under controlled laboratory conditions. PMID:15878297
Vector-matrix-quaternion, array and arithmetic packages: All HAL/S functions implemented in Ada
Klumpp, Allan R.; Kwong, David D.
1986-01-01
The HAL/S avionics programmers have enjoyed a variety of tools built into a language tailored to their special requirements. Ada is designed for a broader group of applications. Rather than providing built-in tools, Ada provides the elements with which users can build their own. Standard avionic packages remain to be developed. These must enable programmers to code in Ada as they have coded in HAL/S. The packages under development at JPL will provide all of the vector-matrix, array, and arithmetic functions described in the HAL/S manuals. In addition, the linear algebra package will provide all of the quaternion functions used in Shuttle steering and Galileo attitude control. Furthermore, using Ada's extensibility, many quaternion functions are being implemented as infix operations; equivalent capabilities were never implemented in HAL/S because doing so would entail modifying the compiler and expanding the language. With these packages, many HAL/S expressions will compile and execute in Ada, unchanged. Others can be converted simply by replacing the implicit HAL/S multiply operator with the Ada *. Errors will be trapped and identified. Input/output will be convenient and readable.
Influence of mental abacus calculation practice on mental arithmetic in children: a fMRI study
International Nuclear Information System (INIS)
Objective: To investigate the influence of mental abacus calculation practice on mental arithmetic in children with functional magnetic resonance imaging (fMRI). Methods: Twelve children who had practiced mental abacus calculation for 3 years and 12 untrained children (The two groups were matched in terms of age, handedness and education) underwent fMRI during mental calculation tasks. The related behavior data were recorded at the same time. All data were analyzed with statistical parametric mapping 2. Results: The calculation accuracy was significantly higher [(95.00±7.16)% vs.(74.26±16.07)%. t=-4.084, P<0.01]; and the reaction time was significantly shorter [(597.91±124.05) ms vs. (770.07± 148.54) ms, t=3.082, P<0.01] in trained group than untrained group. The extent and magnitude of the activated areas were significantly increased in the untrained group compared with the trained group. The activated areas mainly localized in the frontal and parietal lobes in untrained group, while the brain activated areas were few and mainly localized in occipital and parietal lobes in the trained group. Conclusion: Mental abacus calculation can enhance the information processing m some brain areas, and improve the utilization efficiency of neural resources. (authors)
Children's Use of Arithmetic Shortcuts: The Role of Attitudes in Strategy Choice
Directory of Open Access Journals (Sweden)
Katherine M. Robinson
2012-01-01
Full Text Available Current models of strategy choice do not account for children's attitudes towards different problem solving strategies. Grade 2, 3, and 4 students solved three sets of three-term addition problems. On inversion problems (e.g., 4 + 8 − 8, if children understand the inverse relation between the operations, no calculations are required. On associativity problems (e.g., 5 + 27 − 23, if children understand the associative relation between the operations, problem solving can be facilitated by performing subtraction before addition. A brief intervention involving demonstrations of different problem solving strategies followed the first problem set. Shortcut use increased after the intervention, particularly for students who preferred shortcuts to the left-to-right algorithm. In the third set, children were given transfer problems (e.g., 8 + 4 − 8, 4 − 8 + 8, 27 + 5 − 23. Shortcut use was similar to first set suggesting that transfer did occur. That shortcut use increased the most for students who had positive attitudes about the shortcuts suggests that attitudes have important implications for subsequent arithmetic performance.
Context adaptive binary arithmetic coding-based data hiding in partially encrypted H.264/AVC videos
Xu, Dawen; Wang, Rangding
2015-05-01
A scheme of data hiding directly in a partially encrypted version of H.264/AVC videos is proposed which includes three parts, i.e., selective encryption, data embedding and data extraction. Selective encryption is performed on context adaptive binary arithmetic coding (CABAC) bin-strings via stream ciphers. By careful selection of CABAC entropy coder syntax elements for selective encryption, the encrypted bitstream is format-compliant and has exactly the same bit rate. Then a data-hider embeds the additional data into partially encrypted H.264/AVC videos using a CABAC bin-string substitution technique without accessing the plaintext of the video content. Since bin-string substitution is carried out on those residual coefficients with approximately the same magnitude, the quality of the decrypted video is satisfactory. Video file size is strictly preserved even after data embedding. In order to adapt to different application scenarios, data extraction can be done either in the encrypted domain or in the decrypted domain. Experimental results have demonstrated the feasibility and efficiency of the proposed scheme.
Hinault, Thomas; Lemaire, Patrick; Phillips, Natalie
2016-01-01
This study investigated age-related differences in electrophysiological signatures of sequential modulations of poorer strategy effects. Sequential modulations of poorer strategy effects refer to decreased poorer strategy effects (i.e., poorer performance when the cued strategy is not the best) on current problem following poorer strategy problems compared to after better strategy problems. Analyses on electrophysiological (EEG) data revealed important age-related changes in time, frequency, and coherence of brain activities underlying sequential modulations of poorer strategy effects. More specifically, sequential modulations of poorer strategy effects were associated with earlier and later time windows (i.e., between 200- and 550 ms and between 850- and 1250 ms). Event-related potentials (ERPs) also revealed an earlier onset in older adults, together with more anterior and less lateralized activations. Furthermore, sequential modulations of poorer strategy effects were associated with theta and alpha frequencies in young adults while these modulations were found in delta frequency and theta inter-hemispheric coherence in older adults, consistent with qualitatively distinct patterns of brain activity. These findings have important implications to further our understanding of age-related differences and similarities in sequential modulations of cognitive control processes during arithmetic strategy execution.
Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions
Directory of Open Access Journals (Sweden)
Hong Siao
2016-03-01
Full Text Available Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj (resp. (f[xi, xj] we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj (resp. the least common multiple [xi, xj] of x, and xj as its (i, j-entry, respectively. The set S is said to be gcd closed if (xi, xj ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj and (f[xi, xj] if S consists of multiple coprime gcd-closed sets (i.e., S equals the union of S1, …, Sk with k ≥ 1 being an integer and S1, …, Sk being gcd-closed sets such that (lcm(Si, lcm(Sj = 1 for all 1 ≤ i ≠ j ≤ k. This extends the Bourque-Ligh, Hong’s and the Hong-Loewy formulas obtained in 1993, 2002 and 2011, respectively. It also generalizes the famous Smith’s determinant.
[Determination of the retrieval arithmetic of aerosol size distribution measured by DOAS].
Si, Fu-qi; Xie, Pin-hua; Liu, Jian-guo; Zhang, Yu-jun; Liu, Wen-qing; Hiroaki, Kuze; Nobuo, Takeuchi
2008-10-01
Atmospheric aerosol is not only an important factor for the change in global climate, but also a polluting matter. Moreover, aerosol plays a main role in chemical reaction of polluting gases. Determination of aerosol has become an important re- search in the study of atmospheric environment. Differential optical absorption spectroscopy (DOAS) is a very useful technique that allows quantitative measurement of atmospheric trace gas concentrations based on their fingerprint absorption. It also can be used to retrieve aerosol extinction coefficient. In the present work, the method of determination of aerosol size distribution measured by flash DOAS is described, and the arithmetic based on Monte-Carlo is the emphasis. By comparison with the concentration of PM10, visibility and Angstrom wavelength exponent, a good correlation can be found. Application of DOAS in aerosol field not only provides a novel method for aerosol detection, but also extends the field of application of DOAS technology. Especially, aerosol DOAS plays an important role in the study of atmospheric chemistry. PMID:19123420
Arithmetically Cohen-Macaulay sets of points in P^1 x P^1
Guardo, Elena
2015-01-01
This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem. In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra. Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevan...
Suárez-Pellicioni, M; Núñez-Peña, M I; Colomé, A
2013-12-01
This study uses event-related brain potentials to investigate the difficulties that high math anxious individuals face when processing dramatically incorrect solutions to simple arithmetical problems. To this end, thirteen high math-anxious (HMA) and thirteen low math-anxious (LMA) individuals were presented with simple addition problems in a verification task. The proposed solution could be correct, incorrect but very close to the correct one (small-split), or dramatically incorrect (large-split). The two groups did not differ in mathematical ability or trait anxiety. We reproduced previous results for flawed scores suggesting HMA difficulties in processing large-split solutions. Moreover, large-split solutions elicited a late positive component (P600/P3b) which was more enhanced and delayed in the HMA group. Our study proposes that the pattern of flawed scores found by previous studies (and that we replicate) has to do with HMA individuals'difficulties in inhibiting an extended processing of irrelevant information (large-split solutions).
Dynamic-Alphabet Arithmetic Coding%动态字母表算术编码
Institute of Scientific and Technical Information of China (English)
王忠效; 范植华
2001-01-01
研究了动态字母表统计模型的有关性质以及建立动态字母表模型应予以注意的问题.理论与实验表明,动态字母表模型在没有牺牲时间性能的情况下,能够提高预测的准确性,从而获得更好的编码效率.动态字母表对于建立大字符集文种(如汉语)文本压缩的统计模型具有重要意义%This paper addressed the features of dynamic-alphabet model for arithmetic coding and problems pertaining to model building. Both theory and experiments show that without loss of time performance, the dynamic-alphabet model provides more accurate prediction and consequently has better coding efficiency. Dynamic alphabet is a fresh but key concept to the building of statistical model of text compression for any natural language of large alphabet set, such as Chinese.
DEFF Research Database (Denmark)
Høyrup, Jens
. Next it goes on with complicated cases where the arithmetical series is not proportional to 1 – 2 – 3 ..., and the fraction is not an aliquot part. Fibonacci gives an algebraic solution to one variant and also general formulae for all variants – but these do not come from his algebra, and he thus...... cannot have derived them himself. A complete survey of occurrences once again points to al-Andalus. 3. Chapter 15 Section 1 of Fibonacci’s Liber abbaci mainly deals with the ancient theory of means though not telling so. If M is one such mean between A and B, it is shown systematically how each...... of these three numbers can be found if the other two are given – once more by means of algebra, Elements II.5–6, and proportion techniques. The lettering shows that Fibonacci uses an Arabic or Greek source, but no known Arabic or Greek work contains anything similar. However, the structural affinity suggests...
Simple Exact Algorithm for Transistor Sizing of Low-Power High-Speed Arithmetic Circuits
Directory of Open Access Journals (Sweden)
Tooraj Nikoubin
2010-01-01
Full Text Available A new transistor sizing algorithm, SEA (Simple Exact Algorithm, for optimizing low-power and high-speed arithmetic integrated circuits is proposed. In comparison with other transistor sizing algorithms, simplicity, accuracy, independency of order and initial sizing factors of transistors, and flexibility in choosing the optimization parameters such as power consumption, delay, Power-Delay Product (PDP, chip area or the combination of them are considered as the advantages of this new algorithm. More exhaustive rules of grouping transistors are the main trait of our algorithm. Hence, the SEA algorithm dominates some major transistor sizing metrics such as optimization rate, simulation speed, and reliability. According to approximate comparison of the SEA algorithm with MDE and ADC for a number of conventional full adder circuits, delay and PDP have been improved 55.01% and 57.92% on an average, respectively. By comparing the SEA and Chang's algorithm, 25.64% improvement in PDP and 33.16% improvement in delay have been achieved. All the simulations have been performed with 0.13 m technology based on the BSIM3v3 model using HSpice simulator software.
Directory of Open Access Journals (Sweden)
Sayaka Tsutsumi
2011-01-01
Full Text Available Arithmetic-like reasoning has been demonstrated in various animals in captive and seminatural environments, but it is unclear whether such competence is practiced in the wild. Using a hypothetical foraging paradigm, we demonstrate that wild vervet monkeys spontaneously adjust their “foraging behavior” deploying arithmetic-like reasoning. Presented with arithmetic-like problems in artificially controlled feeding conditions, all the monkeys tested attempted to retrieve “artificial prey” according to the quantity of the remainder when the task involved one subtraction only (i.e., “2−1”, while one monkey out of four did so when it was sequentially subtracted twice (i.e., “2−1−1”. This monkey also adjusted his “foraging behavior” according to the quantity of the reminder for a task requiring stepwise mental manipulation (i.e., “(2−1−1”, though the results became less evident. This suggests that vervet monkeys are capable of spontaneously deploying mental manipulations of numerosity for cost-benefit calculation of foraging but that the extent of such capacity varies among individuals. Different foraging strategies might be deployed according to different levels of mental manipulation capacity in each individual in a given population. In addition to providing empirical data, the current study provides an easily adaptable field technique that would allow comparison across taxa and habitat using a uniform method.
Cameron, Kristie E; Clarke, Katrina H; Bizo, Lewis A; Starkey, Nicola J
2016-05-01
The aim of this study was to compare the demand for food under concurrent progressive- and fixed-ratio schedules. Twelve brushtail possums participated in 16 conditions where schedule, progression and food type were varied. An incrementing schedule increased the fixed-ratio requirement within and across sessions and was arranged as either a geometric sequence (base 2), or an arithmetic sequence (step 5). Two foods were tested: a flaked barley and coco-pop(®) mix versus rolled oats. Overall, performance was similar for most possums in the within- and across-session incrementing schedules. An analysis of the estimates of essential value and break point produced the same account of demand for foods under the geometric or arithmetic progressions and within- and across-session procedures for 8 of 12 possums. Six possums showed higher demand for rolled oats compared to flaked barley, and two possums showed higher demand for flaked barley compared to rolled oats. Incrementing ratios within, rather than between sessions using an arithmetic progression was demonstrated to be a time efficient procedure for investigating demand for different food types without affecting conclusions about the relative demand for those foods.
Oyama, Katsunori; Sakatani, Kaoru
2016-01-01
Simultaneous monitoring of brain activity with near-infrared spectroscopy and electroencephalography allows spatiotemporal reconstruction of the hemodynamic response regarding the concentration changes in oxyhemoglobin and deoxyhemoglobin that are associated with recorded brain activity such as cognitive functions. However, the accuracy of state estimation during mental arithmetic tasks is often different depending on the length of the segment for sampling of NIRS and EEG signals. This study compared the results of a self-organizing map and ANOVA, which were both used to assess the accuracy of state estimation. We conducted an experiment with a mental arithmetic task performed by 10 participants. The lengths of the segment in each time frame for observation of NIRS and EEG signals were compared with the 30-s, 1-min, and 2-min segment lengths. The optimal segment lengths were different for NIRS and EEG signals in the case of classification of feature vectors into the states of performing a mental arithmetic task and being at rest. PMID:27526147
Cameron, Kristie E; Clarke, Katrina H; Bizo, Lewis A; Starkey, Nicola J
2016-05-01
The aim of this study was to compare the demand for food under concurrent progressive- and fixed-ratio schedules. Twelve brushtail possums participated in 16 conditions where schedule, progression and food type were varied. An incrementing schedule increased the fixed-ratio requirement within and across sessions and was arranged as either a geometric sequence (base 2), or an arithmetic sequence (step 5). Two foods were tested: a flaked barley and coco-pop(®) mix versus rolled oats. Overall, performance was similar for most possums in the within- and across-session incrementing schedules. An analysis of the estimates of essential value and break point produced the same account of demand for foods under the geometric or arithmetic progressions and within- and across-session procedures for 8 of 12 possums. Six possums showed higher demand for rolled oats compared to flaked barley, and two possums showed higher demand for flaked barley compared to rolled oats. Incrementing ratios within, rather than between sessions using an arithmetic progression was demonstrated to be a time efficient procedure for investigating demand for different food types without affecting conclusions about the relative demand for those foods. PMID:27032293
Quantifying the Impact of Single Bit Flips on Floating Point Arithmetic
Energy Technology Data Exchange (ETDEWEB)
Elliott, James J [ORNL; Mueller, Frank [North Carolina State University; Stoyanov, Miroslav K [ORNL; Webster, Clayton G [ORNL
2013-08-01
In high-end computing, the collective surface area, smaller fabrication sizes, and increasing density of components have led to an increase in the number of observed bit flips. If mechanisms are not in place to detect them, such flips produce silent errors, i.e. the code returns a result that deviates from the desired solution by more than the allowed tolerance and the discrepancy cannot be distinguished from the standard numerical error associated with the algorithm. These phenomena are believed to occur more frequently in DRAM, but logic gates, arithmetic units, and other circuits are also susceptible to bit flips. Previous work has focused on algorithmic techniques for detecting and correcting bit flips in specific data structures, however, they suffer from lack of generality and often times cannot be implemented in heterogeneous computing environment. Our work takes a novel approach to this problem. We focus on quantifying the impact of a single bit flip on specific floating-point operations. We analyze the error induced by flipping specific bits in the most widely used IEEE floating-point representation in an architecture-agnostic manner, i.e., without requiring proprietary information such as bit flip rates and the vendor-specific circuit designs. We initially study dot products of vectors and demonstrate that not all bit flips create a large error and, more importantly, expected value of the relative magnitude of the error is very sensitive on the bit pattern of the binary representation of the exponent, which strongly depends on scaling. Our results are derived analytically and then verified experimentally with Monte Carlo sampling of random vectors. Furthermore, we consider the natural resilience properties of solvers based on the fixed point iteration and we demonstrate how the resilience of the Jacobi method for linear equations can be significantly improved by rescaling the associated matrix.
Age-related differences in children's strategy repetition: A study in arithmetic.
Lemaire, Patrick; Brun, Fleur
2016-10-01
Third and fifth graders (Experiment 1) and fifth and seventh graders (Experiment 2) accomplished computational estimation tasks in which they provided estimates to two-digit arithmetic problems (e.g., 34+68). Participants saw trials, each including three consecutive problems. Each trial was separated by a letter judgment task (i.e., participants needed to say whether a series of four letters included only vowels, only consonants, or both types of letters). On each problem, children were asked to select the better of the following strategies: rounding down (i.e., rounding both operands down to the nearest decades; e.g., 30+60=90) or rounding up (rounding both operands up to the nearest decades; e.g., 40+70=110). Half of the trials were repeated strategy trials (i.e., the better strategy was the same for the first two prime problems and the last target problem) and half were unrepeated strategy trials (i.e., the better strategy was different for prime and target problems). We found that (a) children repeated the same strategy over successive problems, even when they should change strategies to obtain better performance, (b) strategy repetitions decreased with age, (c) repeating the same strategy gave children performance benefits, and (d) these strategy repetition benefits were similar across grades. These effects of strategy repetition during strategy selection and strategy execution have important empirical and theoretical implications regarding how children choose among strategies, how children execute selected strategies on each problem, and how strategic variations change with age.
Ultrafast all-optical arithmetic logic based on hydrogenated amorphous silicon microring resonators
Gostimirovic, Dusan; Ye, Winnie N.
2016-03-01
For decades, the semiconductor industry has been steadily shrinking transistor sizes to fit more performance into a single silicon-based integrated chip. This technology has become the driving force for advances in education, transportation, and health, among others. However, transistor sizes are quickly approaching their physical limits (channel lengths are now only a few silicon atoms in length), and Moore's law will likely soon be brought to a stand-still despite many unique attempts to keep it going (FinFETs, high-k dielectrics, etc.). This technology must then be pushed further by exploring (almost) entirely new methodologies. Given the explosive growth of optical-based long-haul telecommunications, we look to apply the use of high-speed optics as a substitute to the digital model; where slow, lossy, and noisy metal interconnections act as a major bottleneck to performance. We combine the (nonlinear) optical Kerr effect with a single add-drop microring resonator to perform the fundamental AND-XOR logical operations of a half adder, by all-optical means. This process is also applied to subtraction, higher-order addition, and the realization of an all-optical arithmetic logic unit (ALU). The rings use hydrogenated amorphous silicon as a material with superior nonlinear properties to crystalline silicon, while still maintaining CMOS-compatibility and the many benefits that come with it (low cost, ease of fabrication, etc.). Our method allows for multi-gigabit-per-second data rates while maintaining simplicity and spatial minimalism in design for high-capacity manufacturing potential.
NIOS Custom Instruction on Floating-Point Arithmetic%NIOS浮点运算定制指令的实现
Institute of Scientific and Technical Information of China (English)
陈鹏; 蔡雪梅
2011-01-01
To improve the efficiency of floating-point arithmetic on NIOS system, a module of using Verilog to implement singleprecision floating-point addition. subtraction and multiplication is proposed, and its function in Quartus is verified through waveform simulation. According to the custom instruction feature of NIOS ii, adding this module to SOPC Builder, expanding a new hardwarebased floating-point arithmetic instruction, which can be applied in NIOS IDE. Comparing the output and calculating time between NIOS ii software arithmetic and the new hardware floating-point instructions, the supenority of the hardware instruction computation is verified, and a more efficient choice is provided for NIOS in floating-point arirhmetic.%为提高NIOS系统的浮点计算效率,使用Verilog语言实现了单精度浮点数加减及乘法运算的功能模块,并通过波形验证其功能,依据NIOSⅡ定制指令的制定规范,将这一功能添加到SOPC Builder中,扩展出新的基于硬件电路的浮点运算指令,使之在NIOS软件环境中得到应用.通过NIOSⅡ本身软件浮点计算和新增硬件指令进行运算结果和时间上的对比,证实硬件指令计算的优越性,为NIOS下的浮点运算提供了更有效率的选择.
Sabyasachi Samanta; Saurabh Dutta; ,Goutam Sanyal
2011-01-01
In this paper, we have encrypted a text to an array of data bits through arithmetic coding technique. Forthis, we have assigned a unique range for both, a number of characters and groups using those. Usingunique range we may assign range only 10 characters. If we want to encrypt a large number ofcharacters, then every character has to assign a range with their group range of hundred, thousand andso on. Long textual message which have to encrypt, is subdivided into a number of groups with fewc...
Schmalz, Mark S.
1993-09-01
The processing of Boolean imagery compressed by runlength encoding (RLE) frequently exhibits greater computational efficiency than the processing of uncompressed imagery, due to the data reduction inherent in RLE. In a previous publication, we outlined general methods for developing operators that compute over RLE Boolean imagery. In this paper, we present sequential and parallel algorithms for a variety of operations over RLE imagery, including the customary arithmetic and logical Hadamard operations, as well as the global reduce functions of image sum and maximum. RLE neighborhood-based operations, as well as the more advanced RLE operations of linear transforms, connected component labelling, and pattern recognition are presented in the companion paper.
Mosko, J. A.
1984-02-01
It is pointed out that two-channel monopulse direction-finding (DF) systems have been used for many years in such antiradiation homing (ARH) missiles as Shrike and Standard ARM. The present investigation is concerned with the fairly broad topic of two-channel monopulse DF techniques. The entire system is considered in a system overview, and the design of multifilament spirals, with emphasis on dual-mode four-arm spirals, is discussed. Attention is given to radiation impedances and reference surface rotation, the hyperbolic spiral antenna, polarization diversity multimode antennas, and arithmetic subsystems.
Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means
Directory of Open Access Journals (Sweden)
Fan Zhang
2013-01-01
Full Text Available We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b+(1-α1H(a,b0 with a≠b, where M(a,b, A(a,b, He(a,b, H(a,b and H-(a,b denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively.
Bilateral Estimation of Positive Arithmetic Sequence Power and Type%正项等差数列幂和式的双边估计
Institute of Scientific and Technical Information of China (English)
王阳; 孙艳玲; 季晓蕾
2015-01-01
The lower bound estimation of Positive Arithmetic sequence power and type are given. How to give the estimation of upper bound. How to build on bilateral estimationof the positive arithmetic se-quence power and style. According to the different range of index,we strengthen the upper bound estima-tion. And then get bilateral estimation on positive arithmetic sequence power and style. With the help of concavo convex function theory and Lagrange's formula,the upper bound of powerPositive arithmetic se-quence power and type are given. And we get the lower bound on the existing estimating conclusion by lo-cal reinforcement. Finally,the conclusion obtained is all about the bilateral estimation of Positive arithme-tic sequence power and style.%正项等差数列幂和式只给了下界估计，本文借助于函数的凹凸性理论和拉格朗日中值公式，给出正项等差数列幂和式的上界估计，并对已有的下界估计结论进行局部加强。最后，将全部结论综合得到关于正项等差数列幂和式的双边估计。
Effects of cognitive appraisal and mental workload factors on performance in an arithmetic task.
Galy, Edith; Mélan, Claudine
2015-12-01
We showed in a previous study an additive interaction between intrinsic and extraneous cognitive loads and of participants' alertness in an 1-back working memory task. The interaction between intrinsic and extraneous cognitive loads was only observed when participants' alertness was low (i.e. in the morning). As alertness is known to reflect an individual's general functional state, we suggested that the working memory capacity available for germane cognitive load depends on a participant's functional state, in addition to intrinsic and extraneous loads induced by the task and task conditions. The relationships between the different load types and their assessment by specific load measures gave rise to a modified cognitive load model. The aim of the present study was to complete the model by determining to what extent and at what processing level an individual's characteristics intervene in order to implement efficient strategies in a working memory task. Therefore, the study explored participants' cognitive appraisal of the situation in addition to the load factors considered previously-task difficulty, time pressure and alertness. Each participant performed a mental arithmetic task in four different cognitive load conditions (crossover of two task difficulty conditions and of two time pressure conditions), both while their alertness was low (9 a.m.) and high (4 p.m.). Results confirmed an additive effect of task difficulty and time pressure, previously reported in the 1-back memory task, thereby lending further support to the modified cognitive load model. Further, in the high intrinsic and extraneous load condition, performance was reduced on the morning session (i.e. when alertness was low) on one hand, and in those participants' having a threat appraisal of the situation on the other hand. When these factors were included into the analysis, a performance drop occurred in the morning irrespective of cognitive appraisal, and with threat appraisal in the
Lakhani, Gopal
2013-04-01
This article presents four modifications to the JPEG arithmetic coding (JAC) algorithm, a topic not studied well before. It then compares the compression performance of the modified JPEG with JPEG XR, the latest block-based image coding standard. We first show that the bulk of inter/intra-block redundancy, caused due to the use of the block-based approach by JPEG, can be captured by applying efficient prediction coding. We propose the following modifications to JAC to take advantages of our prediction approach. 1) We code a totally different DC difference. 2) JAC tests a DCT coefficient by considering its bits in the increasing order of significance for coding the most significant bit position. It causes plenty of redundancy because JAC always begins with the zeroth bit. We modify this coding order and propose alternations to the JPEG coding procedures. 3) We predict the sign of significant DCT coefficients, a problem is not addressed from the perspective of the JPEG decoder before. 4) We reduce the number of binary tests that JAC codes to mark end-of-block. We provide experimental results for two sets of eight-bit gray images. The first set consists of nine classical test images mostly of size 512 × 512 pixels. The second set consists of 13 images of size 2000 × 3000 pixels or more. Our modifications to JAC obtain extra-ordinary amount of code reduction without adding any kind of losses. More specifically, when we quantize the images using the default quantizers, our modifications reduce the total JAC code size of the images of these two sets by about 8.9 and 10.6%, and the JPEG Huffman code size by about 16.3 and 23.4%, respectively, on the average. Gains are even higher for coarsely quantized images. Finally, we compare the modified JAC with two settings of JPEG XR, one with no block overlapping and the other with the default transform (we denote them by JXR0 and JXR1, respectively). Our results show that for the finest quality rate image coding, the modified
Chung, Kun-Jen
2012-08-01
Cardenas-Barron [Cardenas-Barron, L.E. (2010) 'A Simple Method to Compute Economic order Quantities: Some Observations', Applied Mathematical Modelling, 34, 1684-1688] indicates that there are several functions in which the arithmetic-geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), 'A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives', Applied Mathematical Modelling, 33, 4388-4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), 'Comment on 'Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives', International Journal of Systems Science, 40, 1095-1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), 'A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage', Production Planning and Control, 19, 601-604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic-geometric mean method of Teng et al. (2009), Teng and Goyal (2009) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.
Realization of the Arithmetic Logic Unit Based on QuartusII%基于QuartusⅡ的ALU的实现
Institute of Scientific and Technical Information of China (English)
陈辉; 周自立
2012-01-01
Being the experiment of the arithmetic device parts which belongs to Principle of Computer Organization-ALU, it is teaching point to calculator professional teacher, is also the knowledge of the difficuh comprehension that the majority of students reflects. Quite a few students are unable to complete this experiment nicely. Being a kind of EDA design software, QuartuslI provide many platens integrity design environment. To help the students solve the problem, by introducing two methods about the realization of the arithmetic unit and carrying out a simple ALU, the two methods of the specific implementation are proposed.%计算机组成原理运算器部件ALU实验,一直是计算机专业老师的教学重点,也是多数学生反映的学习难点之一,相当一部分学生不能很好地完成这个实验。QuartusⅡ作为一种EDA设计软件,提供了完整的多平台设计环境。为了帮助学生更好地完成ALU实验,介绍了实现ALU的两种方法,并以实现简单的ALU为例,详细介绍这两种方法的具体实现。
Directory of Open Access Journals (Sweden)
Fazal NOORBASHA
2012-08-01
Full Text Available In this present study includes the Very Large Scale Integration (VLSI system implementation of 200MHz, 8-bit, 90nm Complementary Metal Oxide Semiconductor (CMOS Arithmetic and Logic Unit (ALU processor control with logic gate design style and 0.12µm six metal 90nm CMOS fabrication technology. The system blocks and the behaviour are defined and the logical design is implemented in gate level in the design phase. Then, the logic circuits are simulated and the subunits are converted in to 90nm CMOS layout. Finally, in order to construct the VLSI system these units are placed in the floor plan and simulated with analog and digital, logic and switch level simulators. The results of the simulations indicates that the VLSI system can control different instructions which can divided into sub groups: transfer instructions, arithmetic and logic instructions, rotate and shift instructions, branch instructions, input/output instructions, control instructions. The data bus of the system is 16-bit. It runs at 200MHz, and operating power is 1.2V. In this paper, the parametric analysis of the system, the design steps and obtained results are explained.
An Analysis of the Contents and Pedagogy of Al-Kashi's 1427 "Key to Arithmetic" (Miftah Al-Hisab)
Ta'ani, Osama Hekmat
2011-01-01
Al-Kashi's 1427 "Key to Arithmetic" had important use over several hundred years in mathematics teaching in Medieval Islam throughout the time of the Ottoman Empire. Its pedagogical features have never been studied before. In this dissertation I have made a close pedagogical analysis of these features and discovered several teaching…
Energy Technology Data Exchange (ETDEWEB)
Shilo, L.V. [Kiev State Univ. (Ukraine)
1994-06-05
We study the arithmetic-mean estimate of a homogeneous random field observed on a rectangle and, in particular, the asymptotic behavior of the variance of such an estimate when there are zeros in the spectrum of the process. 6 refs.
On Arithmetic Means for the Navier-Stokes Flows%关于Navier-Stokes流的算术均值
Institute of Scientific and Technical Information of China (English)
张余
2003-01-01
证明了可以选出具有相同的外部条件的三维Navier-Stokes流{u(n)},使其算术均值N=(u(1)+…+u(N))/N有极限并且此极限是Navier-Stokes流,从而部分地为统计流体动力学提供了数学的根据.%It is proved that a sequence {u(n)}of the 3D NavierStokes flows with the same extern al condition can be selected so that the arithmetic means u- N=(u(1)+…+u(N))/Nhas a limit which is a Navier-Stokes flow.This supplies partly a mathematical basis to the statistical fluid mechanics.
Institute of Scientific and Technical Information of China (English)
吴修广; 沈永明; 郑永红
2004-01-01
A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged NavierStokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k - e turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a curent over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.
Karwowski, Damian; Domański, Marek
2016-01-01
An improved context-based adaptive binary arithmetic coding (CABAC) is presented. The idea for the improvement is to use a more accurate mechanism for estimation of symbol probabilities in the standard CABAC algorithm. The authors' proposal of such a mechanism is based on the context-tree weighting technique. In the framework of a high-efficiency video coding (HEVC) video encoder, the improved CABAC allows 0.7% to 4.5% bitrate saving compared to the original CABAC algorithm. The application of the proposed algorithm marginally affects the complexity of HEVC video encoder, but the complexity of video decoder increases by 32% to 38%. In order to decrease the complexity of video decoding, a new tool has been proposed for the improved CABAC that enables scaling of the decoder complexity. Experiments show that this tool gives 5% to 7.5% reduction of the decoding time while still maintaining high efficiency in the data compression.
Otisk, Marek
This paper deals with comments and glosses to the first chapter of the second book of Boethius's Introduction to Arithmetic from the last quarter of the 10th century. Those texts were written by Gerbert of Aurillac (Scholium ad Boethii Arithmeticam Institutionem l. II, c. 1), Abbo of Fleury (commentary on the Calculus by Victorius of Aquitaine, the so-called De numero, mensura et pondere), Notker of Liège (De superparticularibus) and by the anonymous author (De arithmetica Boetii). The main aim of this paper is to show that Boethius's statements about the converting numerical sequences to equality from this work could be interpreted minimally in two different ways. This paper discussed also the application of this topic in other liberal arts (like astronomy, music, grammar etc.) and in playing game called rithmomachia, the medieval philosophers' game.
Dimitriadis, Stavros I.; Sun, Yu; Thakor, Nitish V.; Bezerianos, Anastasios
2016-01-01
Many neuroimaging studies have demonstrated the different functional contributions of spatially distinct brain areas to working memory (WM) subsystems in cognitive tasks that demand both local information processing and interregional coordination. In WM cognitive task paradigms employing electroencephalography (EEG), brain rhythms such as θ and α have been linked to specific functional roles over given brain areas, but their functional coupling has not been extensively studied. Here we analyzed an arithmetic task with five cognitive workload levels (CWLs) and demonstrated functional/effective coupling between the two WM subsystems: the central executive located over frontal (F) brain areas that oscillates on the dominant θ rhythm (Frontalθ/Fθ) and the storage buffer located over parieto-occipital (PO) brain areas that operates on the α2 dominant brain rhythm (Parieto-Occipitalα2/POα2). We focused on important differences between and within WM subsystems in relation to behavioral performance. A repertoire of brain connectivity estimators was employed to elucidate the distinct roles of amplitude, phase within and between frequencies, and the hierarchical role of functionally specialized brain areas related to the task. Specifically, for each CWL, we conducted a) a conventional signal power analysis within both frequency bands at Fθ and POα2, b) the intra- and inter-frequency phase interactions between Fθ and POα2, and c) their causal phase and amplitude relationship. We found no significant statistical difference of signal power or phase interactions between correct and wrong answers. Interestingly, the study of causal interactions between Fθ and POα2 revealed frontal brain region(s) as the leader, while the strength differentiated between correct and wrong responses in every CWL with absolute accuracy. Additionally, zero time-lag between bilateral Fθ and right POa2 could serve as an indicator of mental calculation failure. Overall, our study
Directory of Open Access Journals (Sweden)
Ashkan Emami Ale Agha
2013-06-01
Full Text Available One of the most important concepts in multi programming Operating Systems is scheduling. It helps in choosing the processes for execution. Round robin method is one of the most important algorithms in scheduling. It is the most popular algorithm due to its fairness and starvation free nature towards the processes, which is achieved by using proper quantum time. The main challenge in this algorithm is selection of quantum time. This parameter affects on average Waiting Time and average Turnaround Time in execution queue. As the quantum time is static, it causes less context switching in case of high quantum time and high context switching in case of less quantum time. Increasing context switch leads to high average waiting time, high average turnaround time which is an overhead and degrades the system performance. With respect to these points, the algorithms should calculate proper value for the quantum time. Two main classes of algorithms that are proposed to calculate the quantum time include static and dynamic methods. In static methods quantum time is fixed during the scheduling. Dynamic algorithms are one of these methods that change the value of quantum time in each cycle. For example in one method the value of quantum time in each cycle is equal to the median of burst times of processes in ready queue and for another method this value is equal to arithmetic mean of burst times of ready processes.In this paper we proposed a new method to obtaining quantum time in each cycle based on arithmetic-harmonic mean (HARM. Harmonic mean is calculated by dividing the number of observations by the reciprocal of each number in the series. With examples we show that in some cases it can provides better scheduling criteria and improves the average Turnaround Time and average Waiting Time.
The Tie Effect in Mental Arithmetic%心算加工中tie effect的加工机制
Institute of Scientific and Technical Information of China (English)
田花; 刘昌
2011-01-01
This article is to review the tie effect in simple arithmetic. Tie effect means that simple arithmetic problems with repeated operands （i. e., ties such as 3 ＋ 3,4×4） are solved more quickly and accurately than similar nontie problems （e. g., 3 ＋ 4,4 × 5）. Furthermore, problem size and tie effect so interact that latencies on both ties and nonties increase with the problem size, but the increase is much greater in nonties than in ties. There are two possible explanations for the tie effect, i.e., encoding-based and access- based accounts. Encoding-based accounts propose that the tie advantage occurs because repetition of the same physical stimulus results in faster encoding of ties than of nonties. Alternatively, access-based accounts propose that ties may be easier to solve than nonties because of differences in accessibility in memory or differences in the solution processes. Access-based accounts fall into three categories： familiarity, interference, variability in solution approaches. According to familiarity explanations, acee~ibility so varies with practice that the tie effect is related to the frequency with which problems are encountered. Ties receive more practice and the connections between operands and answers in memory are greater. So ties are solved more quickly. According to interference explanations, ties and nonties are defined as separate categories of problems and the interference is greater within categories than between category. Thus, because the tie category includes relatively few problems, ties received less inhibitory input than nonties. According to solution approach explanations, even simple arithmetic is solved not only by direct retrieval from memory but by nov_retrieval procedures. Ties are solved by direct retrieval procedures and nonties are solved by nonretrieval procedures which are slower than direct retrieval. The encoding-account can＇ t provide reasonable explanations for the tie ~ size interaction. Aceess
Dimitriadis, Stavros I; Sun, Yu; Thakor, Nitish V; Bezerianos, Anastasios
2016-01-01
Many neuroimaging studies have demonstrated the different functional contributions of spatially distinct brain areas to working memory (WM) subsystems in cognitive tasks that demand both local information processing and interregional coordination. In WM cognitive task paradigms employing electroencephalography (EEG), brain rhythms such as θ and α have been linked to specific functional roles over given brain areas, but their functional coupling has not been extensively studied. Here we analyzed an arithmetic task with five cognitive workload levels (CWLs) and demonstrated functional/effective coupling between the two WM subsystems: the central executive located over frontal (F) brain areas that oscillates on the dominant θ rhythm (Frontal(θ)/F(θ)) and the storage buffer located over parieto-occipital (PO) brain areas that operates on the α2 dominant brain rhythm (Parieto-Occipital(α2)/PO(α2)). We focused on important differences between and within WM subsystems in relation to behavioral performance. A repertoire of brain connectivity estimators was employed to elucidate the distinct roles of amplitude, phase within and between frequencies, and the hierarchical role of functionally specialized brain areas related to the task. Specifically, for each CWL, we conducted a) a conventional signal power analysis within both frequency bands at F(θ) and PO(α2), b) the intra- and inter-frequency phase interactions between F(θ) and PO(α2), and c) their causal phase and amplitude relationship. We found no significant statistical difference of signal power or phase interactions between correct and wrong answers. Interestingly, the study of causal interactions between F(θ) and PO(α2) revealed frontal brain region(s) as the leader, while the strength differentiated between correct and wrong responses in every CWL with absolute accuracy. Additionally, zero time-lag between bilateral F(θ) and right PO(a2) could serve as an indicator of mental calculation failure
A low-power Rijndael S-Box based on pass transmission gate and composite field arithmetic
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Using composite field arithmetic in Galois field can result in the compact Rijndael S-Box. However, the power consumption of this solution is too large to be used in resource-limited embedded systems. A full-custom hardware implementation of composite field S-Box is proposed for these targeted domains in this paper. The minimization of power consumption is implemented by optimizing the architecture of the composite field S-Box and using the pass transmission gate (PTG) to realize the logic functions of S-Box. Power simulations were performed using the netlist extracted from the layout. HSPICE simulation results indicated that the proposed S-Box achieves low power consumption of about 130 μW at 10 MHz using 0.25 μm/2.5 V technology, while the consumptions of the positive polarity reed-muller (PPRM) based S-Box and composite field S-Box based on the conventional CMOS logic style are about 240 μW and 420 μW, respectively. The simulations also showed that the presented S-Box obtains better low-voltage operating property, which is clearly relevant for applications like sensor nodes, smart cards and radio frequency identification (RFID) tags.
Deferne, J L; Leeds, A R
1996-08-01
The objective of this study was to test the effect of a supplement of blackcurrant seed oil (BSO), a rich source of gamma-linolenic acid (C18:3n-6) on the resting blood pressure (BP) and cardiovascular reactivity to a psychological stress in borderline hypertensive individuals. Twenty-seven male volunteers found to have a BP lying persistently within the borderline range, were allocated randomly to one of two groups at the end of a 4-week baseline period. The first group received a daily supplement of 6 g safflower oil for the consecutive 8 weeks while the second the same dose of blackcurrant seed oil. In addition to weekly measurements of resting BP, BP and heart rate reactivity to a standardised 5-min test of mental arithmetic were recorded before, and at the end of the supplementation period. BSO inhibited BP reactivity by over 40% (ANOVA for repeated measures diastolic (D) BP P = 0.026, systolic (S) BP P = 0.021). The decrease in DBP for the subjects on BSO was significantly different from the slight changes observed in the safflower group (ANOVA for repeated measures P = 0.018 for time-treatment interaction). We conclude that gamma-linolenic-rich fatty acid preparations are likely to influence cardiovascular control, by mechanisms yet to be clarified.
Directory of Open Access Journals (Sweden)
S.G.Srikantaswamy
2011-12-01
Full Text Available The process of exchanging information is called Communication. The basic Communication system involvestransmitter, receiver and the channel. The data transmitted by the sender reaches receiver through thechannel. The unauthorized parties (cracker,hacker, eavesdropper, or attacker should not be able to access the information at the channel. Therefore transmitting data securely from the sender to the receiver is a very important aspect. A cryptographic system is unconditionally secure if the cipher text produced by the system does not contain enough information to determine uniquely the corresponding plaintext, no matter how much cipher text is available. A cryptographic system is said to be computationally secure if the cost of breaking the cipher exceeds the value of the encrypted information and the time required to break the cipher exceeds the useful lifetime of the content. One time pad system can be called as unconditionally secure algorithm, if the keys (pad usedare truly random in nature. In this paper, we are demonstrating that one-time pad can be used as an efficient encryption scheme by involving arithmetic and logical operations. Here we proposed a new key generation technique, to generate a key of any length just by providing a seed value, to encrypt the message. The problem generating key value has been solved by the use of key generation algorithm.
Guo, Hua; Zheng, Yandong; Zhang, Xiyong; Li, Zhoujun
2016-01-01
In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD) scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD) schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme. PMID:27136550
Directory of Open Access Journals (Sweden)
Hua Guo
2016-04-01
Full Text Available In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme.
Power, Sarah D.; Falk, Tiago H.; Chau, Tom
2010-04-01
Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI). In particular, previous research has shown that NIRS signals recorded from the motor cortex during left- and right-hand imagery can be distinguished, providing a basis for a two-choice NIRS-BCI. In this study, we investigated the feasibility of an alternative two-choice NIRS-BCI paradigm based on the classification of prefrontal activity due to two cognitive tasks, specifically mental arithmetic and music imagery. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while ten able-bodied adults performed mental arithmetic and music imagery within a synchronous shape-matching paradigm. With the 18 filtered AC signals, we created task- and subject-specific maximum likelihood classifiers using hidden Markov models. Mental arithmetic and music imagery were classified with an average accuracy of 77.2% ± 7.0 across participants, with all participants significantly exceeding chance accuracies. The results suggest the potential of a two-choice NIRS-BCI based on cognitive rather than motor tasks.
Directory of Open Access Journals (Sweden)
Jun Won Kim
Full Text Available Theta-phase gamma-amplitude coupling (TGC measurement has recently received attention as a feasible method of assessing brain functions such as neuronal interactions. The purpose of this electroencephalographic (EEG study is to understand the mechanisms underlying the deficits in attentional control in children with attention deficit/hyperactivity disorder (ADHD by comparing the power spectra and TGC at rest and during a mental arithmetic task.Nineteen-channel EEGs were recorded from 97 volunteers (including 53 subjects with ADHD from a camp for hyperactive children under two conditions (rest and task performance. The EEG power spectra and the TGC data were analyzed. Correlation analyses between the Intermediate Visual and Auditory (IVA continuous performance test (CPT scores and EEG parameters were performed.No significant difference in the power spectra was detected between the groups at rest and during task performance. However, TGC was reduced during the arithmetic task in the ADHD group compared with the normal group (F = 16.70, p < 0.001. The TGC values positively correlated with the IVA CPT scores but negatively correlated with theta power.Our findings suggest that desynchronization of TGC occurred during the arithmetic task in ADHD children. TGC in ADHD children is expected to serve as a promising neurophysiological marker of network deactivation during attention-demanding tasks.
An Improved Location Arithmetic for Achieve Directional Sonobuoy and Its TMA%一种改进的声纳浮标定位算法和TMA问题
Institute of Scientific and Technical Information of China (English)
李居伟; 孙明太; 徐以成
2011-01-01
为在航空反潜作战中更加快速精确地测量目标运动要素,对目标定位算法进行改进,并提出基于卡尔曼滤波的目标运动分析方法.根据主动定向声纳浮标“距离和方位联合测量”的特点,给出一种更为直接的加权均值定位算法和定位误差计算方法.并在此基础上,提出了采用卡尔曼滤波器估计目标位置、航速、航向等运动参数的方法.最后采用蒙特卡罗仿真方法,统计分析了系统的误差性能.仿真结果表明,该方法具有较高的目标运动参数估计精度.%In order to achieve undersea target movement elements rapidly and precisely for active directional sonobuoy, the location arithmetic was improved and a method of target motion analysis based on Kaltnan filter was given. According to the characteristic of range-bearing location, the weighted average location arithmetic and its location error were given. The computation complexity of online least squares iteration was efficaciously decreased by this arithmetic. Then, a target motion analysis method based on Kalman filter was given. The target position, velocity and course were estimated by this filter. Finally, the considerable precision was confirmed by the results of Monte Carlo simulation.
浅谈低年级学生口算能力的培养%Discussion on Cultivation of the Ability of Mental Arithmetic of Low Grade Students
Institute of Scientific and Technical Information of China (English)
陈洁璇
2014-01-01
小学是学生计算能力形成的最重要阶段，在低年段培养学生的口算能力特别重要，教师应该提高低年级学生的口算水平。%The primary school is the most important stage for the formation of the students’ calculating ability, the cultivation of students’ mental ability is especially important in low grades, teachers should improve the students, mental arithmetic level in lower grades of.
Let the First Grade Pupils Fall in Love With Mental Arithmetic%让一年级小学生爱上口算
Institute of Scientific and Technical Information of China (English)
徐国华
2014-01-01
通过各种活动变枯燥的计算为丰富的情感体验，让一年级学生在快乐的活动中训练口算能力，从而达到能进行抽象计算的熟练程度。%Through a variety of activities become boring calculation for the rich emotional experience for the first grade students mental arithmetic ability training in happy activities,thus can Proficiency Abstract calculation.
Directory of Open Access Journals (Sweden)
V. U.K.. Sastry
2006-01-01
Full Text Available In this paper, we have developed a block cipher by applying an iterative method. In the process of encryption, we have used a key matrix (K in which all the elements are binary bits. In the process of decryption, we have utilized the modular arithmetic inverse (K-1. In the process of encryption, the elements of the plaintext and the elements of the key are thoroughly mixed so that the strength of the algorithm increases remarkably. In this we have obtained the ciphertext for large blocks of plaintext.
Institute of Scientific and Technical Information of China (English)
张新鹏; 王朔中; 张开文
2003-01-01
A digital watermark as a means for copyright protection may be crippled when a fake mark is embedded on top of it since both watermarks are detectable. In dealing with this problem, a watermarking scheme that does not satisfy the law of commutation is proposed. In this scheme, an order function based on an arithmetic mechanism is employed to identify the embedding order without affecting detection of the regular watermark. An earlier watermark corresponds to a larger value of the order function. In this way, the embedding order or watermarks can be identified according to the order function.
Regis, Germán; Arroyo, Marcelo; Aguirre, Jorge
2005-01-01
Los errores de redondeo introducidos por las diferentes representaciones finitas de los números reales en los lenguajes de programación y su propagación a través de la operaciones aritméticas constituye el problema central del cálculo numérico. Cada aritmética particular de punto flotante induce una forma de propagación distinta. Por ese motivo se han desarrollado numerosas bibliotecas que implementan aritméticas alternativas a las provistas por estos lenguajes. Sin embargo su utilización en ...
Visser, A.
2015-01-01
In this paper we study a new relation between sentences: transducibility. The idea of transducibility is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. Transducibility is based on a converse of Feferman's Theorem: if a sentence is interpretab
Visser, Albert
2014-01-01
In this paper we study a new relation between sentences: the jump relation. The idea of the jump relation is based on an analysis of Feferman's Theorem that the inconsistency of a theory U is interpretable over U. The jump relation is based on a converse of Feferman's Theorem: if a sentence is inter
Linear Integer Arithmetic Revisited
Bromberger, M.; Sturm, T.; Weidenbach, C.
2015-01-01
We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanovic and de Moura constitutes an important step into this direction. Their algorithm CUTSAT is sound, but does not term...
Mieczkowski, Edward
2012-01-01
The set of segments, each of the next is n times bigger than the first one is a simple geometric interpretation of the set $\\mathbb{N}$ of natural numbers. In this paper we investigate the opposite situation. We construct an algebraic structure similar to the set $\\mathbb{N}$ which describes the set of congruent triangles, each of the next has the sides n times bigger than the first one. Later we do the same with the set of congruent tetrahedrons, and finally with a set of simplices of any dimension.
Optical guided wave arithmetic
McAulay, Alastair D.
1999-03-01
Two novel full adder architectures are proposed that can be implemented with optical couplers using fiber optics or integrated optics. The first adder has the advantage over other proposed approaches by requiring only three different component devices: optical logical OR, optical logical NOT, and optical couplers. Configurations of the three components are described that are relatively simple to implement and are expected to function at greater than gigabit per second rates. The second adder requires fewer gates by using additional different gates: analog ADD and thresholding. Methods of implementing in fiber optics and with integrated optics are suggested including the synchronization of the lasers and methods for changing phase. The optical full adder can be used to provide high speed word addition by multiplexing independent addition. The pros and cons of fiber optics versus integrated optics for one architecture versus the other are discussed.
On the Hybrid Mean Value of Two New Arithmetical Functions%两个新的数论函数的混合均值
Institute of Scientific and Technical Information of China (English)
赵珍珍; 赵西卿
2011-01-01
For any positive integer n, a new arithmetical function Ω (n) defined as Ω ( 1 ) = 0, if n ＞ 1 and n =P 1α1 P2α2 … P sαsis standard decomposition of n , (-Ω) ( n ) = α1p 1 + α2p2 +… + αsp s and ( p i is prime number, l ≤ i ≤ s ) .New arithmetical function Sk (n) defined as the smallest positive integer m such that nklm!. That is Sk (n) = min { m: m ∈ N, nk l m ! }. Using the elementary methods the hybrid mean value problem involving (-Ω) (n) and Sk (n) are studied, and a interesting asymptotic formula for it is given.%对任意正整数n,定义数论函数Ω(n)为Ω(1)=0,当n>1,n=pα11pα22…pαss为n的标准分解式, Ω(n)=α1p1+α2p2+…+αsps,其中(pi为素数,1≤i≤s).数论函数Sk(n)定义为Sk(n)=min{m:m∈N,nk|m!},即最小正整数m,使得nk|m!.运用初等方法研究数论函数Ω(n)与Sk(n)的混合均值问题,并得到一个有趣的渐近公式.
Moore, Alex M; vanMarle, Kristy; Geary, David C
2016-10-01
Fluency in first graders' processing of the magnitudes associated with Arabic numerals, collections of objects, and mixtures of objects and numerals predicts current and future mathematics achievement. The quantitative competencies that support the development of fluent processing of magnitude, however, are not fully understood. At the beginning and end of preschool (M=3years 9months at first assessment, range=3years 3months to 4years 3months), 112 children (51 boys) completed tasks measuring numeral recognition and comparison, acuity of the approximate number system, and knowledge of counting principles, cardinality, and implicit arithmetic and also completed a magnitude processing task (number sets test) in kindergarten. Use of Bayesian and linear regression techniques revealed that two measures of preschoolers' cardinal knowledge and their competence at implicit arithmetic predicted later fluency of magnitude processing, controlling domain-general factors, preliteracy skills, and parental education. The results help to narrow the search for the early foundation of children's emerging competence with symbolic mathematics and provide direction for early interventions. PMID:27236038
Difference and dynamic binarization of binary arithmetic coding%差分动态二进制化的二进制算数编码
Institute of Scientific and Technical Information of China (English)
吴江铭
2013-01-01
It provides an overview of the high efficiency compression method CABAC proposed in HEVC which will be published by JCT-VC.Then it optimizes the binarization process of binary arithmetic coding by dynamic Huffman coding and makes the difference before the binarization.At last,it demonstrates the experimental results in comparison with the PAQ to validate the efficiency of the new method difference and dynamic binarization of binary arithmetic coding.%JCT-VC组织公布的HEVC协议草案沿用了H264的CABAC,改进了二进制化过程.在阐述高性能压缩算法CABAC的同时,创新性地提出了动态二进制化算数编码,并预先对数据进行差分.最后,通过压缩Java文件实验证实差分动态二进制化算数编码在压缩率方面有较大的提高,高于PAQ和CABAC.
车载惯性平台稳定位置解算算法%Position arithmetic for a vehicular inertial stabilized platform
Institute of Scientific and Technical Information of China (English)
刘廷霞; 王伟国; 陈健
2012-01-01
According to the idea of the position-self-stabilization of a ship, this paper proposes a position cal- culation arithmetic for an inertia platform based on coordinate conversion. This arithmetic calculates the posi- tion value between the inertia platform and the carrier in real time by coordinate conversion, then the value is used as a position stabilization controllable input to insulate the position interferece of the carrier and to stabi- lize the platform. The experimental result shows that the stabilities of the outer and inner frames for the plat- form are 0. 1 mrad, and 0. 3 mrad, respectively, which satisfies the index requirement of 1 mrad. The position calculation arithmetic for the inertia platform based on coordinate conversion availability solves the stabilization problem for the inertia platform carried by the car and also improves the cost of the entire stabilization system.%根据船摇位置自稳定的思想，提出了基于坐标转换的惯性平台位置稳定解算算法。该算法通过坐标变换实时解算出惯性平台相对载体的位置值并将其作为位置稳定控制的位置环输入，从而有效隔离载体对平台位置的干扰，实现平台的稳定。实验结果表明：平台的外框架稳定精度为0．1mrad，内框架稳定精度为0．3mrad，满足了指标1mrad的要求。该算法有效地解决了车载惯性平台的稳定性问题，提高了整个稳定系统的性价比。
Agaliotis, Ioannis; Teli, Afroditi
2016-01-01
The effectiveness of two instructional interventions was investigated in the context of teaching Arithmetic Combinations (ACs) of multiplication and division to students with Learning Disabilities (LD) or Mild Intellectual Disability (MID). The intervention for the control group (LD = 20, MID = 10) was based on principles of effective instruction,…
大型回转平台调平技术研究%The Researsh of Arithmetic of Level Angle Decomposition When Launcher Turned Around
Institute of Scientific and Technical Information of China (English)
朱宝; 于永胜; 康宁民; 穆忠波
2011-01-01
Using the way of space geometry decomposition,based at abstract space model, a kind of arithmetic of level angle decomposition is calculated. By decomposing current level of vertical sensitive axis direction of level angle sensor to adjust direction when launcher tumed around, auto level adjust of launcher is carried out when don ' t manual adjusting the direction of level angle sensor.%利用空间几何分解,通过建立空间模型,推算出一种水平度分解算法,把大型回转平台回转后当前水平传感器两正交敏感轴方向的水平度分解到可调节控制方位上,实现无需重新调整水平传感器敏感方位下使回转平台回转的自动调平.
International Nuclear Information System (INIS)
Some new theorems have been propounded for the numbers (M-1), as they relate to other numerals, through the basic arithmetical operations, at different bases M. For some reason, we give the proof of the theorems for the case M=10 using mathematical induction, and by Peano's fifth axiom make our generalizations. Comments are made in respect of the numbers (M-1), (in this case 9). Apart from our theorems facilitating mathematical operations, evidences have also been given, from different sources of the interesting properties of this class of numbers, represented in our own case by the numeral 9. The theorems neither violate the divisibility rule for 9 nor are they a consequence of it. From symmetry, a suggestion is made in respect of the possible origin of the numeration in base 10, and the case of a ten dimensional Universe reconsidered. (author). 18 refs, 1 fig., 4 tabs
Hybrid Mean Value Distribution about Two Multiplicative Arithmetical Function%关于两个可乘数论函数的混合均值分布
Institute of Scientific and Technical Information of China (English)
王荣波; 冯强
2015-01-01
基于可乘函数U (n)，V (n)与欧拉函数φ(n)以及R(n)的性质，构造了∑U (n)φ(n)，∑V (n)φ(n)以及∑R(n)U (n) n≤x n≤x n≤x均值分布性质，利用解析的方法，给出几个较为精确的渐近公式。%Based on the multiplicative arithmetical function U(n),V(n),φ(n) and R(n),the function∑U (n)φ(n) , n≤x∑V (n)φ(n) and∑R(n)U(n) are constructed,and their hybrid mean value distribution properties are discussed. By n≤x n≤x using the analytic method,several interesting asymptotic formulae are given.
Zhao, Hong-Quan; Kasai, Seiya; Shiratori, Yuta; Hashizume, Tamotsu
2009-06-17
A two-bit arithmetic logic unit (ALU) was successfully fabricated on a GaAs-based regular nanowire network with hexagonal topology. This fundamental building block of central processing units can be implemented on a regular nanowire network structure with simple circuit architecture based on graphical representation of logic functions using a binary decision diagram and topology control of the graph. The four-instruction ALU was designed by integrating subgraphs representing each instruction, and the circuitry was implemented by transferring the logical graph structure to a GaAs-based nanowire network formed by electron beam lithography and wet chemical etching. A path switching function was implemented in nodes by Schottky wrap gate control of nanowires. The fabricated circuit integrating 32 node devices exhibits the correct output waveforms at room temperature allowing for threshold voltage variation.
An ERP Study of Mix Strategy Selection in Mental Arithmetic%心算活动中混合策略选择的ERP研究
Institute of Scientific and Technical Information of China (English)
陈亚林; 刘昌; 张小将; 徐晓东; 沈汪兵
2011-01-01
考察问题大小、距离、奇偶及答案正误对心算策略选择的影响.采用先答案后算式的呈现方式,记录了15名被试的64导ERP.研究发现,在小问题中,错误答案与正确答案相比,诱发了算术不一致N400,距离和奇偶因素影响其波峰及潜伏期.在大问题中,距离和奇偶因素影响晚期正波,近距离奇偶一致情境诱发了波幅较小的晚期正慢波.表明在混合情境,距离比奇偶信息优先得到加工;在小问题心算中距离和奇偶信息影响答案提取,而在大问题心算中,对于依靠距离信息较难直接判断的小距离问题,在进一步的加工中会借助奇偶信息判断是否采用精确计算策略.%Problem size, split, parity and correctness of answer affect mental arithmetic problem-solving. Behavioral and cognitive neuroscience researches on mental arithmetic showed that there are different strategy selection in problem size effect, split effect, and parity effect. Moreover, these three factors can hardly be distinct from each other. Split and parity even have contradictive effect. These caused confusions in past researches. And also, few researches noticed the mix of the factors. How do people make their choice when these factors are mixed? One hypothesis is that split has priority compare to parity. Moreover, the electrophysiological feathers of parity effect remained unknown. There were also some problems of the presentation mode in past researches. The present study tried to give an answer with a new presentation mode.High-density event-related potentials (Neuroscan) of 15 college students were recorded. The stimuli consisted of mathematic equations between 0 and 60. Each trial began with a fixation cross shown for 500 ms.500ms later, the answer shown for 250ms. Another 500ms later, the equations appeared and remained on the screen for 3000 ms followed by the varied ITI of 800-1200ms. There were 6 blocks, which consisted of 110 trials. All the trials and
Institute of Scientific and Technical Information of China (English)
司继伟; 徐艳丽; 封洪敏; 许晓华; 周超
2014-01-01
采用事件相关电位(ERP)技术和选择/无选法范式，在两位数加法心算和估算中，探索高、低数学焦虑个体的算术计算策略运用及其内在机制。行为结果：数学焦虑效应在策略运用的反应时和正确率指标上的差异都不显著；而脑电结果：高数学焦虑个体的 N400波幅显著高于低数学焦虑个体；选择条件中，估算与心算的数学焦虑效应的N100波幅差异；无选条件中，高低数学焦虑个体N1-P2复合波的波幅和潜伏期差异显著。数学焦虑效应在策略编码(0~250 ms)和策略选择/执行阶段(250 ms之后)存在差异。%As one of the leading researching topics of contemporary cognitive science, strategy use depends on many factors, such as situation, problem characteristics, individual differences including math anxiety, etc. (Siegler, 2007;Imbo& Vandierendonck, 2007).Various theories on arithmetic anxiety have been proposed, however, the role of arithmetic anxiety in strategy utilization and its potential mechanism is still far from clear (Wang&Liu, 2007). The neural mechanism of arithmetic strategies utilization affected by math anxiety still needs further exploring. Event-Related Potentials (ERPs) is usually utilized in exploring brain mechanisms in arithmetic performance, and the choice/no-choice method is a standard method to obtain unbiased data about strategy utilization. In this study, we employed the ERPs and choice/no-choice method to investigate the influence of math anxiety upon individual strategy utilization during arithmetic processing. Revised Mathematics Anxiety Rating Scale (R-MARS) and Trait Anxiety Inventory were used to test 154 students and 34 participants were picked and divided to two groups (17 high math anxiety and 17 low math anxiety). Participants were required to finish the two-digit addition computational mental arithmetic and computational estimation based on applying the ERP technique to test the neurophysiologic
Rui eNouchi; Yasuyuki eTaki; Hikaru eTakeuchi; Takayuki eNozawa; Atsushi eSekiguchi; Ryuta eKawashima
2016-01-01
BackgroundPrevious reports have described that simple cognitive training using reading aloud and solving simple arithmetic calculations, so-called learning therapy, can improve executive functions and processing speed in the older adults. Nevertheless, it is not well-known whether learning therapy improve a wide range of cognitive functions or not. We investigated the beneficial effects of learning therapy on various cognitive functions in healthy older adults.MethodsWe used a single-blinde...
Power, Sarah D.; Kushki, Azadeh; Chau, Tom
2011-10-01
Near-infrared spectroscopy (NIRS) has recently been investigated as a non-invasive brain-computer interface (BCI) for individuals with severe motor impairments. For the most part, previous research has investigated the development of NIRS-BCIs operating under synchronous control paradigms, which require the user to exert conscious control over their mental activity whenever the system is vigilant. Though functional, this is mentally demanding and an unnatural way to communicate. An attractive alternative to the synchronous control paradigm is system-paced control, in which users are required to consciously modify their brain activity only when they wish to affect the BCI output, and can remain in a more natural, 'no-control' state at all other times. In this study, we investigated the feasibility of a system-paced NIRS-BCI with one intentional control (IC) state corresponding to the performance of either mental arithmetic or mental singing. In particular, this involved determining if these tasks could be distinguished, individually, from the unconstrained 'no-control' state. Deploying a dual-wavelength frequency domain near-infrared spectrometer, we interrogated nine sites around the frontopolar locations (International 10-20 System) while eight able-bodied adults performed mental arithmetic and mental singing to answer multiple-choice questions within a system-paced paradigm. With a linear classifier trained on a six-dimensional feature set, an overall classification accuracy of 71.2% across participants was achieved for the mental arithmetic versus no-control classification problem. While the mental singing versus no-control classification was less successful across participants (62.7% on average), four participants did attain accuracies well in excess of chance, three of which were above 70%. Analyses were performed offline. Collectively, these results are encouraging, and demonstrate the potential of a system-paced NIRS-BCI with one IC state corresponding to
Recognition of fabric organization structure based on SMO arithmetic%基于SMO算法的织物组织结构识别
Institute of Scientific and Technical Information of China (English)
任海军; 孙瑞志; 宋强
2009-01-01
提出了一种用机器识别布料结构的方法.该方法采用图像去噪、增强及二值化技术对织物组织图进行预处理,采用经纬像素差值法提取出织物组织结构的特征向量,用序列最小化(SMO)算法进行识别分类,重构出清晰的、便于生产加工的织物组织结构图.实验结果表明,通过该方法对织物组织结构的识别具有较高的准确率.%There is a new method for recognition of fabric organization. Firstly, the image technology is used to preprocess the fabric organization image, and a special way adopted to pick-up the support vector from fabric organization structure. Then, the SMO arithmetic is used to recognize and classify. Lastly, the fabric organization image which facilitates the production and processing is reconstructed. Test results show that this method has a good accuracy on the recognition of fabric organization structure.
Institute of Scientific and Technical Information of China (English)
解晨
2012-01-01
Number theory, was once thought to be beautiful but less useful in pure mathematics. With the development of the times, especially the large prime numbers based on password transmission system of the invention, the number theory algorithms are widely used. However, the use of the current mainstream programming languages such as C, C++, C#, JAVA, Matlab for large numbers of computing program is not very convenient. This article through the use of a suitable for computation of large numbers of minority programming language Common Lisp, on some arithmetical functions are simple convenient realization.% 数论,曾一度被认为是华丽却用处不大的纯数学学科。随着时代的发展,尤其是基于大素数的密码传输系统的发明,使得有关数论的算法被广泛的应用起来。然而,使用当前的主流编程语言如C、C++、C#、JAVA、Matlab等对于大数的运算进行编程并不是很方便。该文试图通过使用一种适合对大数运算进行编程的小众语言Common Lisp,对一些数论函数进行简洁便利的实现。
Institute of Scientific and Technical Information of China (English)
刘巧红; 单贵
2011-01-01
Python is one of the most popular script language, but the performance is a problem.In this paper, we evaluated the performance of integer arithmetic difference between the Python and C languages by experiment, and analyzed the causes of performance difference from the virtual machine source code level.The paper summarizes several common methods of Python script performance optimization, by one of these, we achieved good results on test.%Puthon是最流行的脚本语言之一,但性能较慢.以整数运算为例,通过实验对比评估了Python与C语言性能差异,从虚拟机源代码层面分析了性能差异产生的原因.在性能优化方面,归纳了几种常用的方法,并基于其中一种进行了对比测试,取得了较好效果.
Institute of Scientific and Technical Information of China (English)
李美蓉; 彭勃
2013-01-01
By utilizing some operational laws of pure linguistic variables, this paper proposes an aggregation operator called Induced Pure Linguistic Order Weighted Arithmetic Averaging (IPLOWAA) operator and studies some desirable properties of the IPLOWAA operator. Also, it develops a method of group decision making based on IPLOWAA and PLOWAA operators under multiplicative linguistic preference relations, which is straightforward and takes the known linguistic information into account sufficiently. An illustrative application to risk investment is given to verify the developed approach and to demonstrate its practicality and effectiveness.%利用纯语言变量的运算规律,提出了一种信息集成算子:导出的纯语言有序加权算术平均(IPLOWAA)算子,同时对IPLOWAA算子的性质进行了研究.在群体语言偏好关系下,给出了基于IPLOWAA算子和PLOWAA算子的一种群决策方法,该方法计算简洁方便且能充分利用已有的决策信息.将该方法应用在风险投资中,说明该方法的实用性和有效性.
Churazov, E.; Arevalo, P.; Forman, W.; Jones, C.; Schekochihin, A.; Vikhlinin, A.; Zhuravleva, I.
2016-08-01
We discuss a novel technique of manipulating X-ray images of galaxy clusters to reveal the nature of small-scale density/temperature perturbations in the intra cluster medium (ICM). As we show, this technique can be used to differentiate between sound waves and isobaric perturbations in Chandra images of the Perseus and M87/Virgo clusters. The comparison of the manipulated images with the radio data and with the results of detailed spectral analysis shows that this approach successfully classifies the types of perturbations and helps to reveal their nature. For the central regions (5-100 kpc) of the M87 and Perseus clusters this analysis suggests that observed images are dominated by isobaric perturbations, followed by perturbations caused by bubbles of relativistic plasma and weak shocks. Such a hierarchy is best explained in a "slow" AGN feedback scenario, when much of the mechanical energy output of a central black hole is captured by the bubble enthalpy that is gradually released during buoyant rise of the bubbles. The "image arithmetic" works best for prominent structure and for datasets with excellent statistics, visualizing the perturbations with a given effective equation of state. The same approach can be extended to faint perturbations via cross-spectrum analysis of surface brightness fluctuations in X-ray images in different energy bands.
Energy Technology Data Exchange (ETDEWEB)
Craiovan, B.; Weber, M.; Worlicek, M.; Schneider, M.; Springorum, H.R.; Grifka, J.; Renkawitz, T. [University Medical Center Regensburg, Bad Abbach/Regensburg (Germany). Orthopedic Surgery; Zeman, F. [University Medical Center Regensburg, Bad Abbach/Regensburg (Germany). Center for Clinical Studies
2016-06-15
The aim of this prospective study is to validate a vector arithmetic method for measuring acetabular cup orientation after total hip arthroplasty (THA) and to verify the clinical practice. We measured cup anteversion and inclination of 123 patients after cementless primary THA twice by two examiners on AP pelvic radiographs with a vector arithmetic method and compared with a 3D-CT based reconstruction model within the same radiographic coronal plane. The mean difference between the radiographic and the 3D-CT measurements was -1.4 ±3.9 for inclination and 0.8 ±7.9 for anteversion with excellent correlation for inclination (r=0.81, p < 0.001) and moderate correlation for anteversion (r=0.65, p < 0.001). The intraclass correlation coefficient for measurements on radiographs ranged from 0.98 (95%-CI: 0.98; 0.99) for the first observer to 0.94 (95%-CI: 0.92; 0.96) for the second observer. The interrater reliability was 0.96 (95%-CI: 0.93; 0.98) for inclination and 0.93 (95%-CI: 0.85; 0.96) for anteversion. The largest errors in measurements were associated with an extraordinary pelvic tilt. In order to get a valuable measurement for measuring cup position after THA on pelvic radiographs by this vector arithmetic method, there is a need for a correct postoperative ap view, with special regards to the pelvic tilt for the future.
Realization of Intelligent Neuron PID Control with Relay Self-Tuning Arithmetic%用继电自整定实现神经元PID智能控制
Institute of Scientific and Technical Information of China (English)
楚彦君; 马龙; 巨林仓
2001-01-01
In order to meet the requirement of in dustry process control,new methods for tuning PID need to be applied.The neuron self-tuning PID controller combined with relay self-tuning is presented.The i n itial values for neuron self-tuning PID controller are acquired from relay self -tuning arithmetic,then the control mode is switched to adaptive mode.The intel ligent neuron PID control is thus realized.Its stability is analyzed and the sim ulation by using simulink of matlab is done.The satisfied results are achieved.%当前工业过程对控制品质要求越来越高，需要更先进的PID控制器参数整定方法来满足过程控制的要求。该文提出了神经元自适应PID控制器与PID继电自整定相结合构成PID智能控制系统的方法，即利用PID继电自整定算法获取神经元自适应PID控制器权系数的初值，然后将得到的初值送到神经元自适应PID控制器，并且切换到自适应控制模式，从而实现神经元PID智能控制。同时分析了神经元自适应控制系统的稳定性，用Matlab中的Simulink进行了仿真模拟，得到了满意的结果。
Zelator, Konstantine
2013-01-01
In a paper published by this author in www.academia.edu(see reference[3]), it was established that there exist no three positive integers which are consecutive terms of an arithmetic progression; and whose sum of squares is a perfect or integer square. In that paper, we made use of the 3-parameter formulas which describe the entire set of positive integer solutions of the 4-variable equation, $x^2+y^2+z^2= t^2$ (See reference [1]) In this work, we offer an alternative proof to the above resul...
The Integration of Arithmetic Knowledge and Semantic Knowledge in Addition Facts%加法运算中数学知识和语义知识的整合
Institute of Scientific and Technical Information of China (English)
陈栩茜; 何本炫; 张积家
2012-01-01
采用语义启动数字匹配任务及其变式,探讨在中文背景下“和效应”和语义系统的类比一致性及其产生机制.结果发现,中国学生对“和”目标数字的反应时显著长于对中性目标数字,表明“和效应”是人类的一种强烈的认知倾向;人类通过类比映射方式整合数学知识和语义知识;影响语义加工的因素同样影响数学认知.研究还发现,被试对中性目标数字的抑制难度受语义匹配任务性质的影响,在完成类别不一致的探测词匹配任务时,拒绝中性目标数字的反应时显著长,“和效应”消失,表明“和效应”不仅源自于对“和”目标数字的激活,也源自于对中性目标数字的抑制.%Recently, more and more researchers are interested in the relation between arithmetical cognition system and other cognitive function systems, especially the relation between arithmetical cognition system and the semantic concept system. A study done by Bassok. Pedigo, & Oskarsson (2008) showed that proper semantic context facilitated the processing of arithmetical cognition, whereas improper semantic context blocked the processing of arithmetical cognition. This result implied that people had the strong inclination to integrate the arithmetical knowledge with semantic knowledge. They believed that the integration was processed through the analogical mapping mechanism. This study aimed to further investigate the following questions based on Bassok et al. (2008): 1) mathematical cognition is affected by cultural cognitive activities (Tang, Zhang, Chen, Feng, Ji, Shen, Reiman, & Liu, 2006). However, whether the integration processing mode of arithmetical knowledge and semantic knowledge was cultural universal? 2) Whether the cognitive mechanism which integrated arithmetical knowledge and semantic knowledge was analogical mapping mechanism, or whether it was the necessary condition of analogical mapping mechanism? 3) Whether the factors
Directory of Open Access Journals (Sweden)
Rosemary Rizo-Patrón
2008-12-01
Full Text Available “Intuitive Finitude and Symbolic Infinitude in Husserl’s Philosophy of Arithmetic and Crisis”. Since its inception, Husserl’s phenomenology oscillates between a positive valuation of technical calculus in order to compensate for the limited capacity of human beings, and a denunciation regarding the blindnessthat its extraordinary development has brought about regarding the true nature of scientific and philosophical thinking, in their sense as λ. Likewise, regarding intuition phenomenology oscillates between on one side a positive valuation of the foundational and authentic character of the basic intuitive representations and, on the other, the observation of their radical finitude. This paper explores some salient features of these oscillations.
The Measurement Method of Spherical Domes in The Key to Arithmetic%《算数之钥》中球形穹顶的测量法
Institute of Scientific and Technical Information of China (English)
依里哈木·玉素甫; 麦尔哈巴·西尔亚孜旦
2014-01-01
中世纪中亚数学家阿尔·卡西在《算术之钥》中不但给出了5种伊斯兰建筑风格拱形门和球形穹顶的设计方案，而且用初等方法计算了其中拱形部分的表面积和体积，遗憾的是，他没有给出球形穹顶部分的表面积和体积的具体计算过程，只用文字叙述了用初等数学方法来计算其中第四类球形穹顶表面积和体积的基本思路，并直接给出了球形穹顶表面积和体积分别与其直径平方和直径立方之比的近似值。讨论了阿尔·卡西的初等算法，并用微积分方法来验证其算法的正确性，同时指出阿尔·卡西得到的数据与实际数据之间的误差。%In his book The Key to Arithmetic ,the central Asian mathematician al-Kashi,who belongs to middle ages,not only designed five types of Islamic arches and spherical domes,but also computed the areas and volumes of their arched parts by using elementary method.Unfortunately,he did not provide concrete algorithm about the computation of area and volume of the spherical dome parts,and only literally stated the basic idea of the computation of area and volume of the fourth type spherical dome part.He also provided the approximate values of the ratio of its surface to the square of diameter and the ratio of its volume to the third power of the diameter,respectively.In this paper,we discussed the elementary algo-rithm of al-Kashi and checked its exact value by using calculus,and at the same time,get the error between the two values.
Arithmetical Foundations - Recursion. Evaluation. Consistency
Pfender, Michael
2013-01-01
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\\"odel incompleteness theorems, inconsistency provability for set theory, constructive consistency.
Individual differences in arithmetic fluency
García-Orza, Javier; Rodríguez, José Miguel; Calleja, Marina; Iza, Mauricio; Álvarez-Montesinos, Juan
2016-01-01
Este estudio contrasta la hipótesis de que las dificultades que tienen algunos sujetos en el dominio de las tablas de multiplicar se deban a su incapacidad para afrontar la interferencia. Los resultados no muestran diferencias en medidas de interferencia en un tarea de recuerdo serial entre sujetos con alta y baja habilidad en la resolución de multiplicaciones. Sin embargo, se encuentran diferencias asociadas a su dominio de las representaciones numéricas. Universidad de Málaga. Campus de ...
Arithmetic Memory Is Modality Specific.
Directory of Open Access Journals (Sweden)
Timothy Myers
Full Text Available In regards to numerical cognition and working memory, it is an open question as to whether numbers are stored into and retrieved from a central abstract representation or from separate notation-specific representations. This study seeks to help answer this by utilizing the numeral modality effect (NME in three experiments to explore how numbers are processed by the human brain. The participants were presented with numbers (1-9 as either Arabic digits or written number words (Arabic digits and dot matrices in Experiment 2 at the first (S1 and second (S2 stimuli. The participant's task was to add the first two stimuli together and verify whether the answer (S3, presented simultaneously with S2, was correct. We hypothesized that if reaction time (RT at S2/S3 depends on the modality of S1 then numbers are retrieved from modality specific memory stores. Indeed, RT depended on the modality of S1 whenever S2 was an Arabic digit which argues against the concept of numbers being stored and retrieved from a central, abstract representation.
Directory of Open Access Journals (Sweden)
Verônica Bender Haydu
2006-01-01
Full Text Available The equivalence paradigm has been applied to the development of a variety of procedures applied to teach reading, writing and arithmetic. This work aimed to investigate the effect of teaching stimulus equivalence relations between three different forms of arithmetic sum problems on problem-solving behavior. Seven first grade students of Fundamental Schooling (=Elementary Schooling were submitted to a pre-test, and a post-test with sum problems printed in the form of slave (A, operations (B and word problems (C. The conditional discrimination procedure established relations between A-B and A-C. Six of seven participants responded accordingly to the established classes. The performance of the participants in the post-test was higher than in the pre-test. It was concluded that the establishment of equivalence relations between arithmetic sum problems in the form of slave, operations, and word problems enhanced the performance of the resolution of those types of problems.
Institute of Scientific and Technical Information of China (English)
陈益云
2011-01-01
Based on the analysis of all the traps in financial ratios by using simple arithmetic average,we propose that it should be necessary to introduce chronological average to overcome the defect of the simple arithmetic average that is liable to the influence of extreme values and describes the phenomenon only from a static perspective.Three indicators of the inventory turnover,accounts receivable turnover ratio and return on net assets are used to prove that chronological average can not only dynamically reflect business situation of enterprises but also provide relevant and reliable financial information.%在分析财务比率中因使用简单算术平均数而出现的种种陷阱的基础上,指出了为克服简单算术平均数易受个别或少数极端值影响和只从静态上说明总体水平的缺陷,有必要引入序时平均数,并以存货周转率、应收账款周转率和净资产收益率三个比率进行计算分析说明序时平均数能从动态上反映企业的经营状况,能更好地为企业相关者提供可靠的财务信息。
Directory of Open Access Journals (Sweden)
Michelle Brugnera Cruz Cechin
2013-03-01
Full Text Available este estudo identificou os procedimentos de contagem usados por crianças com deficiência intelectual e verificou os efeitos de um programa de intervenção direcionado ao ensino de fatos aritméticos. Participaram três crianças, entre oito e 12 anos, de uma escola da rede municipal de ensino de Porto Alegre, Rio Grande do Sul, que atende fundamentalmente às classes socioeconômicas baixas. A partir da revisão de literatura sobre os processos cognitivos envolvidos na resolução de problemas aditivos e as implicações para o seu ensino, avaliou-se a eficácia de um modelo de intervenção pedagógica como um recurso para o avanço no uso dos procedimentos de contagem. Foi aplicado um programa em 10 encontros, realizados uma vez por semana, com duração de aproximadamente cinquenta minutos cada. A proposta caracterizou-se pelo ensino direto, explícito e sistemático, através de sequências de instrução, partindo dos procedimentos de contagem usados pelos estudantes, que foram avaliados em dois momentos (pré-teste e pós-teste. Verificou-se que houve um avanço nos procedimentos de contagem utilizados pelas crianças após a intervenção, revelando que o programa foi eficaz. Mesmo intervenções de curta duração, como é o caso desta, podem trazer benefícios importantes para as crianças com deficiência intelectual, benefícios estes que serão a base de seus conhecimentos posteriores.The objective of this study was to identify procedures used for counting by children with intellectual disabilities and to analyze the effects of an intervention program focused on teaching arithmetic facts. Participants were three children between eight and 12 years from a public school in Porto Alegre, Rio Grande do Sul, whose students come mainly from low socioeconomic families. Based on the review of the literature on the cognitive processes involved in the solution of addition problems and the implications for teaching, we evaluated the efficacy
Institute of Scientific and Technical Information of China (English)
郭丽婷; 孙汉银
2014-01-01
As a new insight problem, matchstick arithmetic problems have been used to investigate insight problem sol-ving.However, it is unclear how difficult the different types of matchstick arithmetic problems are and to what ex-tent they exhibit characteristics of insight.In the present study, 68 undergraduates attempted to solve 8 two-move matchstick arithmetic problems either silently or while providing concurrent verbal protocols.The results showed that:1 ) Verbal protocols could be used to examine the cognitive processes during the two-move matchstick arithme-tic problems solving;2) the difficulty did not depend entirely on the levels of constraint relaxation and chunk de-composition;3) there were three types of cognitive components in the 5 types of problems, such as failure, impasse and restructuring, and the restructuring also included the top-down and bottom-up restructuring.Overall, the cog-nitive process of problem solving may be viewed as a continuum between the insight and analysis, and the greater difficult tautology and operator types belonged more to the end of insight, the CD type tended to be in the middle, while the lower difficult hybrid and value types belonged to the end of analysis.Additionally, the closer to the end of insight the problem was, the more bottom-up restructuring it had.%选取68名大学生，随机分为口语报告组和非口语报告组，解决数值型、混合型、分解型、符号型和连等型等五种类型在内的8个两步火柴棍算术问题，以探讨不同难度的两步火柴棍算术问题解决过程中的顿悟认知成分。研究结果：（1）在两步火柴棍算术问题解决过程中，口语报告不存在口语遮蔽效应；（2）两步火柴棍算术问题的难度水平不完全取决于不正确表征；（3）五种题型中都存在失败、僵局和重构三种顿悟认知成分，且都存在自下而上和自上而下两种重构类型。本研究验证了难度水平不同的两步火柴
The Situation Model and Problem Model in Arithmetic Problem Solving%论数学问题解决中情境模型与问题模型的关系
Institute of Scientific and Technical Information of China (English)
和美君; 刘儒德
2012-01-01
情境模型与问题模型是数学问题解决研究中的两个重要概念，前者是对问题所述情境的日常化的定性表征，后者是基于图式知识对问题关键变量的数量关系表征。本文介绍了两种模型的发展历史以及目前存在的争议，并提出未来研究需要解决的问题。%Situation model and problem model are two important concepts in arithmetic problem solving and representation. However, researchers have different opinions about their definitions, roles and relationships in the process of problem solving. Therefore, our aim is to talk about their development history, discriminate the concepts, and reveal the controversies and future study direction. On the basis of general text comprehension theory （Van Dijk ＆ Kintsch, 1983）, Kintsch and Greeno （1985）first proposed the construction of problem models in arithmetic problem solving research field. They argued that problem solvers would construct textbase and problem model, and the latter one was the only high-level representation problem solvers constructed. This left other researchers unsatisfied, and many began to express their own opinions and propose the concept of the situation model. Nathan, Kintsch, and Young （1992） argued that while Kintsch and Greeno（1985） placed too much emphasis on schemata and problem models, the situation model was very important for it could make explicit the implicit conditions in the problem, and could also monitor and even correct possible mistakes in problem models. Then, Moreau and Coquin-Viennot（2003）studied the nature of representation problem solvers constructed through the information types they chose when doing different tasks, and proved that when solving problems, students would construct different representations according to different task requirements, and meanwhile, the mathematical ability of students had a great impact on the their capability of choosing relevant information to construct
Directory of Open Access Journals (Sweden)
Antonio Frías
2007-09-01
Full Text Available En este trabajo identificamos una variable lingüística en los problemas aritméticos verbales de dos pasos, que denominamos “nodo”. Describimos una experiencia con estudiantes de 5º y 6º de primaria (10 y 12 años cuyo fin fue observar si esta variable lingüística tiene o no influencia significativa en la elección de las operaciones necesarias para solucionar este tipo de problemas. Los resultados obtenidos muestran que el número de nodos en un problema de dos pasos tiene efecto significativo en el proceso de resolución. Esta influencia no se ve alterada por otros factores considerados en este estudio. In this work we identify a new factor in two-steps arithmetic word problems, which we denominate "node” factor. We describe an experience with 5th and 6th grade primary students (11 and 12-year-old pupils whose purpose was to observe if this factor has or has not significant influence in the election of the necessary operations to solve this type of problems. The obtained results show that the number of nodes in a problem of two steps has significant effect in the resolution process. This significant influence is not altered by other factors considered in this study.
Institute of Scientific and Technical Information of China (English)
金保明
2012-01-01
Levenberg - Marquardt back propagation ( LMBP) arithmetic which is come from improvement method of back propagation is applied in the upper Minjiang River. LMBP neural network flow flood forecast model is established in annual maximum peak discharge of Shili' an hydrologic gauging station in the upper Minjiang River and the corresponding flood discharge of three hydrologic gauging stations in branch of the upper Minjiang River, which are Qilijie station in Jianxi River, Yangkou station in Futunxi River and Shaxian station in Shaxi River. The working speed is improved markedly and forecasting time is shorten in the model. The results show that forecast accuracy of the model accords with the application requirements.%运用反向传播算法的改进方法LMBP算法,选取闽江上游南平市十里庵水文站最大洪峰流量与其支流建溪建瓯市七里街站、富屯溪顺昌县洋口站、沙溪沙县站3个水文站的相应洪水流量建立LMBP神经网络洪水预报模型.该模型能显著提高运行速度,缩短预报时间.计算结果表明,模型预测精度满足应用要求.
Institute of Scientific and Technical Information of China (English)
孟庆华; 鲍春雨
2012-01-01
A kind of valuation method that stands out self-advantage was established in the paper,considering absoluteness of superior-inferior distinguish to traditional physical education valuation and unconsistency of multi-evaluation conclusions. The author used random simulation arithmetic method basing on probability to judge object's advantage through calculating superior degree of objects. The method is effective by validation,the valuation conclusion with probability was achieved.%针对传统体育教学评价中优劣判别的绝对性,以及多评价结论非一致性问题,构建一种凸显自身优势的自主优势评价方法,评价中运用一种基于概率型随机模拟算法,通过计算各评价对象之间的优胜度,来评判评价对象的优势.经过算例验证方法的有效性,得到带有概率信息的评价结论.
Research On Self-Decetion Making Arithmetic For submarine Evading Active Sonobuoy%潜艇规避主动声纳浮标自主决策算法研究
Institute of Scientific and Technical Information of China (English)
孙明太; 秦锋; 陈遵银
2013-01-01
主动声纳浮标可以实现对潜艇的精确定位,但易被潜艇感知采取机动规避措施,为了有效减少被主动声纳浮标发现的概率和暴露时间,提出了潜艇自主规避的决策算法,并针对一型主动声纳浮标阵探测进行仿真,分析探测概率变化规律,由此验证算法的有效性.%Active sonobuoy can achieve accurate fixing at submarine, but it is detected easely, so the submarine can be evaded. In order to reduce the probability of detection by active sonobuoy and exposure, it presents a self-decetion making arithmetic for submarine evading active sonobuoy. Then it considers a typical array, finds out that rule of the probability of detection and the validity through emulator.
Institute of Scientific and Technical Information of China (English)
何德峰; 黄骅; 王蕾
2013-01-01
考虑优化级多目标优化控制问题,提出一种基于区间运算的字典序多目标模型预测控制算法.对约束线性系统,结合字典序列法和滚动优化原理,建立按优先级定义的分层多目标模型预测控制策略.在此基础上,引入区间运算法则,在线求解预测控制量.通过一双容水箱单输入双输出液位控制,仿真验证了该方法的有效性.%Considering the prioritised multi-objectives control, a lexicographic multi-objectives model predictive control ( MPC) algorithm based on interval arithmetic was proposed. Regarding the constrained linear systems, the lexicographic programming and receding horizon principle were combined to derive a multi-layers multi-objectives MPC scheme in terms of the prioritization of objectives, and to calculate the predictive control actions online. Simulating the liquid-level control of two-tank with single input and double outputs illustrates the effectiveness of this method.
Directory of Open Access Journals (Sweden)
Rui eNouchi
2016-05-01
Full Text Available BackgroundPrevious reports have described that simple cognitive training using reading aloud and solving simple arithmetic calculations, so-called learning therapy, can improve executive functions and processing speed in the older adults. Nevertheless, it is not well-known whether learning therapy improve a wide range of cognitive functions or not. We investigated the beneficial effects of learning therapy on various cognitive functions in healthy older adults.MethodsWe used a single-blinded intervention with two groups (learning therapy group: LT and waiting list control group: WL. Sixty-four elderly were randomly assigned to LT or WL. In LT, participants performed reading Japanese aloud and solving simple calculations training tasks for 6 months. WL did not participate in the intervention. We measured several cognitive functions before and after 6 months intervention periods.ResultsCompared to WL, results revealed that LT improved inhibition performance in executive functions (Stroop: LT (Mean = 3.88 vs. WL (Mean = 1.22, adjusted p =.013 and reverse Stroop LT (Mean = 3.22 vs. WL (Mean = 1.59, adjusted p =.015, verbal episodic memory (logical memory: LT (Mean = 4.59 vs. WL (Mean = 2.47, adjusted p =.015, focus attention(D-CAT: LT (Mean = 2.09 vs. WL (Mean = -0.59, adjusted p =.010 and processing speed compared to the waiting list control group (digit symbol coding: LT (Mean = 5.00 vs. WL (Mean = 1.13, adjusted p =.015 and symbol search: LT (Mean = 3.47 vs. WL (Mean = 1.81, adjusted p =.014.DiscussionThis RCT can showed the benefit of learning therapy on inhibition of executive functions, verbal episodic memory, focus attention, and processing speed in healthy elderly people. Our results were discussed under overlapping hypothesis.Trial registrationThis trial was registered in The University Hospital Medical Information Network Clinical Trials Registry (UMIN000006998.
Directory of Open Access Journals (Sweden)
Nouchi Rui
2012-04-01
Full Text Available Abstract Background Almost all cognitive functions decline with age. Results of previous studies have shown that cognitive training related to everyday life (reading aloud and solving simple arithmetic calculations, namely learning therapy, can improve two cognitive function (executive functions and processing speed in elderly people. However, it remains unclear whether learning therapy engenders improvement of various cognitive functions or not. We investigate the impact of learning therapy on various cognitive functions (executive functions, episodic memory, short-term memory, working memory, attention, reading ability, and processing speed in healthy older adults. Methods We use a single-blinded intervention with two parallel groups (a learning therapy group and a waiting list control group. Testers are blind to the study hypothesis and the group membership of participants. Through an advertisement in local newspaper, 64 healthy older adults are recruited. They will be assigned randomly to a learning therapy group or a waiting list control group. In the learning therapy group, participants are required to perform two cognitive tasks for 6 months: reading Japanese aloud and solving simple calculations. The waiting list group does not participate in the intervention. The primary outcome measure is the Stroop test score: a measure of executive function. Secondary outcome measures are assessments including the following: verbal fluency task, logical memory, first and second names, digit span forward, digit span backward, Japanese reading test, digit cancellation task, digit symbol coding, and symbol search. We assess these outcome measures before and after the intervention. Discussion This report is the first study which investigates the beneficial effects of learning therapy on a wide range of cognitive functions of elderly people. Our study provides sufficient evidence of learning therapy effectiveness. Most cognitive functions, which are
Directory of Open Access Journals (Sweden)
Marcelo Chahon
2006-12-01
Full Text Available O presente trabalho propõe uma revisão do constructo psicológico de metacognição, especialmente enquanto habilidade utilizada em atividades de resolução de problemas e especificamente com relação a problemas aritméticos verbais. Procura-se evidenciar a complexidade dos modelos de desenvolvimento da competência em representar e resolver diferentes problemas envolvendo as quatro operações, ressaltando as implicações pedagógicas sugeridas por ampla literatura. Finalmente, conforme as idéias do Professor Franco Lo Presti Seminerio, é vislumbrada na metacognição um recurso psicopedagógico fundamental à aquisição de autonomia cognitiva pelo jovem aprendiz, cuja eficácia pôde ser observada em sucessivas intervenções experimentais conduzidas pelo Laboratório de Metacognição da UFRJ.The present work proposes a review of the psychological metacognition construct, specially as a skill used in problem solving activities, and specifically in relation to verbal arithmetic problems. It is here attempted to evidence the complexity of the development models regarding the competence in representing and solving different problems involving the four mathematical operations, emphasizing the pedagogical implications suggested by literature. In accordance to the ideas of Professor Franco Seminerio, metacognition is seen as a fundamental psychopedagogical resource to the acquisition of cognitive autonomy by the young apprentice, which effectiveness was observed in experimental interventions conducted by UFRJ Metacognition Laboratory.
Percentage of link load and its arithmetic of air-ground data link%地空数据链链路负载百分比及轮询方式下算法
Institute of Scientific and Technical Information of China (English)
刘明东; 毛玉泉; 高峥
2009-01-01
In the air-ground data link, command and control system sends a large amount of instruction and situation data to airplane. Because the transmissions speed of radio channel is limited, there would be a lot of instructions and situations overstocked in the ground command and control system. Some of these instructions and situations may be disabled because of overtime. It is necessary to adopt a measurement to denote the load and the busy state of the air-ground data link. The ground command and control system can take action to avoid instructions and situations overtime according to this measurement. Percentage of link load is adopted to denote the load and the busy state of the air-ground data link, and its arithmetic is designed.%地空数据链指挥控制系统要向飞机发送大量的指令和态势数据,而无线信道的传输速率有限,这就会有积攒未发出去的指令和态势由于超时而失效的问题.因此有必要引入一个表示数据链路负载状况和繁忙状况的量,使指控系统实时地了解链路的负载情况,采取相应措施.引入链路负载百分比来表示链路的负载和繁忙状况,以所发送的指令和态势不超时为标准,给出了链路负载的算法.
Institute of Scientific and Technical Information of China (English)
赵小见; 赵磊; 陈农
2013-01-01
The CLEAN arithmetic based on Spatial Source Coherence is developed and then applied to the wind tunnel test in the paper. The mechanism for this method is introducing a clean beam to instead the main lobe of beam picture iteratively, and getting rid of side lobe for background noise of wind tunnel or microphones distribution in phase array. The data from test in wind tunnel is optimized with this method. The results show that it improves the resolving power of low frequency noise and increases the signal-to-noise of the aero-acoustics test greatly. In the paper, coefficient K for judging the performance of phase array is also introduced, which including the effect to the resolving power both for frequency and distance from array to sound source plane. To some point, it is helpful to improve the efficiency for the coefficient K inducted.%发展应用了基于相干声源假设的CLEAN优化算法,该算法通过反复引入洁净波束来代替波束图上主瓣,逐步去掉由于背景噪声或者阵列阵元分布特点引入的旁瓣.用该算法对风洞实验结果进行了优化,提高了低频噪声的分辨率和试验的信噪比.还首次提出衡量相阵列声源分辨率的综合指标系数K,它综合反映了不同分析频率、不同阵列与声源平面距离对声源分辨率的影响,在一定程度上可以提高阵列设计的效率.
Energy Technology Data Exchange (ETDEWEB)
March, J.F.
2002-06-01
In order to measure the energy supplied by a solar thermal plant it is necessary to have a heat counter that is suitable for use with the glycol-water mixtures commonly used as thermal carriers in the collector circuit of solar plants. Funded by the Bundesstiftung Umwelt (Federal Foundation for the Environment) and the heat counter industry this project was dedicated to determining the measuring accuracy of throughflow sensors in heat counters operating in an industrially produced glycol-water mixture that is widely used in solar plants, consisting of 50% vol. TYFOCOR L (96% vol. propylene glycol, 4% vol. additives) and 50% vol. water. The only type found suitable for use in solar plants was the impeller counter. In this follow-up study 8 arithmetic units that are widely used in heat counters were examined for their suitability for use in solar thermal plants. [German] Zur Bestimmung der mit einer thermischen Solaranlage gewonnenen Energie werden Waermezaehler benoetigt, die fuer die in den Kollektorkreislaeufen von Solaranlagen ueblicherweise verwendeten Glykol-Wasser-Gemischen als Waermetraeger geeignet sind. In einem von der Deutschen Bundesstiftung Umwelt und von der Waermezaehlerindustrie unterstuetzten Vorhaben, wurde unter Verwendung eines industriell hergestellten und in solaren Anlagen weitverbreiteten Glykol-Wasser-Gemisches, bestehend aus 50 Vol.-% TYFOCOR L (96 Vol.-% Propylenglykol, 4 Vol.-% Additive) und 50 Vol.-% Wasser, die Messrichtigkeit von in Waermezaehlen verwendeten Durchflusssensortypen untersucht. Es erwiesen sich nur die Fluegelradzaehler fuer den Einsatz in Solaranlagen geeignet. In diesem weiterfuehrenden Bericht wurden acht haeufig verwendete Rechenwerke fuer Waermezaehler einer Untersuchung auf ihre Eignung in thermischen Solaranlagen unterzogen. (orig.)
Institute of Scientific and Technical Information of China (English)
文广; 巩明德
2012-01-01
Aiming at the problems about big impact feedback force and bad position tracking of parallel force feedback bilateral hydraulic servo control system, an improved parallel force sense bilateral servo control arithmetic was presented, in which the force error between the master's manipulative force and the slave's resistance was regarded as command signal to control the slave end, the position error was fed back to drive the master end. Valve-controlled hydraulic cylinder and force sensor were used to construct hydraulic servo controller and two-DOF bilateral servo control experimental system was built. The experimental results show that using the control method, the manipulative capability of the master-slave control system is improved. Manipulator can obtain true force tele-presence. It has the characteristics of control briefness, rapid constringency rate, good real-time.%针对并行机构的力反馈双向液压伺服控制中所存在的反馈力冲击大及位置跟随差的问题,提出一种以主、从手之间的力信号作为从动端控制信号,位置信号形成主手控制量的新型力觉反馈控制算法.应用阀控液压缸和力传感器构成液压力伺服控制器,构建力反馈双向伺服控制试验系统.在空载、抓轮胎和抓石块3种负载情况下,分别进行了力、位置跟随性能实验.实验结果表明:该力反馈控制方法既能保证从手对主手的位置跟随精度,又能使主手准确连续地跟随从手受力情况,明显改善了主-从控制系统的操纵性能,操作者能够获得真实的力觉临场感,提高了力反馈透明性.
Institute of Scientific and Technical Information of China (English)
张艳; 薛耀文
2016-01-01
In view of the multi-stage laundering money transfer path optimization decision problems,this paper proposes a multi-stage dynamic path planning model with the maximized amount of money-laundering and minimized risk as the decisionmaking goal on the condition of time pressure.Furthermore,this paper also puts forward an algorithm of solving the model by using the theory of multiple dynamic programming method and the maximum flow algorithm.Finally,the feasibility of the arithmetic has been proved by an example of the algorithm.This model can not only find the characteristic of money laundering behavior from laundering money transfer path,but also discover and track money laundering trails and the entire process,contributing to monitoring effectively all aspects of the money laundering process and reducing the cost of money laundering detection.%针对多阶段洗钱资金转移路径的决策问题,基于多目标优化的思想,构建了以时间约束、总体资金转移量尽可能大以及总体风险尽可能小为决策目标的多阶段洗钱路径优化模型,并利用多重动态规划方法和最大流理论给出了求解该模型的算法,最后通过实例应用验证了该算法的可行性.通过该模型,不仅能够从洗钱资金转移路径观察洗钱行为特征,还能够发现和追踪到洗钱者的洗钱踪迹和全过程,有助于对洗钱行为的各个环节进行有效监控,降低反洗钱侦测成本.
Institute of Scientific and Technical Information of China (English)
邱静; 查静; 雷飞
2012-01-01
该文拟利用被动复合式下向通风降温技术在过渡季节对武汉某高校报告厅室内热环境进行研究,首先根据武汉市气候条件确定过渡季节该报告厅的室内外设计参数,然后通过理论计算确定报告厅采用该技术通风降温的可行性,最后利用计算流体力学( CFD)软件Airpak对过渡季节室内气流组织进行模拟和分析,验证该设计方案的通风效果.由于报告厅进深较大,为了保证其室内温度和风速分布均匀,该文分别对单向和双向两种送排风方案进行了比较研究,结果证明该系统能够替代常规空调解决武汉地区过渡季节利用自然冷源对报告厅的通风降温,不仅节约了能源,还改善了室内空气品质.%Passive hybrid downdraught cooling technique is supposed to be used in a schematic design of university auditorium in Wuhan transition season . Firstly the indoor and outdoor design parameter is set; Secondly the feasibility of using PHDC technique is discussed according to theoretical arithmetic; Lastly, according to Airpak CFD simulation and analysis, the indoor ventilation effect is checked. Because the auditorium is deep-plan , single-sided and double-sided ventilation schemes were compared in this study in order to get evenness index of the indoor temperature and wind velocity . The result proves that PHDC system can replace conventional air-conditionings to solve auditoriums ventilation by using natural cold source during transition season in Wuhan.Not only can energy be saved, but also can indoor air quality be improved.
Institute of Scientific and Technical Information of China (English)
唐衍伟; 陈刚; 刘喜华
2014-01-01
The continuous liquidation trajectory of the single hedged stock is derived under the arithmetic Brownian movements,mean-variance utility,and linear market impact. The parameters analysis shows that the investors are like to liquidate quickly if they are more risk averse or the portfolio ’s variance is larger;if the correlation coefficient is negative,they want to execute more quickly and vice versa;the liquidation velocity changes are opposite to that of the correlation coefficient under the given hedging ratio. The partial liquida-tion’s trajectory is more convex than the full liquidation’s. Sometimes,the investors would over liquidate firstly and then recover the position.%假定股票和期货服从算术布朗运动，投资者效用为均值—方差形式，价格冲击为线性，在连续时间框架下，求解单只股票与股指期货套期保值不完全变现的同步出清问题，得到出清轨迹。参数分析表明：当风险厌恶程度较大、组合标准差越大时，投资者倾向于在出清初期出清较大规模的头寸，以降低后期的风险；当ρ＜0，随套期保值比的增加，投资者更倾向于快速的出清过程，当ρ＞0则相反；在给定套期保值比的情况下，出清速率与相关系数呈反向变化。不完全变现比完全变现的出清轨迹更向下凸，而且可能会出现提前完成出清的情况发生。
Institute of Scientific and Technical Information of China (English)
庞春雷; 赵修斌; 余永林; 宋立梅; 王祝欣
2014-01-01
The low-accuracy strapdown inertial navigation system’(SINS) heading angle can not be achieved in the process of initial alignment,also the GPS direction finding with two antennas requires a long time for initialization.As to that,a new arithmetic is proposed in order to acquire the heading angle faster:the heading angle of the baseline is fixed quickly assisted by the baseline length in the condition of the least square error by searching the attitude;also the attitude is confined by elevation information from SINS’ initial alignment.Then the heading angle is used in the SINS’initial attitude.The model is established,the principle of the new algorithm is discussed,and then some correlative expressions are induced.Experiments indicate that the new method proves proper and credible with simple algorithm and high practicability.The error is no more than 0.2°in pitch precision and yaw precision within 30 sec and initial alignment is accomplished within 100 sec.%针对低精度捷联惯性导航系统无法实现航向角的自对准和全球定位系统双天线测向需要较长时间的初始化问题,研究了二者互相辅助的新算法.即利用 SINS初始对准时的俯仰角信息和已知基线长度进行约束,通过搜索基线姿态角,在二次残差最小的条件下快速确定基线航向角,然后利用该航向角辅助SINS的快速初始对准.建立了互辅算法模型,论述了互辅原理,推导了相关公式.通过实验比较,验证了新算法的正确性及可靠性,30 s内得到了0.2°的俯仰角和航向角误差,100 s内实现了低精度 SINS的初始对准,且算法简单,实用性强.
A New Approach to Fuzzy Arithmetic
Popov, Antony
2010-01-01
This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncerta...
Algebra and Arithmetic of Modular Forms
DEFF Research Database (Denmark)
Rustom, Nadim
In [Rus14b] and [Rus14a], we study graded rings of modular forms over congruence subgroups, with coefficients in subrings A of C, and determine bounds of the weights of modular forms constituting a minimal set of generators, as well as on the degree of the generators of the ideal of relations bet...
Arithmetic Operations on Trapezoidal Fuzzy Numbers
Directory of Open Access Journals (Sweden)
J. Vahidi
2013-10-01
Full Text Available In this paper, several new algebraic mathematics for positive fuzzy numbers of type $(\\overline{a}, \\overline{\\overline{a}}, \\overline{\\overline{\\overline{a}}}, \\overline{\\overline{\\overline{\\overline{a}}}}$ are devised and do not need the computation of $\\alpha$-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type $(\\overline{a}, \\overline{\\overline{a}}, \\overline{\\overline{\\overline{a}}}, \\overline{\\overline{\\overline{\\overline{a}}}}$ are obtained using the basic analytical principles of algebraic mathematics and Taylor series expansion. At the end, Various numerical examples are also solved to demonstrate the use of contrived expressions.
Recursion in second order bounded arithmetic
Castro, Rodrigo
2010-01-01
Se muestra que algunos esquemas recursivos pueden ser ejecutados en las teorías U2i ( i ≥1) de aritmética acotada de segundo orden introducidas por S. Buss. En particular, se demuestra que la clase de las funciones ∑ 11,b - definibles en U2i es cerrada bajo recursión acotada, o, equivalentemente, que U2i puede ∑11,b - definir E2, la segunda clase de Grzegorczyk .
Substitutions in dynamics, arithmetics and combinatorics
Berthé, Valéré; Ferenczi, Sébastien; Mauduit, Christian; Siegel, Anne
2002-01-01
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.
Counting and Arithmetic of the Inca
Directory of Open Access Journals (Sweden)
Ximena Catepillán
2012-01-01
Full Text Available El Imperio Inca ¿ el imperio pre-Colombino más grande del continente Americano ¿ se extendió desde Ecuador hasta Chile central por más de cinco mil millas. La capital fue Cuzco, la que fue establecida en las Alturas de los Andes Peruanos. Esta civilización altamente avanzada desarrolló un sistema contable para organizar el imperio ¿ en particular, para construir una red de caminos de 14.000 millas y una arquitectura monumental. Algunos de los algoritmos que se creen haber sido usados por los Inca para hacer cálculos fue la "yupana". Este antiguo artefacto de cálculo será presentado, entre otras actividades del curso "Matemáticas en Culturas No-Europeas" para estudiantes de todas las áreas de concentración, excepto Matemáticas y Ciencia, ofrecido en la Universidad de Millersville en Pennsylvania.
QArith: Coq Formalisation of Lazy Rational Arithmetic
Niqui, Milad; Bertot, Yves
2003-01-01
In this paper we present the formalisation of the library which is an implementation of rational numbers as binary sequences for both lazy and strict computation. We use the representation also known as the Stern-Brocot representation for rational numbers. This formalisation uses advanced machinery of the theorem prover and applies recent developments in formalising general recursive functions. This formalisation highlights the rôle of type theory both as a tool to verify hand-written program...
Imprecise Arithmetic for Low Power Image Processing
DEFF Research Database (Denmark)
Albicocco, Pietro; Cardarilli, Gian Carlo; Nannarelli, Alberto;
2012-01-01
Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, additio...... and multiplication, in an imprecise manner by simplifying the hardware implementation. With the proposed ”sloppy” operations, we obtain a reduction in delay, area and power dissipation, and the error introduced is still acceptable for applications such as image processing.......Sometimes reducing the precision of a numerical processor, by introducing errors, can lead to significant performance (delay, area and power dissipation) improvements without compromising the overall quality of the processing. In this work, we show how to perform the two basic operations, addition...
Experimental Number Theory, Part I : Tower Arithmetic
Gnang, Edinah K.
2011-01-01
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here refer to as towers. The bijection between numbers and towers provides some insights into unexpected connexions between Number theory, combinatorics and discrete probability theory.
Arithmetic Deformation Theory of Lie Algebras
Rastegar, Arash
2012-01-01
This paper is devoted to deformation theory of graded Lie algebras over $\\Z$ or $\\Z_l$ with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artin local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations. In the second part, we use a version of Schlessinger criteria for functors on the Artinian cat...
Travelling Mathematics - The Fate of Diophantos' Arithmetic
Meskens, Ad
2010-01-01
In this book the author presents a comprehensive study of Diophantos' monumental work known as "Arithmetika", a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing. Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined. Of Arithmetika's 13 books only 6 survi
Essential Incompleteness of Arithmetic Verified by Coq
O'Connor, Russell
2005-01-01
A constructive proof of the Goedel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural numbers, and functions operating on these codes are proved to be primitive recursive. The weak axiom sys...
Fractal surfaces from simple arithmetic operations
García-Morales, Vladimir
2016-04-01
Fractal surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all deterministic bitwise operations on a finite alphabet. It is shown that these models give rise to a roughness exponent H that shapes the resulting spatial patterns, larger values of the exponent leading to coarser surfaces.
Phonon arithmetic in a trapped ion system
Um, Mark; Zhang, Junhua; Lv, Dingshun; Lu, Yao; An, Shuoming; Zhang, Jing-Ning; Nha, Hyunchul; Kim, M. S.; Kim, Kihwan
2016-04-01
Single-quantum level operations are important tools to manipulate a quantum state. Annihilation or creation of single particles translates a quantum state to another by adding or subtracting a particle, depending on how many are already in the given state. The operations are probabilistic and the success rate has yet been low in their experimental realization. Here we experimentally demonstrate (near) deterministic addition and subtraction of a bosonic particle, in particular a phonon of ionic motion in a harmonic potential. We realize the operations by coupling phonons to an auxiliary two-level system and applying transitionless adiabatic passage. We show handy repetition of the operations on various initial states and demonstrate by the reconstruction of the density matrices that the operations preserve coherences. We observe the transformation of a classical state to a highly non-classical one and a Gaussian state to a non-Gaussian one by applying a sequence of operations deterministically.
Institute of Scientific and Technical Information of China (English)
汪维; 刘瑞朝; 吴飚; 周朝阳
2015-01-01
The blast waves parameters in venting area are important in damage assessment of building structures under internal blast.Once the blast waves parameters are certain,the damage level of structures and equipments near the venting area can be assessed.As internal blast wave is the superposition of multi-reflectied waves of initial blast by the inner surfaces of building structure,and the blast waves in venting area is not of the same character as free air blast waves,the traditional engineering arithmetic for blast waves parameters in venting area is not yet applicable.In the paper, based on dimensional analysis,the relationship between venting area blast wave parameters and different structure parameters was analyzed.Then the internal blast shock wave of building structure was simulated by using AUTODYN software.The evolutionary process of internal blast wave was investigated and the blast pressure wave profile in venting area was analyzed.Based on a large number of numerical simulations,the empirical equations for venting area shock waves parameters were summarized,and they can be used as the base of damage assessment of internal building blast.%建筑物内部爆炸泄压口冲击波参数的确定对于建筑物结构毁伤评估具有重要的作用，一旦泄压口冲击波参数确定以后，即可利用相应毁伤判据快速评估泄压口附近结构和设备的毁伤程度。由于内部爆炸波是初始爆炸波经过建筑物内壁面多次反射叠加作用的结果，在泄压口会形成不同于自由场的冲击波，目前还未有泄压口冲击波参数成熟的快速工程算法。为了分析泄压口冲击波参数、总结相应快速经验工程算法，在量纲分析的基础上，提出影响泄压口冲击波峰值压力和冲量相关的无量纲参数。然后利用首先利用 AUTODYN 软件数值仿真研究了特定当量内爆炸作用下冲击波形成的过程，分析了泄压口部冲击波压力波形，并研究了泄压
Institute of Scientific and Technical Information of China (English)
陈楠; 文习山; 蓝磊; 黄玲; 王羽; 杜华珠; 李晔
2011-01-01
输电导线弧垂是导线运行的重要参数,影响电网的安全稳定运行.为实现导线弧垂的准确监测,提出基于导线工频电场(powerfrequency electrical field,PFEF)逆运算的弧垂计算方法.首先根据悬链线方程,基于有限长线电荷建立导线工频电场的三维计算模型.然后根据导线下方工频电场的实时测量数据,在三维电场模型下利用遗传算法(genetic algorithm,GA)反演得到导线的最大弧垂.考虑电场测量数据受外界环境因素和测量条件的影响,采用最小二乘支持向量机(least squares support vector machine,LS-SVM)建立导线原始测量数据的环境因素修正模型,使修正后的测量数据逼近理想条件下的数据.将修正后的电场测量值作为反演模型的目标参考值,进一步提高弧垂的计算精度.对比银川地区某条典型输电导线的测量数据,验证了该算法的有效性.%The sag of transmission line, which influences the security and stability of power grid operation, is an important parameter in power systems. In order to monitor the sag of transmission line accurately, a novel calculation method for line sag based on power frequency electrical field (PFEF) inverse algorithm was presented. At first, a three-dimensional PFEF calculation model was established according to the finite slant charge method, in which the transmission line was expressed with the catenary equation. Then, according to the PFEF measured under the transmission line, the line sag was inverted with the help of genetic algorithm (GA) under the PFEF positive-going arithmetic model presented. Considering the impact of weather and survey condition for the measured data, a revised model based on least squares support vector machine (LS-SVM) was set up. With this model, the effect of outer factor to the measured data was reduced, and the modified measured data approached the ideal value. Since the revised measured data were used as the reference target
Directory of Open Access Journals (Sweden)
Verônica Bender Haydu
2006-01-01
Full Text Available O paradigma da equivalência de estímulos tem sido usado para o desenvolvimento de diversos procedimentos aplicáveis ao ensino de leitura, escrita e aritmética. O objetivo do presente estudo foi o de investigar o efeito do ensino de relações de equivalência entre três formas de apresentação de problemas aritméticos de adição sobre o comportamento de resolver problemas. Sete alunos da 1ª série do ensino fundamental foram submetidos a um pré-teste e pós-teste com problemas de adição impressos nas formas de balança (A, operação (B e sentença lingüística (C. O treino de equivalência de estímulos estabeleceu relações entre A-B e A-C. Seis dos sete participantes responderam de acordo com as classes estabelecidas. O desempenho dos participantes no pós-teste foi superior ao apresentado no pré-teste. Conclui-se que o estabelecimento de relações de equivalência entre problemas aritméticos de adição em forma de balança, operação e sentença lingüística melhorou o desempenho na resolução problemas desses tipos.The equivalence paradigm has been applied to the development of a variety of procedures applied to teach reading, writing and arithmetic. This work aimed to investigate the effect of teaching stimulus equivalence relations between three different forms of arithmetic sum problems on problem-solving behavior. Seven first grade students of Fundamental Schooling (=Elementary Schooling were submitted to a pre-test, and a post-test with sum problems printed in the form of slave (A, operations (B and word problems (C. The conditional discrimination procedure established relations between A-B and A-C. Six of seven participants responded accordingly to the established classes. The performance of the participants in the post-test was higher than in the pre-test. It was concluded that the establishment of equivalence relations between arithmetic sum problems in the form of slave, operations, and word problems enhanced
Directory of Open Access Journals (Sweden)
David Antonio da Costa, Brasil
2014-01-01
Full Text Available Este artigo aborda as concepções relacionadas ao ensino de Aritmética de Pestalozzi, Grube, Parker e Dewey. Tais concepções perpassaram os tempos e deixaram vestígios nos livros didáticos utilizados. Focalizar a investigação no conceito de número presente nos livros didáticos revela importantes contribuições destes autores na constituição da Aritmética como disciplina escolar no Brasil.Palavras-chave: aritmética, número, livro didático. THE CONCEPTIONS AND CONTRIBUTIONS OF PESTALOZZI, GRUBE, PARKER AND DEWEY FOR TEACHING ARITHMETIC IN ELEMENTARY LEVEL: THE CONCEPT OF NUMBER AbstractThis article discusses the concepts related to teaching arithmetic of Pestalozzi, Grube, Parker and Dewey. These concepts permeate time and leave traces in the textbooks used. Focusing research on the concept of number present in textbooks reveals important contributions of these authors in the constitution of Arithmetic as school subject inBrazil.Key-words: arithmetic, number, textbook. LAS CONCEPCIONES Y CONTRIBUCIONES DE PESTALOZZI, GRUBE, PARKER Y DEWEY PARA La ENSEÑANZA DE LA ARITMÉTICA EN EL NIVEL ELEMENTAL: EL CONCEPTO DE NÚMERO ResumenEste artículo aborda los conceptos relacionados con la enseñanza de la aritmética de Pestalozzi, Grube, Parker y Dewey. Estos conceptos impregnan tiempo y dejan huellas en los libros de texto utilizados. Investigación que se centra en el concepto de número presente en los libros de texto revela importantes contribuciones de estos autores en la constitución de la aritmética como asignatura escolar en Brasil.Palabras-clave: aritmética, número, libro de texto. LES CONCEPTIONS ET CONTRIBUTIONS DE PESTALOZZI, GRUBE, PARKER Et DEWEY POUR L'ENSEIGNEMENT DE L'ARITHMÉTIQUE DANS LE NIVEAU ÉLÉMENTAIRE: LE CONCEPT DE NOMBRERésuméCet article présente les concepts liés à l'enseignement de l'arithmétique de Pestalozzi, Grube, Parker et Dewey. Ces concepts imprègnent temps et laissent des traces
Directory of Open Access Journals (Sweden)
Wagner Rodrigues Valente, Brasil
2014-09-01
Full Text Available O texto analisa a produção e a circulação de material utilizado para o ensino de Aritmética que ficou conhecido com o nome de Cartas, Mapas ou Quadros de Parker. O material teve circulação durante toda a primeira metade do século 20. A análise realizada mostra o papel de Lourenço Filho na longa permanência deste dispositivo de ensino, transformado em ícone da pedagogia moderna da matemática na escola primária.Palavras-chave: história da educação matemática, pedagogia intuitiva da aritmética, Lourenço Filho, Cartas de Parker. LOURENÇO FILHO AND MODERN TEACHING ARITHMETIC: PRODUCTION AND CIRCULATION OF A MODEL EDUCATIONALAbstractThe text examines the production and circulation of material used for teaching arithmetic which became known by the name of Tables, Maps and Charts Parker. The material was outstanding during the entire first half of the twentieth century. The analysis shows the role of Lourenço Filho long stay in this teaching device, transformed into an icon of modern pedagogy of mathematics in primary school.Key-words: history of mathematics education, object lessons of arithmetic, Lourenço Filho, Tables Parker.LOURENÇO FILHO Y LA FORMA MODERNA DE LA ENSEÑANZA DE ARITMÉTICA: PRODUCCIÓN Y DISTRIBUCIÓN DE UN MODELO EDUCATIVO ResumenEl texto tiene como objetivo analizar la producción y circulación de material utilizado para la enseñanza de la aritmética que se conoció con el nombre de tablas, mapas y gráficos Parker. El material fue excelente durante toda la primera mitad del siglo 20. El análisis pone de manifiesto el papel de Lourenço Filho como responsable de la larga persistencia de este dispositivo de enseñanza, convertido en un icono de la pedagogía moderna de las matemáticas en la escuela primaria.Palabras-clave: historia de la enseñanza de las matemáticas, pedagogía aritmética intuitiva, Lourenço Filho, Tablas Parker. LOURENÇO FILHO ET L'ENSEIGNEMENT MODERNE DU CALCUL: PRODUCTION ET
Directory of Open Access Journals (Sweden)
Lucimar M.F. de Carvalho
2008-06-01
Full Text Available OBJECTIVE: To investigate different fuzzy arithmetical operations to support in the diagnostic of epileptic events and non epileptic events. METHOD: A neuro-fuzzy system was developed using the NEFCLASS (NEuro Fuzzy CLASSIfication architecture and an artificial neural network with backpropagation learning algorithm (ANNB. RESULTS: The study was composed by 244 patients with a bigger frequency of the feminine sex. The number of right decisions at the test phase, obtained by the NEFCLASS and ANNB was 83.60% and 90.16%, respectively. The best sensibility result was attained by NEFCLASS (84.90%; the best specificity result were attained by ANNB with 95.65%. CONCLUSION: The proposed neuro-fuzzy system combined the artificial neural network capabilities in the pattern classifications together with the fuzzy logic qualitative approach, leading to a bigger rate of system success.OBJETIVO: Investigar diferentes operações aritméticas difusas para auxíliar no diagnóstico de eventos epilépticos e eventos não-epilépticos. MÉTODO: Um sistema neuro-difuso foi desenvolvido utilizando a arquitetura NEFCLASS (NEuro Fuzzy CLASSIfication e uma rede neural artificial com o algoritmo de aprendizagem backpropagation (RNAB. RESULTADOS: A amostra estudada foi de 244 pacientes com maior freqüência no sexo feminino. O número de decisões corretas na fase de teste, obtidas através do NEFCLASS e RNAB foi de 83,60% e 90,16%, respectivamente. O melhor resultado de sensibilidade foi obtido com o NEFCLASS (84,90%; o melhor resultado de especificidade foi obtido com a RNAB (95,65%. CONCLUSÃO: O sistema neuro-difuso proposto combinou a capacidade das redes neurais artificiais na classificação de padrões juntamente com a abordagem qualitativa da logica difusa, levando a maior taxa de acertos do sistema.
Institute of Scientific and Technical Information of China (English)
章勤琼; 徐文彬; Max Stephens
2011-01-01
中国与澳大利亚最新的国家数学课程标准都特别强调数与代数学习衔接的重要性。运用问卷，从以下四个方面分析、比较中澳两国数学教师在这一。问题上的辛学能力：相关数学知识，对数学课程标准理念的解读，对学生数学思考的理解，寅期与长期的教学计划。结果表明，中澳数学教师在总体能力上水平相近，中国教少对于数学知识的理解更为清晰，而澳大利亚教师则在对学生数学思考的理解上表劫得更好。与此同时，在推行国家数学课程标准时，教师教学能力是一个不容忽视的关键因素%Closer connection between the learning of number and algebra has been Valued in new nationalmathematics curriculum in both China and Australia. This exploratory study seeks to characterise teachers＇ capacity to help students corm ect arithmetic learning and emerging algebraic thinking. The study is based on questionnaire given to Australian and Chinese teachers, comprising seven students＇ Solutions of subtraction sentences. Teachers＇ responses to the questionnaire were analysed in terms of four categories, knowledge of mathematics, interpretation of the intentions of the official curriculum documents, understanding of students＇ thinking, and capacity to design appropriate instruction in the short and long term. These four categories form the basis of our construct of teacher capacity. We argue finally that teacher capacity should be regarded as a key element in the developnvent and implementation of National Curriculum in Mathematics in both countries.
Directory of Open Access Journals (Sweden)
Cesar Galera
2003-01-01
Full Text Available Foram realizados dois experimentos para avaliar a natureza da informação armazenada pelo sistema de memória visuo-espacial a curto prazo. No primeiro experimento, uma tarefa de localização espacial foi realizada simultaneamente com tarefas intervenientes de supressão articulatória e de subtração aritmética. A tarefa de supressão articulatória afeta de forma negativa a recordação das letras, mas não a dos padrões visuais. Apesar disso, a recordação das letras se mantém superior à recordação dos padrões visuais. Este resultado sugere que o armazenamento dos padrões visuais não utiliza o laço fonológico, e que a tarefa de supressão articulatória, embora iniba o uso do laço fonológico, pode não inibir o acesso à informação semântica. No segundo experimento estabelecemos o efeito da similaridade visual sobre a capacidade de recordação da posição espacial. Os resultados confirmam o uso de códigos visuais e sugerem que a capacidade de armazenamento de estímulos visuais é limitada, mas não se restringe ao efeito de recência.We investigated the nature of the information stored in visuo-spatial short-term memory in two experiments. In the first experiment, a spatial localization task was performed simultaneously with articulatory suppression and arithmetical subtraction tasks. The articulatory suppression has a negative effect on the performance with letters, but not with visual patterns. Despite that, the recall of the letters is better than the recall of the visual patterns. This result suggests that the storage of the visual patterns does not use the phonological loop, and that the articulatory suppression, even if it inhibits the use of the phonological loop, cannot inhibit the access to the semantic information. In the second experiment we established the effect of the visual similarity on the capacity of memory for the spatial position. The results confirm the use of visual codes and suggest that the
Mental Arithmetic Activates Analogic Representations of Internally Generated Sums
Kallai, Arava Y.; Schunn, Christian D.; Fiez, Julie A.
2012-01-01
The internal representation of numbers generated during calculation has received little attention. Much of the mathematics learning literature focuses on symbolic retrieval of math facts; in contrast, we critically test the hypothesis that internally generated numbers are represented analogically, using an approximate number system. In an fMRI…
Arithmetic progressions that consist only of reduced residues
Directory of Open Access Journals (Sweden)
Paul A. Tanner III
2001-01-01
progressions of w reduced residues modulo m; the number of the same with first term n; the number of the same with mean n; the number of the same with common difference n. With m and odd w fixed, the values of the first two of the last three functions are fixed and equal for all n relatively prime to m; other similar relations exist among these three functions.
The Distribution of Hardy-Littlewood Numbers in Arithmetic Progressions
Rakhmonov, Z. Kh
1990-02-01
An asymptotic formula is obtained for the number of solutions of the congruence \\displaystyle p+n^2\\equiv l\\ (\\operatorname{mod}D),\\qquad p\\leqslant x,\\quad n\\leqslant\\sqrt x,\\quad(l,D)=1, where D is a sufficiently large prime. Bibliography: 7 titles.