Fast Fuzzy Arithmetic Operations
Hampton, Michael; Kosheleva, Olga
1997-01-01
In engineering applications of fuzzy logic, the main goal is not to simulate the way the experts really think, but to come up with a good engineering solution that would (ideally) be better than the expert's control, In such applications, it makes perfect sense to restrict ourselves to simplified approximate expressions for membership functions. If we need to perform arithmetic operations with the resulting fuzzy numbers, then we can use simple and fast algorithms that are known for operations with simple membership functions. In other applications, especially the ones that are related to humanities, simulating experts is one of the main goals. In such applications, we must use membership functions that capture every nuance of the expert's opinion; these functions are therefore complicated, and fuzzy arithmetic operations with the corresponding fuzzy numbers become a computational problem. In this paper, we design a new algorithm for performing such operations. This algorithm is applicable in the case when negative logarithms - log(u(x)) of membership functions u(x) are convex, and reduces computation time from O(n(exp 2))to O(n log(n)) (where n is the number of points x at which we know the membership functions u(x)).
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...
Genetic Programming with Smooth Operators for Arithmetic Expressions
DEFF Research Database (Denmark)
Ursem, Rasmus Kjær; Krink, Thiemo
This paper introduces the smooth operators for arithmetic expressions as an approach to smoothening the search space in Genetic Programming (GP). Smooth operator GP interpolates between arithmetic operators such as * and /, thereby allowing a gradual adaptation to the problem. The suggested...
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 ...
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...
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.
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.
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.
Independence of basic arithmetic operations: evidence from cognitive neuropsychology
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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.
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.
Chapman, Olive
2007-01-01
Mathematical tasks, centered on arithmetic word problems, are discussed as the basis of an approach to facilitate preservice elementary teachers' development of mathematical knowledge for teaching arithmetic operations. The approach consists of three groups of tasks that allow students to reflect on their initial knowledge, explore arithmetic word…
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...
Evaluating the Main Battle Tank Using Fuzzy Number Arithmetic Operations
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Deng Yong
2006-04-01
Full Text Available Since the descriptions and judgements on weapon systems are usually linguistic and fuzzy,it is more realistic to evaluate weapon systems in the framework of fuzzy sets theory. In thispaper, a new method to evaluate the best main battle tank is proposed. It can be seen that theproposed method is more efficient due to the fact that, by canonical representation of arithmeticoperation on fuzzy numbers, simple arithmetic operations on crisp numbers are used, instead ofcomplicated fuzzy numbers operations. In addition, the final scores of each alternative can berepresented as crisp numbers. As a result, the order of alternatives can be determined withoutthe procedure of ranking fuzzy numbers. Finally, a numerical example to evaluate the best mainbattle tanks is used to illustrate the efficiency of the proposed method.
Understanding and Using Principles of Arithmetic: Operations Involving Negative Numbers
Prather, Richard W.; Alibali, Martha W.
2008-01-01
Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…
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 ...
Arithmetic Operations and Factorization using Asynchronous P Systems
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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}
Data Encryption and Decryption Algorithm Using Hamming Code and Arithmetic Operations
Kurapati Sundar Teja; Shanmukha Mallikarjuna Bandaru
2015-01-01
This paper explains the implementation of data encryption and decryption algorithm using hamming code and arithmetic operations with the help of Verilog HDL. As the days are passing the old algorithms are not remained so strong cryptanalyst are familiar with them. Hamming code is one of forward error correcting code which has got many applications. In this paper hamming code algorithm was discussed and the implementation of it was done with arithmetic operations. For high security...
Operation-Specific Encoding in Single-Digit Arithmetic
Zhou, Xinlin
2011-01-01
Solving simple arithmetic problems involves three stages: encoding the problem, retrieving or calculating the answer, and reporting the answer. This study compared the event-related potentials elicited by single-digit addition and multiplication problems to examine the relationship between encoding and retrieval/calculation stages. Results showed…
Data Encryption and Decryption Algorithm Using Hamming Code and Arithmetic Operations
Directory of Open Access Journals (Sweden)
Kurapati Sundar Teja
2015-08-01
Full Text Available This paper explains the implementation of data encryption and decryption algorithm using hamming code and arithmetic operations with the help of Verilog HDL. As the days are passing the old algorithms are not remained so strong cryptanalyst are familiar with them. Hamming code is one of forward error correcting code which has got many applications. In this paper hamming code algorithm was discussed and the implementation of it was done with arithmetic operations. For high security some arithmetic operations are added with hamming code process. A 3-bit data will be encrypted as 14-bit and using decryption process again we will receives 3-bit original data. The implemented design was tested on Spartan3A FPGA kit.
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)
Purpura, David J.; Lonigan, Christopher J.
2013-01-01
Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining…
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
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...
A Modern Advanced Hill Cipher Involving a Permuted Key and Modular Arithmetic Addition Operation
Directory of Open Access Journals (Sweden)
V.U.K. Sastry
2011-05-01
Full Text Available In this paper we have devoted our attention to the study of a block cipher by generalizing advanced Hill cipher by including a permuted key. In this analysis we find that the iteration process, the mix operation and the modular arithmetic operation involved in the cipher mixes the binary bits of the key and the plaintext in a thorough manner. The avalanche effect and the cryptanalysis markedly indicate that the cipher is a strong one.
Operator priming and generalization of practice in adults' simple arithmetic.
Chen, Yalin; Campbell, Jamie I D
2016-04-01
There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication, suggesting that a general addition procedure was primed by the + sign. In Experiment 1 (n = 36), we applied this operator-priming paradigm to rule-based problems (0 + N = N, 1 × N = N, 0 × N = 0) and 1 + N problems with N ranging from 0 to 9. For the rule-based problems, we found both operator-preview facilitation and generalization of practice (e.g., practicing 0 + 3 sped up unpracticed 0 + 8), the latter being a signature of procedure use; however, we also found operator-preview facilitation for 1 + N in the absence of generalization, which implies the 1 + N problems were solved by fact retrieval but nonetheless were facilitated by an operator preview. Thus, the operator preview effect does not discriminate procedure use from fact retrieval. Experiment 2 (n = 36) investigated whether a population with advanced mathematical training-engineering and computer science students-would show generalization of practice for nonrule-based simple addition problems (e.g., 1 + 4, 4 + 7). The 0 + N problems again presented generalization, whereas no nonzero problem type did; but all nonzero problems sped up when the identical problems were retested, as predicted by item-specific fact retrieval. The results pose a strong challenge to the generality of the proposal that skilled adults' simple addition is based on fast procedural algorithms, and instead support a fact-retrieval model of fast addition performance. (PsycINFO Database Record PMID:26461035
Introduction to Projective Arithmetics
Burgin, Mark
2010-01-01
Science and mathematics help people to better understand world, eliminating many inconsistencies, fallacies and misconceptions. One of such misconceptions is related to arithmetic of natural numbers, which is extremely important both for science and everyday life. People think their counting is governed by the rules of the conventional arithmetic and thus other kinds of arithmetics of natural numbers do not exist and cannot exist. However, this popular image of the situation with the natural numbers is wrong. In many situations, people have to utilize and do implicitly utilize rules of counting and operating different from rules and operations in the conventional arithmetic. This is a consequence of the existing diversity in nature and society. To correctly represent this diversity, people have to explicitly employ different arithmetics. To make a distinction, we call the conventional arithmetic by the name Diophantine arithmetic, while other arithmetics are called non-Diophantine. There are two big families ...
Bruno, Adriano; Yasaki, Dan
2008-01-01
The arithmetic of the natural numbers can be extended to arithmetic operations on planar binary trees. This gives rise to a non-commutative arithmetic theory. In this exposition, we describe this arithmetree, first defined by Loday, and investigate prime trees.
All-Optical Logic and Arithmetic Operation using Soliton Control for Tree Architecture Use
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S. Mitatha
2012-01-01
Full Text Available This study has proposed a new design system for basic all-optical logic and arithmetic operation using dark-bright soliton conversion control base on tree architecture. Optical tree architecture and nonlinear materials can provide a significant role for contribution in optical interconnecting network and ultrafast photonic computing system. In operation, the input data for all-optical binary logic can be formed by dark and bright soliton pulses for logic ‘0’ and ‘1’, respectively. By using the dark-bright soliton conversion behaviors, the conversion between dark and bright soliton pulses can be obtained and formed the logic pulse by a π/2 phase shifted device (i.e., an optical coupler. In application, the proposed scheme can be recognized as a simple and flexible system for forming the logic switching system, which can be used for advanced logical system.
Implementation of Arithmetic Operations With Time-Free Spiking Neural P Systems.
Liu, Xiangrong; Li, Ziming; Liu, Juan; Liu, Logan; Zeng, Xiangxiang
2015-09-01
Spiking neural P systems (SN P systems) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In most applications of SN P systems, synchronization plays a key role which means the execution of a rule is completed in exactly one time unit (one step). However, such synchronization does not coincide with the biological fact: in biological nervous systems, the execution times of spiking rules cannot be known exactly. Therefore, a "realistic" system called time-free SN P systems were proposed, where the precise execution time of rules is removed. In this paper, we consider building arithmetical operation systems based on time-free SN P systems. Specifically, adder, subtracter, multiplier, and divider are constructed by using time-free SN P systems. The obtained systems always produce the same computation result independently from the execution time of the rules. PMID:26335555
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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.
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…
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.
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.
Sullivan, Margaret A.
2008-01-01
This thesis examines two problems in on-board computing for space vehicles and develops rules for applying Reduced Precision Redundancy (RPR) as a new method of fault tolerance in Field Programmable Gate Arrays against Single Event Effects due to radiation on orbit. RPR was discovered by Snodgrass in 2006 and was first demonstrated using the single-input CORDIC algorithm. This research applies RPR to elementary multiple-input arithmetic operations (addition, subtraction, multiplication, divi...
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...... 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....... 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...
Conceptual Knowledge of Fraction Arithmetic
Siegler, Robert S.; Lortie-Forgues, Hugues
2015-01-01
Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…
Guthormsen, Amy M; Fisher, Kristie J; Bassok, Miriam; Osterhout, Lee; DeWolf, Melissa; Holyoak, Keith J
2016-04-01
Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials (ERPs)-N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving task, when participants generated labeled answers to semantically aligned and misaligned arithmetic problems (e.g., 6 roses + 2 tulips = ? vs. 6 roses + 2 vases = ?), the second object label in misaligned problems yielded an N400 effect for addition (but not division) problems. In a verification task, when participants judged arithmetically correct but semantically misaligned problem sentences to be "unacceptable," the second object label in misaligned sentences elicited a P600 effect. Thus, depending on task constraints, misaligned problems can show either of two ERP signatures of conceptual disruption. These results show that well-educated adults can integrate mathematical and semantic relations on the rapid timescale of within-domain ERP effects by a process akin to analogical mapping. PMID:25864403
Pankovic, Vladan; Predojevic, Milan
2006-01-01
In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formu...
Reversible arithmetic logic unit for quantum arithmetic
International Nuclear Information System (INIS)
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. (fast track communication)
International Nuclear Information System (INIS)
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on several values of a variable are obtained here. Applications of the above formalism are considered
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.
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...
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
Burgos Gil, José Ignacio; Feliu, E.
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 ...
Trace formulae for arithmetical systems
International Nuclear Information System (INIS)
For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs
New technological design of arithmetics
International Nuclear Information System (INIS)
There are illogical and irrational rules in numbers writing and pronunciation in almost of languages. A part of the aim is to show the electronic applications possibility of logical and systematic rules which are proposed by Raoelina Andriambololona to write and pronounce numbers; we had studied and created the arithmetic operations representation corresponding in binary basis and in hexadecimal basis. The brand new found concept corresponds as well as the method which uses the matrix product calculation, in according with the writing and the pronunciation of numbers. It was shown how to concept the arithmetic operators in digital electronics; and we proposed and assumed to make headway and to do amelioration for technical conception of calculator and arithmetic unite those are at the basic function of all computers and almost domestic sophisticated machine. The left hand side- right hand side and increasing order writing of number is exploited to build a new computer programming for a scientific calculator.
ASIC For Complex Fixed-Point Arithmetic
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
Zariski decompositions on arithmetic surfaces
Moriwaki, Atsushi
2009-01-01
In this paper, we establish the Zariski decompositions of arithmetic R-divisors of continuous type on arithmetic surfaces and investigate several properties. We also develop the general theory of arithmetic R-divisors on arithmetic varieties.
International Nuclear Information System (INIS)
We incorporate the string theory into the number theoretic formulation based on arithmetic geometry. The string theory is generalized p-adically and interpreted on an arithmetic surface. A p-adic multi-loop scattering amplitude is constructed. (orig.)
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-...
Sugahara, K.; Weng, L
2015-01-01
We first introduce global arithmetic cohomology groups for quasi-coherent sheaves on arithmetic varieties, adopting an adelic approach. Then, we establish fundamental properties, such as topological duality and inductive long exact sequences, for these cohomology groups on arithmetic surfaces. Finally, we expose basic structures for ind-pro topologies on adelic spaces of arithmetic surfaces. In particular, we show that these adelic spaces are topologically self-dual.
No Arithmetic Cyclic Quadrilaterals
Beauregard, Raymond A.
2006-01-01
A quadrilateral is arithmetic if its area is an integer and its sides are integers in an arithmetic progression, and it is cyclic if it can be inscribed in a circle. The author shows that no quadrilateral is both arithmetic and cyclic.
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.
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
A Mathematical Basis for an Interval Arithmetic Standard
Bohlender, Gerd; Kulisch, Ulrich
2010-01-01
Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied ...
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.
Adelic divisors on arithmetic varieties
Moriwaki, Atsushi
2013-01-01
In this article, we generalize several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors and Zariski decompositions for arithmetic divisors on arithmetic surfaces, to the case of the adelic arithmetic divisors.
DEFF Research Database (Denmark)
Gil, J. I. Burgos; Feliu, Elisenda
2012-01-01
context, of the higher algebraic Chow groups defined by Bloch. For projective varieties the degree zero group agrees with the arithmetic Chow groups defined by Gillet and Soulé, and in general 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....
Curiosities of arithmetic gases
International Nuclear Information System (INIS)
Statistical mechanical systems with an exponential density of states are considered. The arithmetic analog of parafermions of arbitrary order is constructed and a formula for boson-parafermion equivalence is obtained using properties of the Riemann zeta function. Interactions (nontrivial mixing) among arithmetic gases using the concept of twisted convolutions are also introduced. Examples of exactly solvable models are discussed in detail
A general purpose arithmetic logic unit
International Nuclear Information System (INIS)
A fast arithmetic and logic unit (ALU) has been constructed as a single CAMAC unit. This device has been designed to provide both arithmetic and logical operations on two 16-bit data fields. The ALU will be put into practical use in the energy trigger of the L3 experiment at LEP, CERN. Due to its simplicity and flexibility the circuit may have applications in other high energy physics experiments. In this paper we describe the details of this circuit. (orig.)
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
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 num...
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.
Precision Arithmetic: A New Floating-Point Arithmetic
Wang, Chengpu
2006-01-01
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding range. Its stable rounding error distribution is approximated by a truncated normal distribution. Generic...
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.
Nonstandard arithmetic and reverse mathematics
Keisler, H. Jerome
2006-01-01
We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.
Kazhdan's Theorem on Arithmetic Varieties
Milne, J S
2001-01-01
Define an arithmetic variety to be the quotient of a bounded symmetric domain by an arithmetic group. An arithmetic variety is algebraic, and the theorem in question states that when one applies an automorphism of the field of complex numbers to the coefficients of an arithmetic variety the resulting variety is again arithmetic. This article simplifies Kazhdan's proof. In particular, it avoids recourse to the classification theorems. It was originally completed on March 28, 1984, and distribu...
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
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.
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.
Numerical characterization of nef arithmetic divisors on arithmetic surfaces
Moriwaki, Atsushi
2012-01-01
In this paper, we give a numerical characterization of nef arithmetic R-Cartier divisors of C^0-type on an arithmetic surface. Namely an arithmetic R-Cartier divisor D of C^0-type is nef if and only if D is pseudo-effective and deg(D^2) = vol(D).
An "Arithmetic" Thinker Tackles Algebra
Armstrong, Alayne C.
2006-01-01
Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.
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.
Connecting Arithmetic to Algebra
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
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.
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 ...
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.
International Nuclear Information System (INIS)
Several ways of local timing of the Josephson-junction RSFQ (Rapid Single Flux Quantum) logic elements are proposed, and their peculiarities are discussed. Several examples of serial and parallel pipelined arithmetic blocks using various types of timing are suggested and their possible performance is discussed. Serial devices enable one to perform n-bit functions relatively slowly but using integrated circuits of a moderate integration scale, while parallel pipelined devices are more hardware-wasteful but promise extremely high productivity
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...
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.
Sets with Prescribed Arithmetic Densities
Czech Academy of Sciences Publication Activity Database
Luca, F.; Pomerance, C.; Porubský, Štefan
2008-01-01
Roč. 3, č. 2 (2008), s. 67-80. ISSN 1336-913X R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : generalized arithmetic density * generalized asymptotic density * generalized logarithmic density * arithmetic al semigroup * weighted arithmetic mean * ratio set * R-dense set * Axiom A * delta-regularly varying function Subject RIV: BA - General Mathematics
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...
Graph colorings, flows and arithmetic Tutte polynomial
D'Adderio, Michele; Moci, Luca
2011-01-01
We introduce the notions of arithmetic colorings and arithmetic flows over a graph with labelled edges, which generalize the notions of colorings and flows over a graph. We show that the corresponding arithmetic chromatic polynomial and arithmetic flow polynomial are given by suitable specializations of the associated arithmetic Tutte polynomial, generalizing classical results of Tutte.
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 Data Cube as a Data Intensive Benchmark
Frumkin, Michael A.; Shabano, Leonid
2003-01-01
Data movement across computational grids and across memory hierarchy of individual grid machines is known to be a limiting factor for application involving large data sets. In this paper we introduce the Data Cube Operator on an Arithmetic Data Set which we call Arithmetic Data Cube (ADC). We propose to use the ADC to benchmark grid capabilities to handle large distributed data sets. The ADC stresses all levels of grid memory by producing 2d views of an Arithmetic Data Set of d-tuples described by a small number of parameters. We control data intensity of the ADC by controlling the sizes of the views through choice of the tuple parameters.
FPGA Based Quadruple Precision Floating Point Arithmetic for Scientific Computations
Mamidi Nagaraju; Geedimatla Shekar
2012-01-01
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...
Finite Field Arithmetic and its Application in Cryptography
Ansari, Bijan
2012-01-01
The groundbreaking idea of public key cryptography and the rapid expansion of the internetin the 80s opened a new research area for finite field arithmetic. The large size of fields incryptography demands new algorithms for efficient arithmetic and new metrics for estimatingfinite field operation performance. The area, power, and timing constraints on hand-heldand embedded devices necessitate accurate models to achieve expected goals. Additionally,cryptosystems need to protect their secrets a...
Crystallization of space: Space-time fractals from fractal arithmetic
Aerts, Diederik; Czachor, Marek; Kuna, Maciej
2016-02-01
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.
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.
Design of Floating Point Arithmetic Logic Unit with Universal Gate
Shraddha N. Zanjat; Dr.S.D.Chede; Prof.B.J.Chilke
2014-01-01
A floating point arithmetic and logic unit design using pipelining is proposed. By using pipeline with ALU design, ALU provides a high performance. With pipelining plus parallel processing concept ALU execute multiple instructions simultaneously. Floating point ALU unit is formed by combination of arithmetic modules (addition, subtraction, multiplication, division), Universal gate module. Each module is divided into sub-module. Bits selection determines which operation takes place at a partic...
MCNPX graphics and arithmetic tally upgrades
International Nuclear Information System (INIS)
MCNPX tallies and cross-sections are plotted using the MCPLOT package. We report on an assortment of upgrades to MCPLOT that are intended to improve the appearance of two-dimensional tally and cross-section plots. We have also expanded the content and versatility of the MCPLOT 'help' command. Finally, we describe the initial phase of capability implementation to post-process tally data using arithmetic operations. These improvements will enable users to better display and manipulate simulation results. (authors)
Coherent states, pseudodifferential analysis and arithmetic
International Nuclear Information System (INIS)
Basic questions regarding families of coherent states include describing some constructions of such and the way they can be applied to operator theory or partial differential equations. In both questions, pseudodifferential analysis is important. Recent developments indicate that they can contribute to methods in arithmetic, especially modular form theory. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
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...
Efficient Unified Arithmetic for Hardware Cryptography
SAVAŞ, Erkay; Savas, Erkay; Koç, Çetin Kaya; Koc, Cetin Kaya
2008-01-01
The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF(q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1], the US federal Digital Signature Standard [2], elliptic curve cryptography [3, 4], and also recently identity based cryptography [5, 6]. Most popular finite fields that are heavily used in cryptographic applications due to elliptic curve based s...
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.
New properties of arithmetic groups
Energy Technology Data Exchange (ETDEWEB)
Platonov, Vladimir P [Scientific Research Institute for System Studies of RAS (Russian Federation)
2011-01-25
New substantial results including the solutions of a number of fundamental problems have been obtained in the last decade or so: the first and rather unexpected examples of arithmetic groups with finite extensions that are not arithmetic were constructed; a criterion for arithmeticity of such extensions was found; deep rigidity theorems were proved for arithmetic subgroups of algebraic groups with radical; a theorem on the finiteness of the number of conjugacy classes of finite subgroups in finite extensions of arithmetic groups was proved, leading to numerous applications, in particular, this theorem made it possible to solve the Borel-Serre problem (1964) on the finiteness of the first cohomology of finite groups with coefficients in an arithmetic group; the problem posed more than 30 years ago on the existence of finitely generated integral linear groups that have infinitely many conjugacy classes of finite subgroups was solved; the arithmeticity question for solvable groups was settled. Similar problems were also solved for lattices in Lie groups with finitely many connected components. This paper is a survey of these results. Bibliography: 27 titles.
New properties of arithmetic groups
International Nuclear Information System (INIS)
New substantial results including the solutions of a number of fundamental problems have been obtained in the last decade or so: the first and rather unexpected examples of arithmetic groups with finite extensions that are not arithmetic were constructed; a criterion for arithmeticity of such extensions was found; deep rigidity theorems were proved for arithmetic subgroups of algebraic groups with radical; a theorem on the finiteness of the number of conjugacy classes of finite subgroups in finite extensions of arithmetic groups was proved, leading to numerous applications, in particular, this theorem made it possible to solve the Borel-Serre problem (1964) on the finiteness of the first cohomology of finite groups with coefficients in an arithmetic group; the problem posed more than 30 years ago on the existence of finitely generated integral linear groups that have infinitely many conjugacy classes of finite subgroups was solved; the arithmeticity question for solvable groups was settled. Similar problems were also solved for lattices in Lie groups with finitely many connected components. This paper is a survey of these results. Bibliography: 27 titles.
Periodic orbits in arithmetical chaos
International Nuclear Information System (INIS)
Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the unconstrained motions of particles on two dimensional surfaces of constant negative curvature whose fundamental groups are given by number theoretical statements (arithmetic Fuchsian groups). It is shown that the mean multiplicity of lengths l of periodic orbits grows asymptotically like c x el/2/l, l → ∞. Moreover, the constant c (depending on the arithmetic group) is determined. (orig.)
Arakelov theory of noncommutative arithmetic surfaces
Borek, Thomas
2008-01-01
The purpose of this paper is to initiate Arakelov theory in a noncommutative setting. More precisely, we are concerned with noncommutative arithmetic surfaces. We introduce a version of arithmetic intersection theory on noncommutative arithmetic surfaces and we prove an arithmetic Riemann-Roch theorem in this setup.
On the concavity of the arithmetic volumes
Ikoma, Hideaki
2013-01-01
In this note, we study the differentiability of the arithmetic volumes along arithmetic R-divisors, and give some equality conditions for the Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big arithmetic R-divisors.
Some studies on arithmetical chaos in classical and quantum mechanics
International Nuclear Information System (INIS)
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furthermore, the arithmetical systems are distinguished by a structure that appears as a generalization of geometric symmetries. These pseudosymmetries occur in the quantization of the classical arithmetic systems as Hecke operators, which form an infinite algebra of self-adjoint operators commuting with the Hamiltonian. The statistical properties of quantum energies in the arithmetical systems have previously been identified as exceptional. They do not fit into the general scheme of random matrix theory. It is shown with the help of a simplified model for the spectral form factor how the spectral statistics in arithmetical quantum chaos can be understood by the properties of the corresponding classical geodesic length spectra. A decisive role is played by the exponentially increasing multiplicities of lengths. The model developed for the level spacings distribution and for the number variance is compared to the corresponding quantities obtained from quantum energies for a specific arithmetical system. Finally, the convergence properties of a representation for the Selberg zeta function as a Dirichlet series are studied. It turns out that the exceptional classical and quantum mechanical properties shared by the arithmetical systems prohibit a convergence of this important function in the physically interesting domain. (orig.)
Remarks on the arithmetic restricted volumes and the arithmetic base loci
Ikoma, Hideaki
2014-01-01
In this paper, we collect some fundamental properties of the arithmetic restricted volumes (or the arithmetic multiplicities) of the adelically metrized line bundles. The arithmetic restricted volume has the concavity property and characterizes the arithmetic augmented base locus as the null locus. We also show a generalized Fujita approximation for the arithmetic restricted volume.
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 undecidable, and connected to the consistency sentence for the ambient formal system in roughly the same manner as G\\"odel and Jeroslow's sentences. Finally, I consider a sentence which is related to the Henkin sentence "I am provable" in the same way that first two arithmetizations are related to G\\"odel and Jeroslaw's sentences. I show that this sentence is provable, using L\\"ob's theorem, as in the standard proof of the Henkin sentence.
Inequalities for semistable families of arithmetic varieties
Kawaguchi, Shu; Moriwaki, Atsushi
1997-01-01
In this paper, we will consider a generalization of Bogomolov's inequality and Cornalba-Harris-Bost's inequality to semistable families of arithmetic varieties under the idea that geometric semistability implies a certain kind of arithmetic positivity. The first one is an arithmetic analogue of the relative Bogomolov's inequality proved by the second author. We also establish the arithmetic Riemann-Roch formulae for stable curves over regular arithmetic varieties and generically finite morphi...
Primitive geodesic lengths and (almost) arithmetic progressions
Lafont, Jean-François; McReynolds, D. B.
2014-01-01
In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length ...
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
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
Using fuzzy arithmetic in containment event trees
International Nuclear Information System (INIS)
The use of fuzzy arithmetic is proposed for the evaluation of containment event trees. Concepts such as improbable, very improbable, and so on, which are subjective by nature, are represented by fuzzy numbers. The quantitative evaluation of containment event trees is based on the extension principle, by which operations on real numbers are extended to operations on fuzzy numbers. Expert knowledge is considered as state of the base variable with a normal distribution, which is considered to represent the membership function. Finally, this paper presents results of an example calculation of a containment event tree for the CAREM-25 nuclear power plant, presently under detailed design stage at Argentina. (author)
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
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.
McNeil, Nicole M.; Rittle-Johnson, Bethany; Hattikudur, Shanta; Petersen, Lori A.
2010-01-01
This study examined if solving arithmetic problems hinders undergraduates' accuracy on algebra problems. The hypothesis was that solving arithmetic problems would hinder accuracy because it activates an operational view of equations, even in educated adults who have years of experience with algebra. In three experiments, undergraduates (N = 184)…
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...
Predicting Arithmetic Abilities: The Role of Preparatory Arithmetic Markers and Intelligence
Stock, Pieter; Desoete, Annemie; Roeyers, Herbert
2009-01-01
Arithmetic abilities acquired in kindergarten are found to be strong predictors for later deficient arithmetic abilities. This longitudinal study (N = 684) was designed to examine if it was possible to predict the level of children's arithmetic abilities in first and second grade from their performance on preparatory arithmetic abilities in…
An arithmetic Lefschetz-Riemann-Roch theorem
Tang, Shun
2015-01-01
In this article, we consider regular arithmetic schemes in the context of Arakelov geometry, endowed with an action of the diagonalisable group scheme associated to a finite cyclic group. For any equivariant and proper morphism of such arithmetic schemes, which is smooth over the generic fibre, we define a direct image map between corresponding higher equivariant arithmetic K-groups and we discuss its transitivity property. Then we use the localization sequence of higher arithmetic K-groups a...
Is the conventional interval-arithmetic correct?
Andrzej Piegat; Marek Landowski
2012-01-01
Interval arithmetic as part of interval mathematics and Granular Computing is unusually important for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic thinking, Computing with Words, grey systems, fuzzy arithmetic and probabilistic arithmetic. However, the mostly used con...
Differential forms on arithmetic jet spaces
Borger, James; Buium, Alexandru
2009-01-01
We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we discuss the de Rham cohomology of some specific arithmetic jet spaces.
On Volumes of Arithmetic Line Bundles
Yuan, Xinyi
2008-01-01
We show an arithmetic generalization of the recent work of Lazarsfeld-Mustata which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.
Heights for line bundles on arithmetic surfaces
Jahnel, Joerg
1995-01-01
For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on the Jacobian defined by the Theta divisor.
Solutions to Arithmetic Convolution Equations
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629. ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
Arithmetic theory of brick tilings
International Nuclear Information System (INIS)
A new, 'arithmetic', approach to the algebraic theory of brick tilings is developed. This approach enables one to construct a simple classification of brick tilings in Zd and to find new proofs of several classical results on brick packing and tilings in Zd. In addition, possible generalizations of results on integer brick packing to the Euclidean plane R2 are investigated
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…
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.
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.
A Short Survey on Arithmetic Transforms and the Arithmetic Hartley Transform
Cintra, R. J.; de Oliveira, H. M.
2015-01-01
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced: the Arithmetic Hartley transform. The interpolation process is shown to be the key element of the a...
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
Uncertainty propagation in fault trees using a quantile arithmetic methodology
International Nuclear Information System (INIS)
A methodology based on Quantile Arithmetic, the probabilistic analog to Interval Analysis (Dempster 1969), is proposed for the computation of uncertainty propagation in Fault Tree Analysis (Apostolakis 1977). The basic events' continuous probability density functions are represented by equivalent discrete distributions through dividing them into a number of quantiles N. Quantile Arithmetic is then used to perform the binary arithmetical operations corresponding to the logical gates in the Boolean expression for the Top Event of a given Fault Tree. The computational characteristics of the proposed methodology as compared with the exact analytical solutions are discussed for the cases of the summation of M normal variables. It is further compared with the Monte Carlo method through the use of the efficiency ratio defined as the product of the labor and error ratios. (orig./HP)
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 Operations Beyond Floating Point Number Precision
Wang, Chih-Yueh; Yin, Chen-Yang; Chen, Hong-Yu; Chen, Yung-Ko
2010-01-01
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical and electronics engineering industries, it is not commonly utilized in scientific computing, because scientific notation is adequate in most cases. We present an undergraduate project that deals with such calculations beyond a machine's numerical limit, kn...
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.
Arithmetical chaos and violation of universality in energy level statistics
International Nuclear Information System (INIS)
A class of strongly chaotic systems revealing a strange arithmetical structure is discussed whose quantal energy levels exhibit level attraction rather than repulsion. As an example, the nearest-neighbour level spacings for Artin's billiard have been computed in a large energy range. It is shown that the observed violation of universality has its root in the existence of an infinite number of hermitian operators (Hecke operators) which commute with the Hamiltonian and generate mongeneric correlations in the eigenfunctions. (orig.)
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.
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...
Arithmetical chaos and quantum cosmology
International Nuclear Information System (INIS)
In this paper, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass automorphic forms and recent mathematical results about arithmetical dynamical systems. The predictions of the billiard model give precise automorphic properties for the wavefunction (Maass-Hecke eigenform), the asymptotic number of quantum states (Selberg asymptotics for PSL(2,Z)), the distribution for the level spacing statistics (the Poissonian one) and the absence of scarred states. The most interesting implication of this model is perhaps that the discrete spectrum is fully embedded in the continuous one.
Arithmetic geometry and number theory
Weng, Lin
2006-01-01
Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of specia
A Bertini-type theorem for free arithmetic linear series
Ikoma, Hideaki
2015-01-01
In this paper, we prove a version of the arithmetic Bertini theorem asserting that there exists a strictly small and generically smooth section of a given arithmetically free graded arithmetic linear series.
Arithmetic of quantum entropy function
International Nuclear Information System (INIS)
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS2 x S2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
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…
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.
Some results on uniform arithmetic circuit complexity
DEFF Research Database (Denmark)
Frandsen, Gudmund Skovbjerg; Valence, Mark; Barrington, David A. Mix
1994-01-01
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...
Szemeredi's theorem and problems on arithmetic progressions
International Nuclear Information System (INIS)
Szemeredi's famous theorem on arithmetic progressions asserts that every subset of integers of positive asymptotic density contains arithmetic progressions of arbitrary length. His remarkable theorem has been developed into a major new area of combinatorial number theory. This is the topic of the present survey.
Numerical Magnitude Representations Influence Arithmetic Learning
Booth, Julie L.; Siegler, Robert S.
2008-01-01
This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be…
Error-correcting codes in computer arithmetic.
Massey, J. L.; Garcia, O. N.
1972-01-01
Summary of the most important results so far obtained in the theory of coding for the correction and detection of errors in computer arithmetic. Attempts to satisfy the stringent reliability demands upon the arithmetic unit are considered, and special attention is given to attempts to incorporate redundancy into the numbers themselves which are being processed so that erroneous results can be detected and corrected.
Prevalence of Combined Reading and Arithmetic Disabilities
Dirks, Evelien; Spyer, Ginny; van Lieshout, Ernest C. D. M.; de Sonneville, Leo
2008-01-01
This study assesses the prevalence of combined reading and arithmetic disabilities in 799 Dutch schoolchildren using standardized school achievement tests. Scores of arithmetic, word recognition, reading comprehension, and spelling of children in fourth and fifth grade were used. The main interest involved the co-occurrence of word recognition and…
Directory of Open Access Journals (Sweden)
Patrick Lemaire
2010-10-01
Full Text Available In this paper, we provide an overview of three important issues regarding working-memory/executive functions (WM/EF, strategies, and cognitive development in the domain of arithmetic. One goal of this overview is to bring some lights on the depth and breadth of the most valuable contributions that André Vandierendonck and his collaborators made on these issues. First, we consider strategic aspects of arithmetic performance and strategic development in arithmetic. Second, the role of WM/EF on arithmetic performance and arithmetic strategies is discussed. Finally, some data are reported on how age-related changes in WM/EF affect strategic development in arithmetic. For each of these issues, we highlight how the works carried out by André Vandierendonck and his colleagues, when integrated in the broader context of research on cognitive arithmetic, contributed to our further understanding of participants' performance and age-related changes in this performance.
Level statistics in arithmetical and pseudo-arithmetical chaos
International Nuclear Information System (INIS)
We investigate a long-standing riddle in quantum chaos, posed by certain fully chaotic billiards with constant negative curvature whose periodic orbits are highly degenerate in length. Depending on the boundary conditions for the quantum wavefunctions, the energy spectra either have uncorrelated levels usually associated with classical integrability or conform to the 'universal' Wigner-Dyson type although the classical dynamics in both cases is the same. The resolution turns out surprisingly simple. The Maslov indices of orbits within multiplets of degenerate length either yield equal phases for the respective Feynman amplitudes (and thus Poissonian level statistics) or give rise to amplitudes with uncorrelated phases (leading to Wigner-Dyson level correlations). The recent semiclassical explanation of spectral universality in quantum chaos is thus extended to the latter case of 'pseudo-arithmetical' chaos. (fast track communication)
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.
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 ... time, simplified versions of such integrity constraints that can be tested before the execution of any update. In this way, virtually no time is spent for optimization or rollbacks at run time. Both set and bag semantics are considered....
Plain Polynomial Arithmetic on GPU
International Nuclear Information System (INIS)
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.
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.
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.
Hardware Implementations of GF (2m Arithmetic Using Normal Basis
Directory of Open Access Journals (Sweden)
Turki F. Al-Somani
2006-01-01
Full Text Available This study presents a survey of algorithms used in field arithmetic over GF (2m using normal basis and their hardware implementations. These include the following arithmetic field operations: addition, squaring, multiplication and inversion. This study shows that the type II Sunar-Koc multiplier is the best multiplier with a hardware complexity of m2 AND gates + XOR gates and a time complexity of TA+ (1+ l log2 (m l Tx. The study also show that the Itoh-Tsujii inversion algorithm was the best inverter and it requires almost log2 (m-1 multiplications.
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.
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.
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…
Patrick Lemaire
2010-01-01
In this paper, we provide an overview of three important issues regarding working-memory/executive functions (WM/EF), strategies, and cognitive development in the domain of arithmetic. One goal of this overview is to bring some lights on the depth and breadth of the most valuable contributions that André Vandierendonck and his collaborators made on these issues. First, we consider strategic aspects of arithmetic performance and strategic development in arithmetic. Second, the role of WM/EF on...
Obstacle problem for Arithmetic Asian options
Laura Monti; Andrea Pascucci
2009-01-01
We prove existence, regularity and a Feynman-Ka\\v{c} representation formula of the strong solution to the free boundary problem arising in the financial problem of the pricing of the American Asian option with arithmetic average.
L(2)-cohomology of arithmetic varieties.
Saper, L; Stern, M
1987-08-01
The L(2)-cohomology of arithmetic quotients of bounded symmetric domains is studied. We establish the conjecture of Zucker equating the L(2)-cohomology of these spaces to the intersection cohomology of their Baily-Borel compactifications. PMID:16593866
L2-cohomology of arithmetic varieties
Saper, Leslie; Stern, Mark
1987-01-01
The L2-cohomology of arithmetic quotients of bounded symmetric domains is studied. We establish the conjecture of Zucker equating the L2-cohomology of these spaces to the intersection cohomology of their Baily-Borel compactifications. PMID:16593866
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...
Complete Program Synthesis for Linear Arithmetic
Mayer, Mikael
2010-01-01
Synthesis of programs or their fragments is a way to write programs by providing only their meaning without worrying about the implementation details. It avoids the drawback of writing sequential code, which might be difficult to check, error-prone or tedious. Our contribution is to provide complete program synthesis algorithms with unbounded data types in decidable theories. We present synthesis algorithms for Linear Rational Arithmetic, Linear Integer Arithmetic and Parametrized Linear Inte...
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 ...
Quantile arithmetic methodology for uncertainty propagation in fault trees
International Nuclear Information System (INIS)
A methodology based on quantile arithmetic, the probabilistic analog to interval analysis, is proposed for the computation of uncertainties propagation in fault tree analysis. The basic events' continuous probability density functions (pdf's) are represented by equivalent discrete distributions by dividing them into a number of quantiles N. Quantile arithmetic is then used to performthe binary arithmetical operations corresponding to the logical gates in the Boolean expression of the top event expression of a given fault tree. The computational advantage of the present methodology as compared with the widely used Monte Carlo method was demonstrated for the cases of summation of M normal variables through the efficiency ratio defined as the product of the labor and error ratios. The efficiency ratio values obtained by the suggested methodology for M = 2 were 2279 for N = 5, 445 for N = 25, and 66 for N = 45 when compared with the results for 19,200 Monte Carlo samples at the 40th percentile point. Another advantage of the approach is that the exact analytical value of the median is always obtained for the top event
Grabner, Roland H; Rütsche, Bruno; Ruff, Christian C; Hauser, Tobias U
2015-07-01
The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulation of this key region. In the present study we addressed these questions by applying transcranial direct current stimulation (tDCS) over the left PPC during a short-term training that simulates the typical path of arithmetic skill acquisition (specifically the transition from effortful procedural to memory-based problem-solving strategies). Sixty participants received either anodal, cathodal or sham tDCS while practising complex multiplication and subtraction problems. The stability of the stimulation-induced learning effects was assessed in a follow-up test 24 h after the training. Learning progress was modulated by tDCS. Cathodal tDCS (compared with sham) decreased learning rates during training and resulted in poorer performance which lasted over 24 h after stimulation. Anodal tDCS showed an operation-specific improvement for subtraction learning. Our findings extend previous studies by demonstrating that the left PPC is causally involved in arithmetic learning (and not only in arithmetic performance) and that even a short-term tDCS application can modulate the success of arithmetic knowledge acquisition. Moreover, our finding of operation-specific anodal stimulation effects suggests that the enhancing effects of tDCS on learning can selectively affect just one of several cognitive processes mediated by the stimulated area. PMID:25970697
Dynamic mental number line in simple arithmetic.
Yu, Xiaodan; Liu, Jie; Li, Dawei; Liu, Hang; Cui, Jiaxin; Zhou, Xinlin
2016-05-01
Studies have found that spatial-numerical associations could extend to arithmetic. Addition leads to rightward shift in spatial attention while subtraction leads to leftward shift (e.g., Knops et al. 2009; McCrink et al. 2007; Pinhas & Fischer 2008), which is consistent with the hypothesis of static mental number line (MNL) for arithmetic. The current investigation tested the hypothesis of dynamic mental number line which was shaped by the relative magnitudes of two operands in simple arithmetic. Horizontal and vertical electrooculograms (HEOG and VEOG) during simple arithmetic were recorded. Results showed that the direction of eye movements was dependent on the relative magnitudes of two operands. Subtraction was associated with larger rightward eye movements than addition (Experiment 1), and smaller-operand-first addition (e.g., 2+9) was associated with larger rightward eye movement than larger-operand-first addition (e.g., 9+2) only when the difference of two operands was large (Experiment 2). The results suggest that the direction of the mental number line could be dynamic during simple arithmetic, and that the eyes move along the dynamic mental number line to search for solutions. PMID:26645825
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.
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...
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 in large GF(2(exp n))
Cameron, Kelly
1993-01-01
The decoding of Reed Solomon (BCH) codes usually requires large numbers of calculations using GF(2(exp n)) arithmetic. Though efficient algorithms and corresponding circuits for performing basic Galois field arithmetic are known, many of these techniques either become very slow or else require an inordinate amount of circuitry to implement when the size of the Galois field becomes much larger than GF(2(exp 8)). Consequently, most currently available Reed-Solomon decoders are built using small fields, such as GF(2(exp 8)) or GF(2(exp 10)), even though significant coding efficiencies could often be obtained if larger symbol sizes, such as GF(2(exp 16)) or GF(2(exp 32)), were used. Algorithms for performing the basic arithmetic required to decode Reed-Solomon codes have been developed explicitly for use in these large fields. They are discussed in detail.
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.
p-adic path set fractals and arithmetic
Abram, William; Lagarias, Jeffrey C.
2012-01-01
This paper considers a class C(Z_p) of closed sets of the p-adic integers obtained by graph-directed constructions analogous to those of Mauldin and Williams over the real numbers. These sets are characterized as collections of those p-adic integers whose p-adic expansions are describeed by paths in the graph of a finite automaton issuing from a distinguished initial vertex. This paper shows that this class of sets is closed under the arithmetic operations of addition and multiplication by p-...
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
2010-07-01
... 40 Protection of Environment 6 2010-07-01 2010-07-01 false How do I convert my 1-hour arithmetic... SOURCES Operator Training and Qualification Monitoring § 60.2943 How do I convert my 1-hour arithmetic... emissions at 7 percent oxygen. (b) Use Equation 2 in § 60.2975 to calculate the 12-hour rolling averages...
Arithmetic algorithms for error-coded operands.
Avizienis, A.
1973-01-01
Arithmetic algorithms for separate and nonseparate codes are considered. The nonseparate AN code is formed when an uncoded operand X is multiplied by the check modulus A to give the coded operand AX. The separate codes are the residue code, and the inverse-residue code, which has significant advantages in fault detection of repeated-use faults. A set of algorithms for low-cost AN-coded operands is discussed together with questions of their implementation in a byte-organized arithmetic processor. Algorithms for inverse-residue coded operands of the STAR computer are also examined.
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...
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...
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…
Intersection pairing for arithmetic cycles with degenerate Green currents
Moriwaki, Atsushi
1998-01-01
In this note, we would like to propose a suitable extension of the arithmetic Chow group of codimension one, in which the Hodge index theorem holds. We also prove an arithmetic analogue of Bogomolov's instability theorem for rank 2 vector bundles on arbitrary regular projective arithmetic varieties.
Price, Gavin R; Mazzocco, Michèle M M; Ansari, Daniel
2013-01-01
Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence. PMID:23283330
Mathematical Fuzzy Logic and Axiomatic Arithmetic
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
Linz : Johannes Kepler Universität, 2010 - (Cintula, P.; Klement, E.; Stout, L.). s. 63-63 [Linz Seminar on Fuzzy Set Theory /31./. 03.02.2010-07.02.2010, Linz] Institutional research plan: CEZ:AV0Z10300504 Keywords : mathematical fuzzy logic * axiomatic arithmetic Subject RIV: BA - General Mathematics
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.
Circuit lower bounds in bounded arithmetics
Czech Academy of Sciences Publication Activity Database
Pich, Ján
2015-01-01
Roč. 166, č. 1 (2015), s. 29-45. ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Keywords : bounded arithmetic * circuit lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.548, year: 2014 http://www.sciencedirect.com/science/article/pii/S0168007214000888
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.
Backgrounds of arithmetic and geometry an introduction
Miron, Radu
1995-01-01
The book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures.
Approximate counting by hashing in bounded arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2009-01-01
Roč. 74, č. 3 (2009), s. 829-860. ISSN 0022-4812 R&D Projects: GA AV ČR IAA1019401 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * approximate counting * universal hashing Subject RIV: BA - General Mathematics Impact factor: 0.631, year: 2009
Improved closeness centrality using arithmetic mean approach
Ruslan, Nuraimi; Sharif, Shamshuritawati
2015-12-01
In this paper, we improved the mathematical formulation of closeness centrality measure for weighted network. The proposed measure is used arithmetic mean approach and the performance is successfully better than the existing closeness centrality. This measure can be used as a measure of influential nodes.
Modular arithmetic weight and cyclic shifting.
Hartman, W. F.
1972-01-01
This note shows that the modular arithmetic weight of an integer is invariant to the cyclic shifts of its radix-2 form. This result leads to a reduced search for the minimum weight codeword in a cyclic AN-code as well as to a better understanding of previous work.
Non-commutative arithmetic circuits with division
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Wigderson, A.
2015-01-01
Roč. 11, Article 14 (2015), s. 357-393. ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/
Fuzzy Logic and Arithmetical Hierarchy III
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2001-01-01
Roč. 68, č. 1 (2001), s. 129-142. ISSN 0039-3215 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: AV0Z1030915 Keywords : fuzzy logic * basic fuzzy logic * Lukasiewicz logic * Godel logic * product logic * arithmetical hierarchy Subject RIV: BA - General Mathematics
Non-commutative arithmetic circuits with division
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Wigderson, A.
2015-01-01
Roč. 11, Article 14 (2015), s. 357-393. ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/ articles /v011a014/
Fuzzy Logic and Arithmetical Hierarchy IV
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
Berlin : Logos Verlag, 2004 - ( Hendricks , V.; Neuhaus, F.; Pedersen, S.; Scheffler, U.; Wansing, H.), s. 107-115 ISBN 3-8325-0475-3 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: CEZ:AV0Z1030915 Keywords : fuzzy logic * arithmetical hierarchy Subject RIV: BA - General Mathematics
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…
Kühn, Ulf; Müller, Jan Steffen
2012-01-01
We give an explicitly computable lower bound for the arithmetic self-intersection number of the dualizing sheaf on a large class of arithmetic surfaces. If some technical conditions are satisfied, then this lower bound is positive. In particular, these technical conditions are always satisfied for minimal arithmetic surfaces with simple multiplicities and at least one reducible fiber, but we have also used our techniques to obtain lower bounds for some arithmetic surfaces with non-reduced fib...
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. PMID:26265429
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.
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.
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
Rodic, Maja; Zhou, Xinlin; Tikhomirova, Tatiana; Wei, Wei; Malykh, Sergei; Ismatulina, Victoria; Sabirova, Elena; Davidova, Yulia; Tosto, Maria Grazia; Lemelin, Jean-Pascal; Kovas, Yulia
2015-01-01
The present study evaluated 626 5-7-year-old children in the UK, China, Russia, and Kyrgyzstan on a cognitive test battery measuring: (1) general skills; (2) non-symbolic number sense; (3) symbolic number understanding; (4) simple arithmetic--operating with numbers; and (5) familiarity with numbers. Although most inter-population differences were…
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.
Floating-Point Arithmetic on Round-to-Nearest Representations
Kornerup, Peter; Panhaleux, Adrien
2012-01-01
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an encoding which is essentially an ordinary 2's complement representation with an appended round-bit. Not only is this rounding a constant time operation, so is also sign inversion, both of which are at best log-time operations on ordinary 2's complement representations. Addition, multiplication and division is defined in such a way that rounding information can be carried along in a meaningful way, at minimal cost. Based on the fixed-point encoding we here define a floating point representation, and describe to some detail a possible implementation of a floating point arithmetic unit employing this representation, including also the directed roundings.
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.
Recursive double-size fixed precision arithmetic
Chabot, Christophe; Dumas, Jean-Guillaume; 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 co...
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 $(p)≠ 0$.
Set Theory and Arithmetic in Fuzzy Logic
Czech Academy of Sciences Publication Activity Database
Běhounek, Libor; Haniková, Zuzana
Cham : Springer, 2015 - (Montagna, F.), s. 63-89 ISBN 978-3-319-06232-7. - (Outstanding Contributions to Logic. 6) R&D Projects: GA ČR GPP103/10/P234; GA ČR GAP202/10/1826 Institutional support: RVO:67985807 Keywords : fuzzy set theory * fuzzy logic * naive comprehension * non-classical arithmetic Subject RIV: BA - General Mathematics
Randomness, pseudorandomness and models of arithmetic
Pudlák, P.
2013-01-01
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\\cal M$, a common element $\\iota$ of these models and a probability distribution on $\\cal M$, such that for every pseudorandom sequence $s$, the probability that $s(\\iota)=1$ holds true in a random model from $\\cal M$ is equal to 1/2.
Real closures of models of weak arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil; Kolodziejczyk, L.. A.
2013-01-01
Roč. 52, 1-2 (2013), s. 143-157. ISSN 0933-5846 R&D Projects: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545 Institutional support: RVO:67985840 Keywords : bounded arithmetic * real-closed field * recursive saturation Subject RIV: BA - General Mathematics http://link.springer.com/article/10.1007%2Fs00153-012-0311-x
A sorting network in bounded arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2011-01-01
Roč. 162, č. 4 (2011), s. 341-355. ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * sorting network * proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.450, year: 2011 http://www.sciencedirect.com/science/article/pii/S0168007210001272
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...
Set Theory and Arithmetic in Fuzzy Logic
Czech Academy of Sciences Publication Activity Database
Běhounek, Libor; Haniková, Zuzana
Cham: Springer, 2015 - (Montagna, F.), s. 63-89. (Outstanding Contributions to Logic. 6). ISBN 978-3-319-06232-7 R&D Projects: GA ČR GPP103/10/P234; GA ČR GAP202/10/1826 Institutional support: RVO:67985807 Keywords : fuzzy set theory * fuzzy logic * naive comprehension * non-classical arithmetic Subject RIV: BA - General Mathematics
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...
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
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...
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...
Implicit Learning of Arithmetic Regularities Is Facilitated by Proximal Contrast
Prather, Richard W.
2012-01-01
Natural number arithmetic is a simple, powerful and important symbolic system. Despite intense focus on learning in cognitive development and educational research many adults have weak knowledge of the system. In current study participants learn arithmetic principles via an implicit learning paradigm. Participants learn not by solving arithmetic equations, but through viewing and evaluating example equations, similar to the implicit learning of artificial grammars. We expand this to the symbo...
Arithmetic on a Distributed-Memory Quantum Multicomputer
Van Meter, R; Nemoto, K; Itoh, K M; Meter, Rodney Van; Nemoto, Kae; Itoh, Kohei M.
2006-01-01
We evaluate the performance of quantum arithmetic algorithms run on a distributed quantum computer (a quantum multicomputer). We vary the node capacity and I/O capabilities, and the network topology. The tradeoff of choosing between gates executed remotely, through ``teleported gates'' on entangled pairs of qubits (telegate), versus exchanging the relevant qubits via quantum teleportation, then executing the algorithm using local gates (teledata), is examined. We show that the teledata approach performs better, and that carry-ripple adders perform well when the teleportation block is decomposed so that the key quantum operations can be parallelized. A node size of only a few logical qubits performs adequately provided that the nodes have two transceiver qubits. A linear network topology performs acceptably for a broad range of system sizes and performance parameters. We therefore recommend pursuing small, high-I/O bandwidth nodes and a simple network. Such a machine will run Shor's algorithm for factoring lar...
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 processing (β = .23, t(155) = 3.07, p < .01) as specific predictors of arithmetical performance. PMID:27320030
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.
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
Arithmetic, mutually unbiased bases and complementary observables
International Nuclear Information System (INIS)
Complementary observables in quantum mechanics may be viewed as Frobenius structures in a dagger monoidal category, such as the category of finite dimensional Hilbert spaces over the complex numbers. On the other hand, their properties crucially depend on the discrete Fourier transform and its associated quantum torus, requiring only the finite fields that underlie mutually unbiased bases. In axiomatic topos theory, the complex numbers are difficult to describe and should not be invoked unnecessarily. This paper surveys some fundamentals of quantum arithmetic using finite field complementary observables, with a view considering more general axiom systems.
Functional verification of floating point arithmetic unit
International Nuclear Information System (INIS)
For continuous real-time reactivity monitoring of PFBR reactivity safety channel, a FPGA based reactivity meter has been developed by Electronics Division, BARC. Verification of designs involved in Safety Critical systems is very important and necessary. Functional verification of this design is presently carried out by EID, IGCAR. In Reactivity meter, Floating Point Arithmetic Unit (FPAU) is a major and very important sub module, which needs to be completely verified first. Two types of verifications are possible: Functional verification and Formal verification. This paper discusses and shares the experiences of functional verification of FPAU module for all special floating point numbers. (author)
Arithmetic fundamental groups and moduli of curves
International Nuclear Information System (INIS)
This is a short note on the algebraic (or sometimes called arithmetic) fundamental groups of an algebraic variety, which connects classical fundamental groups with Galois groups of fields. A large part of this note describes the algebraic fundamental groups in a concrete manner. This note gives only a sketch of the fundamental groups of the algebraic stack of moduli of curves. Some application to a purely topological statement, i.e., an obstruction to the subjectivity of Johnson homomorphisms in the mapping class groups, which comes from Galois group of Q, is explained. (author)
ARITHMETIC PROGRESSIONS FOR COUNTING PRIME NUMBERS
Directory of Open Access Journals (Sweden)
V.J.DEVASIA
2014-11-01
Full Text Available In this paper two arithmetic progressions are proposed for listing and counting the prime numbers less than or equal to a given integer. From these progressions, how one can filter out prime numbers is the topic of discussion in this paper. An easy to implement formula is presented to compute the number of primes by eliminating the number of composite numbers in an iterative and recursive manner. Numerical examples are presented to demonstrate how the procedure works in an efficient and simple way.
Stock, Pieter; Desoete, Annemie; Roeyers, Herbert
2010-01-01
In a 3-year longitudinal study, 471 children were classified, based on their performances on arithmetic tests in first and second grade, as having persistent arithmetic disabilities (AD), persistent low achieving (LA), persistent typical achieving, inconsistent arithmetic disabilities (DF1), or inconsistent low achieving in arithmetic. Significant…
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...
Arithmetic intersection on a Hilbert modular surface and the Faltings height
Yang, Tonghai
2013-01-01
In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles in a Hilbert modular surface over $\\mathbb Z$. As applications, we obtain the first `non-abelian' Chowla-Selberg formula, which is a special case of Colmez's conjecture; an explicit arithmetic intersection formula between arithmetic Humbert surfaces and CM cycles in the arithmetic Siegel modular variety of genus two; Lauter's conjecture about the denominat...
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...
Higher Arithmetic Sequence and Its Implicit Common Difference
Directory of Open Access Journals (Sweden)
Wu Qu
2015-12-01
Full Text Available The concept of k-order sequence of first order arithmetic sequence has been defined by mathematical induction based on finite difference theory. It has been proved this sequence is higher arithmetic sequence. Meanwhile the sum formula and the derivation of its implicit common difference have been given.
Higher Arithmetic Sequence and Its Implicit Common Difference
Wu Qu
2015-01-01
The concept of k-order sequence of first order arithmetic sequence has been defined by mathematical induction based on finite difference theory. It has been proved this sequence is higher arithmetic sequence. Meanwhile the sum formula and the derivation of its implicit common difference have been given.
The behaviour of eigenstates of arithmetic hyperbolic manifolds
International Nuclear Information System (INIS)
In this paper we study some problems arising from the theory of Quantum Chaos, in the context of arithmetic hyperbolic manifolds. We show that there is no strong localization (''scarring'') onto totally geodesic submanifolds. Arithmetic examples are given, which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom. (orig.)
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...—Arithmetic Steps I. Example Illustrating Aggregate Analysis: ASSUMPTIONS: Disbursements: $360 for...
Children's Acquisition of Arithmetic Principles: The Role of Experience
Prather, Richard; Alibali, Martha W.
2011-01-01
The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…
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…
A novel chaotic encryption scheme based on arithmetic coding
International Nuclear Information System (INIS)
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail
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.
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.
Is integer arithmetic fundamental to mental processing?: the mind's secret arithmetic.
Snyder, A.W.; Mitchell, D.J.
1999-01-01
Unlike the ability to acquire our native language, we struggle to learn multiplication and division. It may then come as a surprise that the mental machinery for performing lightning-fast integer arithmetic calculations could be within us all even though it cannot be readily accessed, nor do we have any idea of its primary function. We are led to this provocative hypothesis by analysing the extraordinary skills of autistic savants. In our view such individuals have privileged access to lower ...
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.
The arithmetic basis of special relativity
International Nuclear Information System (INIS)
Under relatively general particle and rocket frame motions, it is shown that, for special relativity, the basic concepts can be formulated and the basic properties deduced using only arithmetic. Particular attention is directed toward velocity, acceleration, proper time, momentum, energy, and 4-vectors in both space-time and Minkowski space, and to relativistic generalizations of Newton's second law. The resulting mathematical simplification is not only completely compatible with modern computer technology, but it yields dynamical equations that can be solved directly by such computers. Particular applications of the numerical equations, which are either Lorentz invariant or are directly related to Lorentz-invariant formulas, are made to the study of a relativistic harmonic oscillator and to the motion of an electric particle in a magnetic field. (author)
Pinel, Philippe; Dehaene, Stanislas
2010-01-01
Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific…
On Arithmetic Densities of Sets of Generalized Integers
Czech Academy of Sciences Publication Activity Database
Porubský, Štefan
Book 4, Volume 1. Kyiv : Institute of Mathematics, NAS of Ukraine, 2008, s. 132-136. ISBN 978-966-02-4891-5. [International Conference on Analytic Number Theory and Spatial Tessellation /4./. Kyiv (UA), 22.09.2008-28.09.2008] R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : asymptotic density * logarithmic density * weighted means * arithmetical semigroup * arithmetic function * generalized arithmetic density * topological density Subject RIV: BA - General Mathematics
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
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
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
Hindman's Theorem: An Ultrafilter Argument in Second Order Arithmetic
Towsner, Henry
2009-01-01
Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.
Dependence of arithmetic functions and differential transcendence of Dirichlet series
International Nuclear Information System (INIS)
Different kinds of dependence (linear and algebraic) are investigated in the domain of arithmetic functions under addition and convolution, while measures of differential transcendence are derived in the domain of Dirichlet series. (author). 18 refs
Verification of Linear (In)Dependence in Finite Precision Arithmetic
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2014-01-01
Roč. 8, č. 3-4 (2014), s. 323 -328. ISSN 1661-8289 Institutional support: RVO:67985807 Keywords : linear dependence * linear independence * pseudoinverse matrix * finite precision arithmetic * verification * MATLAB file Subject RIV: BA - General Mathematics
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...
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.
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.
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.
Arithmetic for the unification of quantum mechanics and general relativity
International Nuclear Information System (INIS)
In the paper we bring attention to description of complex systems in terms of self-organization processes of prime integer relations. Revealed through the unity of two equivalent forms, arithmetical and geometrical, the description may have the potential for the unification of quantum mechanics and general relativity. Remarkably, based on integers and controlled by arithmetic only such processes can define nonlocal correlations between parts of a complex system and the geometry of their spacetimes.
Pu600 energy window arithmetic of plutonium isotopes ratio
International Nuclear Information System (INIS)
The idea of calculating plutonium isotopes ratio using Pu600 energy window (630-670 keV) was put forward by the LLNL. And plutonium isotopes ratio arithmetic on Pu600 energy window was developed in this paper. Some γ energy spectra of two plutonium samples were calculated on this arithmetic, and the results are consistent with the results from PC/FRAM. (authors)
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...
Is integer arithmetic fundamental to mental processing?: the mind's secret arithmetic.
Snyder, A W; Mitchell, D J
1999-03-22
Unlike the ability to acquire our native language, we struggle to learn multiplication and division. It may then come as a surprise that the mental machinery for performing lightning-fast integer arithmetic calculations could be within us all even though it cannot be readily accessed, nor do we have any idea of its primary function. We are led to this provocative hypothesis by analysing the extraordinary skills of autistic savants. In our view such individuals have privileged access to lower levels of information not normally available through introspection. PMID:10212449
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.
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.
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
Reading, arithmetic, and task orientation--how are they related?
Lundberg, Ingvar; Sterner, Görel
2006-12-01
A sample of 60 children in Grade 3 was followed over one year. In the first year, an extensive battery of assessments was used including aspects of reading, arithmetic, and working memory. Teachers rated the children on 7-point scales on various motivational dimensions summarized to a total score tentatively called task orientation. In the follow-up assessment one year later, the testing and teacher ratings were repeated. The cross-sectional correlations between reading, arithmetic, and task orientation were all high (about +.70). The high correlation between reading and arithmetic decreased significantly when task orientation was partialed out, and it was further reduced when working memory as assessed by backward digit span was added to the controlling factors. Also, teacher ratings of cognitive ability and language development accounted for some of the common variance between reading and arithmetic. The correlation between task orientation and school achievement cannot be causally interpreted in cross-sectional designs. Some support for a "causal" hypothesis, however, was obtained in crosslagged correlation analyses indicating that task orientation in Grade 3 may have a causal impact on the level of performance in reading, and in arithmetic in Grade 4. Most likely, however, there is also a reciprocal relationship. PMID:17849205
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 .
CMIS arithmetic and multiwire news for QCD on the connection machine
International Nuclear Information System (INIS)
Our collaboration has been running Wilson fermion QCD simulations on various Connection Machines for over a year and a half. During this time, we have continually optimized our code for operations found in the fermion matrix inversion. Our current version of the matrix inversion is written almost entirely in CMIS (Connection Machine Instruction Set), and utilizes both high-speed arithmetic and multiwire 'news' (nearest-neighbor communications). We present details of how these and other features of our code are implemented on the CM-2. (orig.)
Grounding Concepts An Empirical Basis for Arithmetical Knowledge
Jenkins, C S
2008-01-01
Grounding Concepts tackles the issue of arithmetical knowledge, developing a new position which respects three intuitions which have appeared impossible to satisfy simultaneously: a priorism, mind-independence realism, and empiricism.Drawing on a wide range of philosophical influences, but avoiding unnecessary technicality, a view is developed whereby arithmetic can be known through the examination of empirically grounded concepts. These are concepts which, owing to their relationship to sensory input, are non-accidentally accurate representations of the mind-independent world. Examination of
Degrading Precision Arithmetics for Low-power FIR Implementation
DEFF Research Database (Denmark)
Albicocco, Pietro; Cardarilli, Gian Carlo; Nannarelli, Alberto; Petricca, Massimo; Re, Marco
2011-01-01
dissipation is mandatory. After a review of the possible "standard" optimization techniques, the paper addresses aggressive methodologies where power and area savings are obtained by introducing the concept of "Degrading Precision Arithmetic" (DPA). Three different approaches are discussed: DPA-I, based 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...
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
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
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.
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...
Matrix inequalities for the difference between arithmetic mean and harmonic mean
Liao, Wenshi; Wu, Junliang
2015-01-01
Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.
The Development of Arithmetic Principle Knowledge: How Do We Know What Learners Know?
Prather, Richard W.; Alibali, Martha W.
2009-01-01
This paper reviews research on learners' knowledge of three arithmetic principles: "Commutativity", "Relation to Operands", and "Inversion." Studies of arithmetic principle knowledge vary along several dimensions, including the age of the participants, the context in which the arithmetic is presented, and most importantly, the type of knowledge…
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...
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 .
Embedding adaptive arithmetic coder in chaos-based cryptography
International Nuclear Information System (INIS)
In this study an adaptive arithmetic coder is embedded in the Baptista-type chaotic cryptosystem for implementing secure data compression. To build the multiple lookup tables of secure data compression, the phase space of chaos map with a uniform distribution in the search mode is divided non-uniformly according to the dynamic probability estimation of plaintext symbols. As a result, more probable symbols are selected according to the local statistical characters of plaintext and the required number of iterations is small since the more probable symbols have a higher chance to be visited by the chaotic search trajectory. By exploiting non-uniformity in the probabilities under which a number of iteration to be coded takes on its possible values, the compression capability is achieved by adaptive arithmetic code. Therefore, the system offers both compression and security. Compared with original arithmetic coding, simulation results on Calgary Corpus files show that the proposed scheme suffers from a reduction in compression performance less than 12% and is not susceptible to previously carried out attacks on arithmetic coding algorithms. (general)
Tame symbols and reciprocity laws on arithmetic surfaces
Liu, Dongwen
2012-01-01
We define and study tame symbols for two-dimensional local fields, which are closely related to Kato's residue homomorphisms in Milnor $K$-theory and also explicitly related to Contou-Carrere symbols. As applications we establish several reciprocity laws for tame symbols on arithmetic surfaces.
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.
Deduction arithmetic of continuous measurement the radon daughters potential energy
International Nuclear Information System (INIS)
According to continuous measurement the radon daughters potential energy, the deduction arithmetic is presented. And the theoretical formula, coefficient, calculation error, method of sampling and measurement, condition of calibration are given. The calculation error of this method is less than 4%. This method is suitable for environmental measurement for it's high sensitivity when sampling with low flow rate. (authors)
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
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…
Towards Metamathematics of Weak Arithmetics over Fuzzy Logic
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
2011-01-01
Roč. 19, č. 3 (2011), s. 467-475. ISSN 1367-0751 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : weak arithmetic s * mathematical fuzzy logic * Gödel’s theorem * essential undecidability Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2011
Arithmetic and Aging: Impact of Quantitative Knowledge and Processing Speed
Rozencwajg, Paulette; Schaeffer, Olivier; Lefebvre, Virginie
2010-01-01
The main objective of this study was to examine how quantitative knowledge ("Gq" in the CHC model) and processing speed ("Gs" in the CHC model) affect scores on the WAIS-III Arithmetic Subtest (Wechsler, 2000) with aging. Two age groups were compared: 30 young adults and 25 elderly adults. For both age groups, "Gq" was an important predictor of…
Numerical Predictors of Arithmetic Success in Grades 1-6
Lyons, Ian M.; Price, Gavin R.; Vaessen, Anniek; Blomert, Leo; Ansari, Daniel
2014-01-01
Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across…
Unconscious Addition: When We Unconsciously Initiate and Follow Arithmetic Rules
Ric, Francois; Muller, Dominique
2012-01-01
This research shows that people can unconsciously initiate and follow arithmetic rules (e.g., addition). Participants were asked to detect whether a symbol was a digit. This symbol was preceded by 2 digits and a subliminal instruction: "add" or a control instruction. Participants were faster at identifying a symbol as a number when the symbol was…
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…
Fragments of bounded arithmetic and the lengths of proofs
Czech Academy of Sciences Publication Activity Database
Pudlák, Pavel
2008-01-01
Roč. 73, č. 4 (2008), s. 1389-1406. ISSN 0022-4812 R&D Projects: GA AV ČR IAA1019401 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * length proofs * Herbrand´s theorem Subject RIV: BA - General Mathematics Impact factor: 0.439, year: 2008
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
A codesign case study: implementing arithmetic functions in FPGAs
DEFF Research Database (Denmark)
Klotchkov, I. V.; Pedersen, Steen
Different ways of implementing and designing arithmetic functions for 16/32 bit integers in FPGA technology are studied. A comparison of four different design methods is also included. The results are used to increase the overall system performance in a dedicated 3D image analysis prototype system...
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.
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…
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.
Representations in the Sixteenth-Century Arithmetic Books
Madrid, María José; Maz-Machado, Alexander; León-Mantero, Carmen
2015-01-01
The research on the History of Mathematics and Mathematics Education has on textbook a useful tool to provide diverse types of information; this fact has led to the realization of many different studies focus on them. In this context, this work analyzes eight different sixteenth-century arithmetic books to know the different types of…
Arithmetic crystal classes of magnetic symmetries
International Nuclear Information System (INIS)
The symmetries and properties of a broad class of magnetic crystals are described by magnetic space groups which contain both (unitary) spatial symmetry operations and their combinations with the (anti-unitary operation of) time inversion, 0. The spatial symmetry operations form a halving, non-magnetic, space group H of the magnetic group M such that M=H+aH. As an abstract group the magnetic group M is isomorphic to a non-magnetic group G. The anti-unitary operator a is simply the time inversion 0 when M is a grey group but a product of time inversion with some spatial operation belonging to the coset G-H when M is a black-and-white group. (Author)
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: ...
Steinke, Thomas; 10.4204/EPTCS.24.19
2010-01-01
Multiplication of n-digit integers by long multiplication requires O(n^2) operations and can be time-consuming. In 1970 A. Schoenhage and V. Strassen published an algorithm capable of performing the task with only O(n log(n)) arithmetic operations over the complex field C; naturally, finite-precision approximations to C are used and rounding errors need to be accounted for. Overall, using variable-precision fixed-point numbers, this results in an O(n(log(n))^(2+Epsilon))-time algorithm. However, to make this algorithm more efficient and practical we need to make use of hardware-based floating-point numbers. How do we deal with rounding errors? and how do we determine the limits of the fixed-precision hardware? Our solution is to use interval arithmetic to guarantee the correctness of results and determine the hardware's limits. We examine the feasibility of this approach and are able to report that 75,000-digit base-256 integers can be handled using double-precision containment sets. This clearly demonstrates...
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...
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
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...
A CABAC codec of H.264AVC with secure arithmetic coding
Neji, Nihel; Jridi, Maher; Alfalou, Ayman; Masmoudi, Nouri
2013-02-01
This paper presents an optimized H.264/AVC coding system for HDTV displays based on a typical flow with high coding efficiency and statics adaptivity features. For high quality streaming, the codec uses a Binary Arithmetic Encoding/Decoding algorithm with high complexity and a JVCE (Joint Video compression and encryption) scheme. In fact, particular attention is given to simultaneous compression and encryption applications to gain security without compromising the speed of transactions [1]. The proposed design allows us to encrypt the information using a pseudo-random number generator (PRNG). Thus we achieved the two operations (compression and encryption) simultaneously and in a dependent manner which is a novelty in this kind of architecture. Moreover, we investigated the hardware implementation of CABAC (Context-based adaptive Binary Arithmetic Coding) codec. The proposed architecture is based on optimized binarizer/de-binarizer to handle significant pixel rates videos with low cost and high performance for most frequent SEs. This was checked using HD video frames. The obtained synthesis results using an FPGA (Xilinx's ISE) show that our design is relevant to code main profile video stream.
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.
To what extent are arithmetic progressions of fractional parts stochastic?
International Nuclear Information System (INIS)
For the sequence of residues of division of n members of an arithmetic progression by a real number N, it is proved that the Kolmogorov stochasticity parameter λn tends to 0 as n tends to infinity when the progression step is commensurable with N. In contrast, for the case when the step is incommensurable with N, examples are given in which the stochasticity parameter λn not only does not tend to 0, but even takes some arbitrary large values (infrequently). Too small and too large values of the stochasticity parameter both indicate a small probability that the corresponding sequence is random. Thus, long arithmetic progressions of fractional parts are apparently much less stochastic than for geometric progressions (which provide moderate values of the stochasticity parameter, similar to its values for genuinely random sequences)
An efficient adaptive arithmetic coding image compression technology
International Nuclear Information System (INIS)
This paper proposes an efficient lossless image compression scheme for still images based on an adaptive arithmetic coding compression algorithm. The algorithm increases the image coding compression rate and ensures the quality of the decoded image combined with the adaptive probability model and predictive coding. The use of adaptive models for each encoded image block dynamically estimates the probability of the relevant image block. The decoded image block can accurately recover the encoded image according to the code book information. We adopt an adaptive arithmetic coding algorithm for image compression that greatly improves the image compression rate. The results show that it is an effective compression technology. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
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.
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)
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...
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...
General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2009-01-01
Roč. 193, č. 2 (2009), s. 109-129. ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172
The transition constant for arithmetic hyperbolic reflection groups
International Nuclear Information System (INIS)
Using the results and methods of our papers [1], [2], we show that the degree of the ground field of an arithmetic hyperbolic reflection group does not exceed 25 in dimensions n≥6, and 44 in dimensions 3, 4, 5. This significantly improves our estimates obtained in [2]-[4]. We also use recent results in [5] and [6] to reduce the last bound to 35. We also review and correct the results of [1], §1.
On theories of bounded arithmetic for NC1
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2011-01-01
Roč. 162, č. 4 (2011), s. 322-340. ISSN 0168-0072 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * circuit complexity * propositional translation Subject RIV: BA - General Mathematics Impact factor: 0.450, year: 2011 http://www.sciencedirect.com/science/article/pii/S0168007210001260
On the arithmetic of fractal dimension using hyperhelices
International Nuclear Information System (INIS)
A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension
Automated methods for formal proofs in simple arithmetics and algebra
Chaieb, Amine
2008-01-01
In an LCF-like theorem prover, any proof must be produced from a small set of inference rules. The development of automated proof methods in such systems is extremely important. In this thesis we study the following question: How should we integrate a proof procedure in an LCF-like theorem prover, both in general and in the special case of arithmetics? We investigate three integration paradigms and present several proof procedures. These include universal and weak existe...
Alternating minima and maxima, Nash equilibria and bounded arithmetic
Czech Academy of Sciences Publication Activity Database
Pudlák, Pavel; Thapen, Neil
2012-01-01
Roč. 163, č. 5 (2012), s. 604-614. ISSN 0168-0072 R&D Projects: GA AV ČR IAA100190902 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * bounded arithmetic * search problems Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2012 http://www.sciencedirect.com/science/article/pii/S016800721100090X
The geometry of efficient arithmetic on elliptic curves
Kohel, David
2015-01-01
The arithmetic of elliptic curves, namely polynomial addition and scalar multiplication, can be described in terms of global sections of line bundles on $E\\times E$ and $E$, respectively, with respect to a given projective embedding of $E$ in $\\mathbb{P}^r$. By means of a study of the finite dimensional vector spaces of global sections, we reduce the problem of constructing and finding efficiently computable polynomial maps defining the addition morphism or isogenies to linear algebra. We dem...
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...
Topological Aspects of Infinitude of Primes in Arithmetic Progressions
Czech Academy of Sciences Publication Activity Database
Marko, F.; Porubský, Štefan
2015-01-01
Roč. 140, č. 2 (2015), s. 221-237. ISSN 0010-1354 R&D Projects: GA ČR(CZ) GAP201/12/2351 Institutional support: RVO:67985807 Keywords : coset topology * topological semigroup * topological density * Dirichlet theorem on primes * arithmetical progression * maximal ideal * ring of finite character * residually finite ring * infinitude of primes * pseudoprime Subject RIV: BA - General Mathematics Impact factor: 0.453, year: 2014
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.
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.
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 +…
Arithmetic of p-adic modular forms
Gouvêa, Fernando Quadros
1988-01-01
The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.
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...
Rinne, Luke F; Mazzocco, Michèle M M
2014-01-01
Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance. PMID:24988539
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...
Luke F. Rinne; Mazzocco, Michèle M. M.
2014-01-01
Does knowing when mental arithmetic judgments are right—and when they are wrong—lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the “calibration” of mental arithmetic judgments—that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration ...
Directory of Open Access Journals (Sweden)
Luke F Rinne
Full Text Available Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75 and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.
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.
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
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......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...... bound [7]. We investigate these decision procedures in the context of multicore parallelism with the hope of exploiting multicore powers. Unfortunately, we are not aware of any prior parallelism research related to decision procedures for PA. The closest work is the preliminary results on parallelism...
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.
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 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.
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.
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.
Abelian groups and quadratic residues in weak arithmetic
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2010-01-01
Roč. 56, č. 3 (2010), s. 262-278. ISSN 0942-5616 R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * abelian group * Fermat's little theorem * quadratic reciprocity Subject RIV: BA - General Mathematics Impact factor: 0.361, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/malq.200910009/abstract;jsessionid=9F636FFACB84C025FD90C7E6880350DD.f03t03
On the Brauer group of an arithmetic scheme
International Nuclear Information System (INIS)
For an Enriques surface V over a number field k with a k-rational point we prove that the l-component of Br(V)/Br(k) is finite if and only if l≠2. For a regular projective smooth variety satisfying the Tate conjecture for divisors over a number field, we find a simple criterion for the finiteness of the l-component of Br'(V)/Br(k). Moreover, for an arithmetic model X of V we prove a variant of Artin's conjecture on the finiteness of the Brauer group of X. Applications to the finiteness of the l-components of Shafarevich-Tate groups are given
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
International Nuclear Information System (INIS)
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance nε. Their rate is evaluated via Euler characteristic arguments and their distance using Z2-systolic geometry. This construction answers a question of Zémor [“On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction,” in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259–273], who asked whether homological codes with such parameters could exist at all
Scheduling of iterative algorithms on FPGA with pipelined arithmetic unit
Czech Academy of Sciences Publication Activity Database
Šůcha, P.; Pohl, Zdeněk; Hanzálek, Zdeněk
Washington DC : IEEE Computer Society, 2004, s. 404-412. ISBN 0-7695-2148-7. [IEEE Real-Time and Embedded Technology and Applications Symposium 2004 /10./. Toronto (CA), 25.05.2004-28.05.2004] R&D Projects: GA MŠk(CZ) LN00B096 Institutional research plan: CEZ:AV0Z1075907 Keywords : cyclic scheduling * monoprocessor * iterative algorithms * integer linear programming * FPGA Subject RIV: IN - Informatics, Computer Science http://library.utia.cas.cz/separaty/2008/ZS/pohl-scheduling of iterative algorithms on fpga with pipelined arithmetic unit.pdf
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 ...
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...
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
Rourke, Byron P.; Conway, James A.
1997-01-01
Reviews current research on brain-behavior relationships in disabilities of arithmetic and mathematical reasoning from both a neurological and a neuropsychological perspective. Defines developmental dyscalculia and the developmental importance of right versus left hemisphere integrity for the mediation of arithmetic learning and explores…
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…
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
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…
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.
A Collaborative Cross Number Puzzle Game to Enhance Elementary Students' Arithmetic Skills
Chen, Yen-Hua; Lin, Chiu-Pin; Looi, Chee-Kit; Shao, Yin-juan; Chan, Tak-Wai
2012-01-01
In traditional mathematics education, students have typically been asked to solve lots of tedious and uninteresting exercises for developing the arithmetic skills of addition and subtraction. The paper provides an account of learning arithmetic skills in a more interesting way through the collaborative playing of a puzzle game. 83 students in…
Arithmetic Performance of Children with Cerebral Palsy: The Influence of Cognitive and Motor Factors
van Rooijen, Maaike; Verhoeven, Ludo; Smits, Dirk-Wouter; Ketelaar, Marjolijn; Becher, Jules G.; Steenbergen, Bert
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 specifically, the relative influence of non-verbal…
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…
A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks
Jones, Ian; Pratt, Dave
2012-01-01
Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…
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…
Spontaneous Meta-Arithmetic as the First Step toward School Algebra
Caspi, Shai; Sfard, Anna
2012-01-01
Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the "official" algebraic form of talk. In this paper we take a look at the very beginning of…
The Effect of Illustrations in Arithmetic Problem-Solving: Effects of Increased Cognitive Load
Berends, Inez E.; van Lieshout, Ernest C. D. M.
2009-01-01
Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…
Vasilyeva, Marina; Laski, Elida V.; Shen, Chen
2015-01-01
The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…
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
Number word structure in first and second language influences arithmetic skills
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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
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
IMAGE HIDING IN DNA SEQUENCE USING ARITHMETIC ENCODING
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Prof. Samir Kumar Bandyopadhyay
2011-05-01
Full Text Available Recently, biological techniques become more and more popular, as they are applied to many kinds of applications, authentication protocols, biochemistry, and cryptography. One of the most interesting biology techniques is deoxyribo nucleic acid and using it in such domains. Hiding secret data in deoxyribo nucleic acid becomes an important and interesting research topic. Some researchers hide the secret data in transcribed deoxyribo nucleic acid, translated ribo nucleic acid regions, or active coding segments where it doesn't mention to modify the original sequence, but others hide data in non-transcribed deoxyribo nucleic acid, non-translated ribo nucleic acid regions, or active coding segments. Unfortunately, these schemes either alter the functionalities or modify the original deoxyribo nucleic acid sequences. DNA has the ability to store large amount of digital data. This paper presents a method to hide an image in DNA sequence using arithmetic encoding.
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...
Arithmetic circuits of the noisy-or models
Czech Academy of Sciences Publication Activity Database
Vomlel, Jiří; Savický, Petr
Aalborg : Aalborg University, 2008 - (Jaeger, M.; Nielsen, T.), s. 297-304 [the Fourth European Workshop on Probabilistic Graphical Models (PGM'08). Hirtshals (DK), 17.09.2008-19.09.2008] R&D Projects: GA MŠk 1M0572; GA ČR GA201/08/0539; GA MŠk(CZ) 1M0545 Grant ostatní: GA ČR(XE) Eurocores LogICCCC Project FP005; GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10750506 Keywords : Bayesian network * artithmetic circuit * canonical model Subject RIV: IN - Informatics, Computer Science http://library.utia.cas.cz/separaty/2008/MTR/vomlel- arithmetic %20circuits%20of%20the%20noisy-or%20models.pdf
On the Brauer group of an arithmetic scheme. II
International Nuclear Information System (INIS)
Let π: x→Spec A be an arithmetic model of a regular smooth projective variety V over a number field k. We prove the finiteness of H1(Spec A,R1π*Gm) under the assumption that π*Gm=Gm for the etale topology. (This assumption holds automatically if all geometric fibres of π are reduced and connected.) If a prime l does not divide Card([NS(V otimes k-bar)]tors), V(k)≠0, and the Tate conjecture holds for divisors on V, then the l-primary component Br'(X)(l) is finite. We also study finiteness properties of the Brauer group of a Calabi-Yau variety V of dimension ≥2 over a number field
Low degree polynomial equations arithmetic, geometry and topology
Kollár, J
1996-01-01
These are the notes of my lectures at the 1996 European Congress of Mathematicians. Polynomials appear in mathematics frequently, and we all know from experience that low degree polynomials are easier to deal with than high degree ones. It is, however, not clear that there is a well defined class of ``low degree" polynomials. For many questions, polynomials behave well if their degree is low enough, but the precise bound on the degree depends on the concrete problem. It turns out that there is a collection of basic questions in arithmetic, algebraic geometry and topology all of which give the same class of ``low degree" polynomials. The aim of this lecture is to explain these properties and to provide a survey of the known results.
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.
Square lattice Ising model χ-tilde(5) ODE in exact arithmetic
International Nuclear Information System (INIS)
We obtain in exact arithmetic the order 24 linear differential operator L24 and the right-hand side E(5) of the inhomogeneous equation L24(Φ(5)) = E(5), where Φ(5)=χ-tilde(5)-χ-tilde(3)/2+χ-tilde(1)/120 is a linear combination of n-particle contributions to the susceptibility of the square lattice Ising model. In Bostan et al (2009 J. Phys. A: Math. Theor. 42 275209), the operator L24 (modulo a prime) was shown to factorize into L12(left)·L12(right); here we prove that no further factorization of the order 12 operator L12(left) is possible. We use the exact ODE to obtain the behaviour of χ-tilde(5) at the ferromagnetic critical point and to obtain a limited number of analytic continuations of χ-tilde(5) beyond the principal disc defined by its high temperature series. Contrary to a speculation in Boukraa et al (2008 J. Phys. A: Math. Theor. 41 455202), we find that χ-tilde(5) is singular at w = 1/2 on an infinite number of branches.
Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence
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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
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Feiyan Chen
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.
International Nuclear Information System (INIS)
The aim of the paper is to show an effective application of multiple-precision arithmetic to numerical computations of ill-posed problems. Multiple-precision arithmetic enables us to realize virtually numerical computations without rounding errors, and we apply it, without any stabilization methods, to an inverse acoustic scattering problem to obtain remarkable results. We also introduce our new multiple-precision arithmetic environment exflib, which is designed and implemented for fast computation of large scale scientific numerical simulations, and it works with the language C++ and FORTRAN90
Children's Use of Arithmetic Shortcuts: The Role of Attitudes in Strategy Choice
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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.
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.
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.
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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
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...
Redesigning Arithmetic for Student Success: Supporting Faculty to Teach in New Ways
Bickerstaff, Susan; Lontz, Barbara; Cormier, Maria Scott; Xu, Di
2014-01-01
This chapter describes a promising new approach to teaching developmental arithmetic and prealgebra, and presents research findings that demonstrate how a faculty support network helped instructors adopt new teaching strategies and gain confidence in teaching the reformed course.
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.
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
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...
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.
Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits
Khayutin, Ilya
2015-01-01
We describe new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn over number fields. These invariants are constructed by studying the double quotient of a linear algebraic group by a maximal torus. Using the new invariants we significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. Packets of periodic torus orbits are natural collections of torus orbits coming from a single adelic tor...
International Nuclear Information System (INIS)
The first-order neutron transport equation is solved by the least-squares finite element method based on the discrete ordinates discretization. The angular dependent rebalance (ADR) acceleration arithmetic and its extrapolate method are given. The numerical results of some benchmark problems demonstrate that the arithmetic can shorten the CPU time to 34% ∼ 50% and it is effective even for the strong scattering problem. (authors)
An identity for a class of arithmetical functions of several variables
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Pentti Haukkanen
1993-06-01
Full Text Available Johnson [1] evaluated the sum Ã¢ÂˆÂ‘d|n|C(d;r|, where C(n;r denotes Ramanujan's trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions of several variables and deduce as special cases the previous evaluations.
Mental arithmetic and non-speech office noise: An exploration of interference-by-content
Nick Perham; Helen Hodgetts; Simon Banbury
2013-01-01
An interference-by-content account of auditory distraction - in which the impairment to task performance derives from the similarity of what is being recalled and what is being ignored - was explored concerning mental arithmetic performance. Participants completed both a serial recall and a mental arithmetic task in the presence of quiet, office noise with speech (OS) and office noise without speech (ONS). Both tasks revealed that the two office noise condition′s significantly impaired perfor...
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...
Strategies of solving arithmetic word problems in students with learning difficulties in mathematics
Kalan, Marko
2015-01-01
Problem solving as an important skill is, beside arithmetic, measure and algebra, included in standards of school mathematics (National Council of Teachers of Mathematics) (NCTM, 2000) and needed as a necessary skill for successfulness in science, technology, engineering and mathematics (STEM) (National Mathematics Advisory Panel, 2008). Since solving of human problems is connected to the real life, the arithmetic word problems (in short AWP) are an important kind of mathematics tasks in scho...
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Charles H Hillman
2014-05-01
Full Text Available The current study investigated the influence of cardiorespiratory fitness on arithmetic cognition in forty 9-10 year old children. Measures included a standardized mathematics achievement test to assess conceptual and computational knowledge, self-reported strategy selection, and an experimental arithmetic verification task (including small and large addition problems, which afforded the measurement of event-related brain potentials (ERPs. No differences in math achievement were observed as a function of fitness level, but all children performed better on math concepts relative to math computation. Higher fit children reported using retrieval more often to solve large arithmetic problems, relative to lower fit children. During the arithmetic verification task, higher fit children exhibited superior performance for large problems, as evidenced by greater d’ scores, while all children exhibited decreased accuracy and longer reaction time for large relative to small problems, and incorrect relative to correct solutions. On the electrophysiological level, modulations of early (P1, N170 and late ERP components (P3, N400 were observed as a function of problem size and solution correctness. Higher fit children exhibited selective modulations for N170, P3 and N400 amplitude relative to lower fit children, suggesting that fitness influences symbolic encoding, attentional resource allocation and semantic processing during arithmetic tasks. The current study contributes to the fitness-cognition literature by demonstrating that the benefits of cardiorespiratory fitness extend to arithmetic cognition, which has important implications for the educational environment and the context of learning.
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
Circular Interval Arithmetic Applied on LDMT for Linear Interval System
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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
Zeta functions of regular arithmetic schemes at s=0
Morin, Baptiste
2011-01-01
Lichtenbaum conjectured in \\cite{Lichtenbaum} the existence of a Weil-\\'etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme $\\mathcal{X}$ at $s=0$ in terms of Euler-Poincar\\'e characteristics. Assuming the (conjectured) finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over $\\mathrm{Spec}(\\mathbb{Z})$. In particular, we compute (unconditionally) the right Weil-\\'etale cohomology of number rings and projective spaces over number rings. We state a precise version of Lichtenbaum's conjecture, which expresses the vanishing order (resp. the special value) of the Zeta function $\\zeta(\\mathcal{X},s)$ at $s=0$ as the rank (resp. the determinant) of a single perfect complex of abelian groups $R\\Gamma_{W,c}(\\mathcal{X},\\mathbb{Z})$. Then we relate this conjecture to Soul\\'e's conjecture and to the Tamagawa Number Conjecture. Lichtenbaum's conjecture for projective spaces over the r...
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.)
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...
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...
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.
Interval-type and affine arithmetic-type techniques for handling uncertainty in expert systems
Ceberio, Martine; Kreinovich, Vladik; Chopra, Sanjeev; Longpre, Luc; Nguyen, Hung T.; Ludascher, Bertram; Baral, Chitta
2007-02-01
Expert knowledge consists of statements Sj (facts and rules). The facts and rules are often only true with some probability. For example, if we are interested in oil, we should look at seismic data. If in 90% of the cases, the seismic data were indeed helpful in locating oil, then we can say that if we are interested in oil, then with probability 90% it is helpful to look at the seismic data. In more formal terms, we can say that the implication "if oil then seismic" holds with probability 90%. Another example: a bank A trusts a client B, so if we trust the bank A, we should trust B too; if statistically this trust was justified in 99% of the cases, we can conclude that the corresponding implication holds with probability 99%. If a query Q is deducible from facts and rules, what is the resulting probability p(Q) in Q? We can describe the truth of Q as a propositional formula F in terms of Sj, i.e., as a combination of statements Sj linked by operators like &, [logical or], and [not sign]; computing p(Q) exactly is NP-hard, so heuristics are needed. Traditionally, expert systems use technique similar to straightforward interval computations: we parse F and replace each computation step with corresponding probability operation. Problem: at each step, we ignore the dependence between the intermediate results Fj; hence intervals are too wide. Example: the estimate for P(A[logical or][not sign]A) is not 1. Solution: similar to affine arithmetic, besides P(Fj), we also compute P(Fj&Fi) (or P(Fj1&...&Fjd)), and on each step, use all combinations of l such probabilities to get new estimates. Results: e.g., P(A[logical or][not sign]A) is estimated as 1.
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
Schudlo, Larissa C.; Chau, Tom
2014-02-01
Objective. Near-infrared spectroscopy (NIRS) has recently gained attention as a modality for brain-computer interfaces (BCIs), which may serve as an alternative access pathway for individuals with severe motor impairments. For NIRS-BCIs to be used as a real communication pathway, reliable online operation must be achieved. Yet, only a limited number of studies have been conducted online to date. These few studies were carried out under a synchronous paradigm and did not accommodate an unconstrained resting state, precluding their practical clinical implication. Furthermore, the potentially discriminative power of spatiotemporal characteristics of activation has yet to be considered in an online NIRS system. Approach. In this study, we developed and evaluated an online system-paced NIRS-BCI which was driven by a mental arithmetic activation task and accommodated an unconstrained rest state. With a dual-wavelength, frequency domain near-infrared spectrometer, measurements were acquired over nine sites of the prefrontal cortex, while ten able-bodied participants selected letters from an on-screen scanning keyboard via intentionally controlled brain activity (using mental arithmetic). Participants were provided dynamic NIR topograms as continuous visual feedback of their brain activity as well as binary feedback of the BCI's decision (i.e. if the letter was selected or not). To classify the hemodynamic activity, temporal features extracted from the NIRS signals and spatiotemporal features extracted from the dynamic NIR topograms were used in a majority vote combination of multiple linear classifiers. Main results. An overall online classification accuracy of 77.4 ± 10.5% was achieved across all participants. The binary feedback was found to be very useful during BCI use, while not all participants found value in the continuous feedback provided. Significance. These results demonstrate that mental arithmetic is a potent mental task for driving an online system
Effects of vocalization on cardiovascular and electrodermal responses during mental arithmetic.
Tomaka, J; Blascovich, J; Swart, L
1994-10-01
This study assessed the contribution of vocalization to autonomic responses during mental arithmetic. Specifically this study compared the autonomic responses of subjects during aloud and silent phases of repeated mental arithmetic tasks. The results were consistent for both tasks. As expected, heart rate and skin conductance responses were elevated during the aloud phases. Preejection period and cardiac output reactions, however, were greater during the silent phases. Furthermore, stroke volume declined during the aloud phases, but was maintained near resting levels during the silent phases. There were no phase effects for systolic pressure, diastolic pressure, or total peripheral resistance. The pattern of autonomic responses between aloud and silent phases of mental arithmetic suggest that the relationship between vocalization and autonomic response is not unidirectional but varies depending on the physiological parameter under investigation. PMID:7876036
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
Study on judgment arithmetic for the symmetric attribute of plutonium material in sealed container
International Nuclear Information System (INIS)
The symmetric attribute is an important attribute of plutonium component in nuclear weapon. When the shape of radioactive source with uniform distribution is symmetric on axial direction, measured values of activity in the symmetric direction comply with the normal distribution. Based on this principle, a kind of judgment's arithmetic that can judge the attribute of plutonium in the container is established combining Shapiro Wilk small sample normal distribution test method and F-distribution test method of deleting singular valve with location method of singular value. Experimental data of three models has been analyzed using this judgment's arithmetic. The results show that this judgment's arithmetic can determine accurately the symmetric of plutonium component. (authors)
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...
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.
Peacock's "History of Arithmetic", an Attempt to reconcile empiricism to universality
Durand-Richard, Marie-José
2010-01-01
Lorsque l'algébriste Whig anglican George Peacock (1791-1858) présente sa nouvelle conception de l'algèbre symbolique en 1830, il a déjà écrit une "History of Arithmetic", impressionnante mais peu connue, publiée dans l'Encyclopaedia Metropolitana en 1846. Cet article analyse les orientations philosophiques qui nourrissent cette "History of Arithmetic", et en quoi elles affirment déjà sa conception de l'algèbre comme une étape dans le processus de symbolisation des opérations. En tant que tut...
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.
Reducibility of cocycles under a Brjuno-R\\"ussmann arithmetical condition
Chavaudret, Claire
2011-01-01
The arithmetics of the frequency and of the rotation number play a fun- damental role in the study of reducibility of analytic quasi-periodic cocycles which are sufficiently close to a constant. In this paper we show how to generalize previous works by L.H.Eliasson which deal with the diophantine case so as to implement a Brjuno-Russmann arithmetical condition both on the frequency and on the rotation number. Our approach adapts the Poschel-Russmann KAM method, which was previously used in the problem of linearization of vector fields, to the problem of reducing cocycles.
Arithmetic error codes - Cost and effectiveness studies for application in digital system design.
Avizienis, A.
1971-01-01
The application of error-detecting or error-correcting codes in digital computer design requires studies of cost and effectiveness tradeoffs to supplement the knowledge of their theoretical properties. General criteria for cost and effectiveness studies of error codes are developed, and results are presented for arithmetic error codes with the low-cost check modulus 2 super a - 1. Both separate (residue) and nonseparate (AN) codes are considered. The class of multiple arithmetic error codes is developed as an extension of low-cost single codes.
Compensating arithmetic ability with derived fact strategies in Broca's aphasia: a case report.
Puvanendran, Kalaiyashni; Dowker, Ann; Demeyere, Nele
2016-04-01
We investigated derived fact strategy use in RR, an aphasic patient with severely impaired working memory (no phonological loop), and 16 neurologically healthy matched controls. Participants were tested on derived fact strategy use in multi-digit addition, subtraction, multiplication, and division. RR's accuracy only differed from controls in multiplication. He was as quick as controls in addition and subtraction when able to use the strategies, though significantly slower in addition, division, and multiplication without strategies. Our findings suggest the phonological loop is non-essential for multi-digit arithmetic, and derived fact strategies can help speed up arithmetic in individuals with impaired working memory. PMID:26647359
On the structure of arithmetic sums of Cantor sets with constant ratios of dissection
International Nuclear Information System (INIS)
We investigate conditions which imply that the topological structure of the arithmetic sum of two Cantor sets with constant ratios of dissection at each step is either: a Cantor set, a finite union of closed intervals, or three mixed models (L, R and M-Cantorval). We obtain general results that apply in particular for the case of homogeneous Cantor sets, thus generalizing the results of Mendes and Oliveira. The method used here is new in this context. We also produce results regarding the arithmetic sum of two affine Cantor sets of a special kind
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…
Berg, Derek H.
2008-01-01
The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing…
Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.
2012-01-01
The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems…
Gilmore, Camilla K.; Bryant, Peter
2008-01-01
Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…
2010-07-01
... of 40 CFR part 60, section 4.3, to calculate the daily geometric average concentrations of sulfur... 40 Protection of Environment 8 2010-07-01 2010-07-01 false How do I convert my 1-hour arithmetic... convert my 1-hour arithmetic averages into appropriate averaging times and units? (a) Use the equation...
2010-07-01
... 40 Protection of Environment 6 2010-07-01 2010-07-01 false How do I convert my 1-hour arithmetic...-hour arithmetic averages into appropriate averaging times and units? (a) Use the equation in § 60.1935... calculate the 4-hour or 24-hour daily block averages (as applicable) for concentrations of carbon monoxide....
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.
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.
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.
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
Singular value and arithmetic-geometric mean inequalities for operators
Albadawi, Hussien
2012-01-01
A singular value inequality for sums and products of Hilbert space operators is given. This inequality generalizes several recent singular value inequalities, and includes that if $A$, $B$, and $X$ are positive operators on a complex Hilbert space $H$, then \\begin{equation*} s_{j}\\left( A^{^{1/2}}XB^{^{1/2}}\\right) \\leq \\frac{1}{2}\\left\\Vert X\\right\\Vert \\text{ }s_{j}\\left( A+B\\right) \\text{, \\ }j=1,2,\\cdots\\text{,} \\end{equation*} which is equ...
Algorithms and arithmetic operators for computing the $\\eta_T$ pairing in characteristic three
Beuchat, Jean-Luc; Brisebarre, Nicolas; Detrey, Jérémie; Okamoto, Eiji; Shirase, Masaaki; Takagi, Tsuyoshi
2008-01-01
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 discuss several algorithms to compute the $\\eta_T$ pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes ...
Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
DEFF Research Database (Denmark)
Lange, Tanja
2005-01-01
The ideal class group of hyperelliptic curves can be used in cryptosystems based on the discrete logarithm problem. In this article we present explicit formulae to perform the group operations for genus 2 curves. The formulae are completely general but to achieve the lowest number of operations we...
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
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…
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…
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.
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 relation between the mental number line and arithmetic competencies.
Link, Tanja; Nuerk, Hans-Christoph; Moeller, Korbinian
2014-01-01
In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links number line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded number line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and number magnitude comparison. Assuming that both number line tasks assess the same underlying mental number line representation, unbounded number line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded number line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded number line estimation tasks do not assess the same underlying spatial-numerical representation. Rather, the observed association between bounded number line estimation and numerical/arithmetic competencies may be driven by additional numerical processes (e.g., proportion judgement, addition/subtraction) recruited to solve the task. PMID:24547767
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…
Inhibiting Interference from Prior Knowledge: Arithmetic Intrusions in Algebra Word Problem Solving
Khng, Kiat Hui; Lee, Kerry
2009-01-01
In Singapore, 6-12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13-17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is…
Spatial Skills as a Predictor of First Grade Girls' Use of Higher Level Arithmetic Strategies
Laski, Elida V.; Casey, Beth M.; Yu, Qingyi; Dulaney, Alana; Heyman, Miriam; Dearing, Eric
2013-01-01
Girls are more likely than boys to use counting strategies rather than higher-level mental strategies to solve arithmetic problems. Prior research suggests that dependence on counting strategies may have negative implications for girls' later math achievement. We investigated the relation between first-grade girls' verbal and spatial skills and…
Spontaneous Meta-Arithmetic as a First Step toward School Algebra
Caspi, Shai; Sfard, Anna
2012-01-01
Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…
Fägerstam, Emilia; Samuelsson, Joakim
2014-01-01
This study aims to explore the influence of outdoor teaching among students, aged 13, on arithmetic performance and self-regulation skills as previous research concerning outdoor mathematics learning is limited. This study had a quasi-experimental design. An outdoor and a traditional group answered a test and a self-regulation skills questionnaire…
The effects of eating or skipping breakfast on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Participants, randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by age [8.8 yrs (B: ...
Linguistic and Spatial Skills Predict Early Arithmetic Development via Counting Sequence Knowledge
Zhang, Xiao; Koponen, Tuire; Räsänen, Pekka; Aunola, Kaisa; Lerkkanen, Marja-Kristiina; Nurmi, Jari-Erik
2014-01-01
Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in…
On Tool Support for Duration Calculus on the Basis of Presburger Arithmetic
DEFF Research Database (Denmark)
Hansen, Michael Reichhardt; Brekling, Aske Wiid
ongoing work, we report on our experiences with implementing the model-checking algorithm in [12], which reduces model checking to checking formulas of Presburger arithmetic. The model-checking algorithm generates Presburger formulas that may have sizes being exponential in the chop depth of the Duration...
The effects of morning nutritional status on ERP correlates of mental arithmetic were studied in preadolescents differing in experience (age) and mathematical skills. Children [right-handed; IQ > 80), randomly assigned to treatment [eat (B) or skip (SB) breakfast (each, n = 41)], were sub-grouped by...
International Nuclear Information System (INIS)
The continuous measuring for environmental radon and radon progeny is the premise to calculate the radiation dose from radon precisely. An intelligent measuring apparatus for environmental radon and radon progeny using scintillation cell and filter-sampling technique with deduction arithmetic is described. The measuring theory, structures of the apparatus and some measuring data of standard radon chamber and offices are given detail. (authors)
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…
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…
Multiple Paths to Mathematics Practice in Al-Kashi's "Key to Arithmetic"
Taani, Osama
2014-01-01
In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…
The weekly measurement deviations of indoor radon concentration from the annual arithmetic mean
International Nuclear Information System (INIS)
The difference between weekly measurements and the annual arithmetic mean of radon concentration CRn,Indoor was studied in the Czech Republic. The deviations were analysed for 1537 weekly measurements which were consecutively obtained in 29 rooms over a period of 1 year and the annual arithmetic mean was calculated for each particular room. The relationship of the deviations to three meteorological parameters (i.e. outside temperature, atmospheric pressure, and weekly rainfall) and to the sequential number of a calendar week was studied. The effect of atmospheric pressure and weekly rainfall was not significant. The deviation between a weekly measurement and the annual arithmetic mean depended significantly on outside weekly average temperatures. If the average outside weekly temperature was below 10 deg. C, the radon concentration was systematically higher than that of the annual arithmetic mean. The deviation variability was lower up to a temperature of 10 deg. C. If the weekly average outdoor temperature was higher than 10 deg. C, the uncertainty of a weekly measurement of radon concentration was also higher. (author)
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…
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…
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.
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)
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…
Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure
Czech Academy of Sciences Publication Activity Database
Fränzle, M.; Herde, C.; Teige, T.; Ratschan, Stefan; Schubert, T.
2007-01-01
Roč. 1, - (2007), s. 209-236. ISSN 1574-0617 Grant ostatní: AVACS(DE) SFB/TR 14 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval-based arithmetic constraint solving * SAT modulo theories Subject RIV: BA - General Mathematics
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
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…
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…
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
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.
A multifunctional arithmetical processor model integrated inside a single molecule.
Liu, Yu; Jiang, Wei; Zhang, Heng-Yi; Li, Chun-Ju
2006-07-27
Improving the processing power of molecules remains the challenge for molecular logic and computation. Here we report a 2-phenylimidazo[4,5-f][1,10]phenanthroline (PIPH)-based three-state molecular switch by controlling its unique emission and absorption spectra in the acid and base condition. On one hand, PIPH can perform simultaneously the functions of an "AND" gate and an "XOR" gate, capable of operating as a half-adder, and the "off-on-off" function as well as comparison function by monitoring its fluorescent spectral changes. On the other hand, the molecule can also implement in parallel the functions of an "XOR" gate and two "INH" gates by monitoring its absorption spectral changes, which constructs two half-subtractors. The cooperative operation of comparator and half-subtractor makes general subtraction operation become possible, which is discussed conceptually in the report. PMID:16854125
International Nuclear Information System (INIS)
The Nuclear Regulatory Commission's annual summary of licensed nuclear power reactor data is based primarily on the report of operating data submitted by licensees for each unit for the month of December because that report contains data for the month of December, the year to date (in this case calendar 1990) and cumulative data, usually from the date of commercial operation. The data is not independently verified, but various computer checks are made. The report is divided into two sections. The first contains summary highlights and the second contains data on each individual unit in commercial operation. Section 1 capacity and availability factors are simple arithmetic averages. Section 2 items in the cumulative column are generally as reported by the licensee and notes as to the use of weighted averages and starting dates other than commercial operation are provided
International Nuclear Information System (INIS)
The Nuclear Regulatory Commissions annual summary of licensed nuclear power reactor data is based primarily on the report of operating data submitted by licensees for each unit for the month of December, the year to date (in this case calendar year 1993) and cumulative data, usually for the date of commercial operation. The data is not independently verified, but various computer checks are made. The report is divided into two sections. The first contains summary highlights and the second contains data on each individual unit in commercial operation. Section 1 capacity and availability factors are simple arithmetic averages. Section 2 items in the cumulative column are generally as reported by the licensee and notes as to the use of weighted averages and starting dates other than commercial operation are provided
Czech Academy of Sciences Publication Activity Database
Otisk, Marek
2014-01-01
Roč. 5, - (2014), s. 33-56. ISSN 2038-3657 Institutional support: RVO:67985955 Keywords : Boethius * arithmetic * Gerbert of Aurillac * Abbo of Fleury * Notker of Liège Subject RIV: AA - Philosophy ; Religion
RELATING ARITHMETICAL TECHNIQUES OF PROPORTION TO GEOMETRY: THE CASE OF INDONESIAN TEXTBOOKS
DEFF Research Database (Denmark)
Wijayanti, Dyana
2015-01-01
. Considering 6 common Indonesian textbooks in use, we describe how proportion is explained and appears in examples and exercises, using an explicit reference model of the mathematical organizations of both themes. We also identify how the proportion themes of the geometry and arithmetic domains are linked. Our......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...... results show that the explanation in two domains has different approach, but basically they are mathematically related....
A hand full of numbers: a role for offloading in arithmetics learning?
Directory of Open Access Journals (Sweden)
AnneliseJúlioCosta
2011-12-01
Full Text Available Finger counting has been associated to arithmetic learning in children. We examined children with (n = 14 and without (n = 84 mathematics learning difficulties with ages between 8 to 11 years. Deficits in finger gnosia were found in association to mathematical difficulties. Finger gnosia is particularly relevant for the performance in word problems requiring active manipulation of small magnitudes in the range between 1 and 10. Moreover, the deficits in finger gnosia cannot be attributed to a shortage in working memory capacity but rather to a specific inability to use fingers to transiently represent magnitudes, tagging to be counted objects and reducing the cognitive load necessary to solve arithmetic problems. Since finger gnosia is more related to symbolic than to nonsymbolic magnitude processing, finger-related representation of magnitude seems to be an important link for learning the mapping of analog onto discrete symbolic magnitudes.
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.
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.
To what extent are stochastic the arithmetical progressions of the fractional parts?
International Nuclear Information System (INIS)
For the residues of the division of the n members of an arithmetical progression by a real number N is proved the tending to 0 of the Kolmogorov's stochasticity parameter λn, when n tends to infinity, providing that the progression step is commensurable with N. On the contrary, when the step is incommensurable with N, the paper describes some examples, where the stochasticity parameter λn does not tend to zero, and even attains (infrequently) some arbitrary large values. Both the too small and the too large values of the stochasticity parameter show the small probability of the randomness of the sequence, for which they have been counted. Thus, the long arithmetical progressions' stochasticity degree is much smaller than that of the geometrical progressions (which provide temperate values of the stochasticity parameter, similarly to its value for the genuinely random sequences). (author)
Cryptanalysis of a chaos-based cryptosystem with an embedded adaptive arithmetic coder
International Nuclear Information System (INIS)
In this paper, we analyse a new chaos-based cryptosystem with an embedded adaptive arithmetic coder, which was proposed by Li Heng-Jian and Zhang J S (Li H J and Zhang J S 2010 Chin. Phys. B 19 050508). Although this new method has a better compression performance than its original version, it is found that there are some problems with its security and decryption processes. In this paper, it is shown how to obtain a great deal of plain text from the cipher text without prior knowledge of the secret key. After discussing the security and decryption problems of the Li Heng-Jian et al. algorithm, we propose an improved chaos-based cryptosystem with an embedded adaptive arithmetic coder that is more secure. (general)
Effects of cold-pressor and mental arithmetic on pupillary light reflex
International Nuclear Information System (INIS)
Dynamic pupillary light reflex (PLR) is a simple neurological test that can be useful for assessment of autonomic disorders. In this study, we investigated the changes in PLR induced by mental arithmetic task and cold pressor trials which are often applied in research as model systems to elicit autonomic responses. PLR was recorded before, during and after mental arithmetic and cold pressor tasks in 20 healthy adults (ten males and ten females). Stress-induced sympathetic activation was evident as shown in the increased blood pressure during both tasks. Although the pupillary constriction amplitude did not show significant changes, both constriction time and redilation time changed during the tasks. A significant gender effect was observed in cold pressor that suggested more sympathetic activation in males and faster parasympathetic activation in females in response to light stimulation under cold pressor. (paper)
International Nuclear Information System (INIS)
The first-order neutron transport equation was solved by the least-squares finite element method based on the discrete ordinates discretization. For the traditional source iteration method is very slowly for the optically thick diffusive medium, sometime even divergent especially for the scattering ratio is close to unity, so the acceleration method should be proposed. There is only diffusive synthetical acceleration (DSA) for the discontinuous finite element method (DFEM) and almost no one for the least- squares finite element method. The additive angular dependent rebalance (AADR) acceleration arithmetic and its extrapolate method were given, in which the additive modification was used. It was applied to solve the transport equation with fixed source, fission source, in optically thick diffusive regions and with unstructured-mesh. The numerical results of benchmark problems demonstrate that the arithmetic can shorten the CPU time about 1.5-2 times and give high precise. (authors)
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.
Arithmetic Encoding Based Dynamic Source Routing for Ad-Hoc Networks
Directory of Open Access Journals (Sweden)
Ajay Koul
2008-01-01
Full Text Available An ad hoc network is a collection of mobile stations forming a temporary network without the aid of any centralized coordinator. Routing messages are an essential component of Mobile Adhoc Networks, as each packet needs to be passed quickly through intermediate nodes from source to destination. Internal threats due to changes in the node behaviour that target the routing discovery or maintenance phase of the routing protocol and security challenges can however lead to insecure communication in MANETS. We proposed a model that found the improper behaviour of the nodes and eliminated them. Also it provided secure routing mechanism of sharing messages between source and destination by modifying and making use of Arithmetic encoding that not only saved the bandwidth but also provided the security by crypting the data. The reason we chose Arithmetic coding was because it typically enabled very high coding efficiency and provided better security.
Ashkenazi, Sarit; Rosenberg-Lee, Miriam; Tenison, Caitlin; Menon, Vinod
2011-01-01
Developmental dyscalculia (DD) is a disability that impacts math learning and skill acquisition in school-age children. Here we investigate arithmetic problem solving deficits in young children with DD using univariate and multivariate analysis of fMRI data. During fMRI scanning, 17 children with DD (ages 7–9, grades 2 and 3) and 17 IQ- and reading ability-matched typically developing (TD) children performed complex and simple addition problems which differed only in arithmetic complexity. Wh...
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.
Molina, Marta; Mason, John
2009-01-01
Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-te...
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.
Canavesio, Maria Luisa
2013-01-01
Teaching and learning in a foreign language: the CLIL approach in Europe, in Italy, in Trentino. Monitoring a CLIL pilot programme at Primary school in Italy: Context Analysis and Curriculum Study. Arithmetic facts and language of acquisition effects in Primary school children: Experiment 1,2,3 and 4. Arithmetic facts in Primary school children:Does the language of acquisition really matter? Experiment 5 and 6.
Extensions of linear regression models based on set arithmetic for interval data
Blanco-Fernández, Angela; García-Bárzana, Marta; Colubi, Ana; Kontoghiorghes, Erricos J.
2012-01-01
Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a unique equation based on the interval arithmetic. Moreover, extensions to the multiple case are addressed. The associated least-squares estimation problem are solved. Empirical results and a real-life application are presented in order to show the applicability ...
The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis
2015-01-01
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 trans...
C. Limongelli; R. Pirastu
2012-01-01
In this work we describe the use of truncated p-adic expansion of handling rational numbers by parallel algorithms for symbolic computation. As a case study we propose a parallel implementation for solving linear systems over the rationals. The parallelization is based on a multiple homomorphic image technique and the result is recovered by a parallel version of the Chinese remainder algorithm. Using a MIMD machine, we compare the proposed implementation with the classical modular arithmetic,...
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.
Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem
Czech Academy of Sciences Publication Activity Database
Thapen, Neil
2011-01-01
Roč. 50, 7-8 (2011), s. 665-680. ISSN 1432-0665 R&D Projects: GA AV ČR IAA100190902; GA MŠk LC505; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * proof complexity * search problems Subject RIV: BA - General Mathematics Impact factor: 0.341, year: 2011 http://www.springerlink.com/content/l19kr20362065t86/
A computer program based on quasi-newton arithmetic for the simulation of Purex process
International Nuclear Information System (INIS)
In order to predict the distribution and chemical behaviors of U, Pu, nitric acid in the Purex process of spent fuel reprocessing, a computer program is developed. The mathematical model of the program is based on quasi-Newton arithmetic. The distribution profiles of 1 A and 2 D are calculated by the computer program, and the calculated results are in good agreement with the experimental results. A conclusion can be drown that the program shows better astringency and precision
International Nuclear Information System (INIS)
A condition for second-order companion form digital filters with time variant nondeterministic saturation overflow arithmetic to be free of limit cycles was previously given by Ooba. The condition corresponds to a region which is a subset of the stability triangle. In the present paper, time invariant deterministic saturation nonlinearities are considered. It is shown that, with such nonlinearities, the system is free of limit cycles in whole of the stability triangle
The film optical parameter fitting from soft x ray reflectance using Genetic Arithmetic
International Nuclear Information System (INIS)
The optical constants, thickness and surface roughness are important parameters of film. Genetic Arithmetic (GA) is used to get these optical parameters from soft x ray reflectance fitting. The theory and steps of GA are introduced here. The reflectance data from theory calculation and experiment measuring are analyzed, the results indicate that GA has high accuracy and fast calculation speed in film optical parameter fitting. (authors)
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....
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...
Analysing teachers' belief system referring to the teaching and learning of arithmetic
Bräunling, Katinka; Eichler, Andreas
2015-01-01
In this paper, we want to discuss the structure of teachers' belief systems. Firstly, we discuss teachers' belief systems from a theoretical perspective including characteristics of beliefs systems like its cluster structure, the central-ity of beliefs or the hierarchy of beliefs. Afterwards, we analyse the beliefs of one primary teacher emphasising particularly the structural aspects of this teacher's system of beliefs concerning the teaching and learning of arithmetic. Finally, we discuss p...
Dutch arithmetic, samurai and warships: teaching of Western mathematics in pre-Meiji Japan
Heeffer, Albrecht
2012-01-01
This paper discusses the scarce occasions in which Japan came into contact with Western arithmetic and algebra before the Meiji restoration of 1868. It concentrates on the reception of Dutch works during the last decades of the Tokugawa shogunate and the motivations to study and translate these books. While some studies based on Japanese sources have already been published on this period, this paper draws from Dutch sources and in particular on witness accounts from Dutch officers at the Naga...
GSFAP Adaptive Filtering Using Log Arithmetic for Resource-Constrained Embedded Systems
Czech Academy of Sciences Publication Activity Database
Tichý, Milan; Schier, Jan; Gregg, D.
2010-01-01
Roč. 9, č. 3 (2010), s. 1-31. ISSN 1539-9087 R&D Projects: GA MŠk 7H09005 Institutional research plan: CEZ:AV0Z10750506 Keywords : FPGA * DSP * logarithmic arithmetic * affine projection Subject RIV: BD - Theory of Information Impact factor: 1.057, year: 2010 http://library.utia.cas.cz/separaty/2010/ZS/tichy-0341115.pdf
Frequency up-conversion and arbitrary sum arithmetic of lights with orbital angular momentum
Li, Yan; Ding, Dong-Sheng; Zhang, Wei; Shi, Shuai; Shi, Bao-Sen
2014-01-01
Frequency sum of two light beams carrying orbital angular momentum (OAM) in quasi-phase matching crystals was reported for the first time. The situations in which one light carried OAM and the other is in Gaussian mode and both beams carried OAM were studied in detail. An arbitrary sum arithmetic of lights with OAM was demonstrated in the conversion process. Our study is very promising in constructing hybrid OAM-based optical communication networks and all optical switching.
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.
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.
Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic
Taani, Osama
2013-07-01
In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.
Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.
Wasner, Mirjam; Nuerk, Hans-Christoph; Martignon, Laura; Roesch, Stephanie; Moeller, Korbinian
2016-06-01
Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes. PMID:26895483
Heuristics and representational change in two-move matchstick arithmetic tasks
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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.
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