Search results for "arithmetic"
showing 10 items of 271 documents
Characters that agree on prime-power-order elements
2003
Emulating Human Supervision in an Intelligent Tutoring System for Arithmetical Problem Solving
2014
This paper presents an intelligent tutoring system (ITS) for the learning of arithmetical problem solving. This is based on an analysis of a) the cognitive processes that take place during problem solving; and b) the usual tasks performed by a human when supervising a student in a one-to-one tutoring situation. The ITS is able to identify the solving strategy that the student is following and offer adaptive feedback that takes into account both the problem's constraints and the decisions previously made by the user. An observational study shows the ITS's accuracy at emulating expert human supervision, and a randomized experiment reveals that the ITS significantly improves students' learning…
From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults
1998
A number of theories of mental arithmetic suggest that the ability to solve simple addition and subtraction problems develops from an algorithmic strategy toward a strategy based on the direct retrieval of the result from memory. In the experiment presented here, 2nd and 12th graders were asked to solve two tasks of number and alphabet arithmetic. The subjects transformed series of 1 to 4 numbers or letters (item span) by adding or subtracting an operand varying from 1 to 4 (operation span). Although both the item and operation span were associated with major and identical effects in the case of both numbers and letters at 2nd grade, such effects were clearly observable only in the case of …
Abelian gradings on upper-triangular matrices
2003
Let G be an arbitrary finite abelian group. We describe all possible G-gradings on an upper-triangular matrix algebra over an algebraically closed field of characteristic zero.
Design and simulation of efficient combinational circuits based on a new XOR structure in QCA technology
2021
AbstractQuantum-dot cellular automata (QCA), due to its unique characteristics like low power consumption, nanoscale design, and high computing speed is considered as an emerging technology, and it can be used as an alternative for CMOS technology in circuit design for quantum computers in the near future. XOR gate has many applications in the design of digital circuits in QCA. In this paper, an efficient novel structure of XOR gate is proposed in QCA. Also, a novel 1-bit comparator circuit, 1-bit full adder, binary to gray and gray to binary convertor code based on the proposed XOR is designed and simulated using QCADesigner 2.0.3. The simulation results demonstrated that the proposed stru…
Multiprojective spaces and the arithmetically Cohen-Macaulay property
2019
AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.
The expressive power of the shuffle product
2010
International audience; There is an increasing interest in the shuffle product on formal languages, mainly because it is a standard tool for modeling process algebras. It still remains a mysterious operation on regular languages.Antonio Restivo proposed as a challenge to characterize the smallest class of languages containing the singletons and closed under Boolean operations, product and shuffle. This problem is still widely open, but we present some partial results on it. We also study some other smaller classes, including the smallest class containing the languages composed of a single word of length 2 which is closed under Boolean operations and shuffle by a letter (resp. shuffle by a l…
Some models of inductive syntactical synthesis from sample computations
2005
The paper is a survey of several models of inductive program synthesis from sample computations. Synthesis tools are basically syntactical: the synthesis is based on the detection of "regular" fragments related with "shuffled" arithmetical progressions. Input sample computations are supposed to be "representative": they have to "reflect" all loops occurring in the target program. Programs are synthesized in nontraditional form of "generalized" regular expressions having Cleene stars and unions for loops and CASE-like operators. However, if input samples are somehow "annotated" (we consider two different approaches), then loops can be synthesized in more traditional WHILE-form, where loop co…
Analysis of compressor architectures in MOS current-mode logic
2010
This paper is concerned with the design and the comparison of different compressor architectures for high performance multipliers in MOS current-mode logic (MCML). More specifically, three architectures have been designed for 3-2, 4-2 and 5-2 compressors and two architectures for 7-2 compressors. The various implementations for each type of compressor have been compared one another. This investigation indicates that the architectures based exclusively on three-level MCML gates are the most suitable for MCML implementation in terms of speed, power consumption and area. Design guidelines are provided to improve compressor performance. All the compressors were designed in a TSMC 180nm CMOS tec…