Is the Limit Process Commutative with the Division Operation?

2019 ◽  
Vol 29 (1) ◽  
pp. 143-156
Author(s):  
Seung Ju Baek ◽  
Younggi Choi
Keyword(s):  
Limit Process ◽  
Division Operation

scholarly journals On division operation of any numbers: introducing a new technique

2021 ◽  
Vol 1836 (1) ◽  
pp. 012055
Author(s):  
O A Safiati ◽  
Dafik ◽  
T D Prastiti
Keyword(s):  
New Technique ◽  
A New Technique ◽  
Division Operation

A NOVEL DIVISION ALGORITHM AND ARCHITECTURES FOR PARALLEL AND SEQUENTIAL PROCESSING

2005 ◽  
Vol 14 (02) ◽  
pp. 281-295
Author(s):  
K. TATAS ◽  
D. J. SOUDRIS ◽  
D. SIOMOS ◽  
A. THANAILAKIS
Keyword(s):  
Variable Number ◽  
Point Of View ◽  
Division Algorithm ◽  
Cost Performance ◽  
Sequential Processing ◽  
Trade Offs ◽  
Computation Analysis ◽  
Division Operation ◽  
Partial Division

A new algorithm for reducing the division operation to a series of smaller divisions is introduced. Partitioning the dividend into segments, we perform divisions, shifts, and accumulations taking into account the weight of dividend bits. Each partial division can be performed by any existing division algorithm. From an algorithmic point of view, computation analysis is performed in comparison with the existing algorithms. From an implementation point of view, since the division can be performed by any existing divider, the designer can choose the divider which best meets his specifications. Although the algorithm is presented for integer numbers, it can be easily generalized for fractions, since it is only a matter of representation. Two possible implementations of the algorithm, namely the sequential and parallel are derived, with several variations, allowing performance, cost, and cost/performance trade-offs. Exhaustive comparisons of the derived implementations with many existing implementations in terms of area cost, performance, and cost/performance are done. A plethora of alternative implementations can be derived due to a variable number of partitions.

scholarly journals Improved Modular Division Implementation with the Akushsky Core Function

Computation ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Mikhail Babenko ◽  
Andrei Tchernykh ◽  
Viktor Kuchukov
Keyword(s):  
Approximate Method ◽  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Division Algorithm ◽  
Incorrect Result ◽  
Core Function ◽  
Residue Number ◽  
Division Operation

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

scholarly journals THE CONTEXT OF ARCHIPELAGO TRADITIONAL CAKE TO EXPLORE STUDENTS’ UNDERSTANDING IN INTEGERS DIVISION CLASS VII

2019 ◽  
Vol 14 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Elis Muslimah Nuraida ◽  
Ratu Ilma Indra Putri
Keyword(s):  
Junior High School ◽  
Design Research ◽  
Mathematics Learning ◽  
Learning Trajectory ◽  
Mathematics Problems ◽  
Learning Path ◽  
Starting Point ◽  
Hypothetical Learning Trajectory ◽  
Integer Division ◽  
Division Operation

This study aims to explore the students’ mathematical understanding in integer division operation through the context of archipelago traditional cakes in class VII. This research is related to the Indonesian Realistic Mathematics Approach (PMRI) as a learning approach used. The methodology used in this study is Design Research consisting of three stages: preliminary design, experimental design, and retrospective analysis. The study was conducted on VII grade students of Palembang 1 Junior High School. The learning path (Hypothetical Learning Trajectory) in design research plays an important role as a research design and instrument. The Hypothetical Learning Trajectory (HLT) was developed together with a series of activities using the context of archipelago traditional cakes such as: omelette roll, bakpia, milk pie, etc. The medium used in this study was the Students’ Activity Sheet. The results of this study indicate that exploration using the context of traditional archipelago cakes can help students understanding in multiplication and division of integers. The conclusion of this study is the use of archipelago traditional cakes as starting point in mathematics learning in integer division operation material helps the students to explore their understanding in solving mathematics problems.

Limit motion of an Ornstein–Uhlenbeck particle on the equilibrium manifold of a force field

1997 ◽  
Vol 34 (04) ◽  
pp. 924-938
Author(s):  
Antonella Calzolari ◽  
Federico Marchetti
Keyword(s):  
Force Field ◽  
Gradient Force ◽  
Asymptotically Stable ◽  
Natural Conditions ◽  
Uhlenbeck Process ◽  
Limit Process ◽  
Damping Coefficients ◽  
Ornstein Uhlenbeck Process ◽  
Limit Motion ◽  
Force Intensity

In this paper we consider a position–velocity Ornstein-Uhlenbeck process in an external gradient force field pushing it toward a smoothly imbedded submanifold of . The force is chosen so that is asymptotically stable for the associated deterministic flow. We examine the asymptotic behavior of the system when the force intensity diverges together with the diffusion and the damping coefficients, with appropriate speed. We prove that, under some natural conditions on the initial data, the sequence of position processes is relatively compact, any limit process is constrained on , and satisfies an explicit stochastic differential equation which, for compact , has a unique solution.

scholarly journals Bahadur-Kiefer theorems for the product-limit process

1990 ◽  
Vol 35 (2) ◽  
pp. 276-294 ◽  
Author(s):  
Jan Beirlant ◽  
John H.J. Einmahl
Keyword(s):  
Limit Process ◽  
Product Limit

scholarly journals The advance of cultivation at its northern European limit: Process or event?

The Holocene ◽  
2016 ◽  
Vol 27 (3) ◽  
pp. 427-438 ◽  
Author(s):  
Maria Lahtinen ◽  
Markku Oinonen ◽  
Miikka Tallavaara ◽  
James WP Walker ◽  
Peter Rowley-Conwy
Keyword(s):  
Population Size ◽  
Iron Age ◽  
Pollen Analysis ◽  
Probability Distributions ◽  
Archaeological Sites ◽  
Limit Process ◽  
Northern European ◽  
Complex Process

Dates for early cultivation in Finland obtained from pollen analysis and remains from archaeological sites are compared with the changes in population size derived from the summed calendar-year probability distributions. The results from these two independent proxies correlate strongly with one another indicating that population size and the advance of farming were closely linked to each other. Moreover, the results show that the adaptation and development of farming in this area was a complex process comprising several stages and with major differences between regions The most intensive expansion having occurred in and after the Iron Age. It is therefore more accurate to describe the introduction of farming into the area as a long-lasting process, rather than an event.

scholarly journals Multitype Bienaymé–Galton–Watson processes escaping extinction

2009 ◽  
Vol 41 (01) ◽  
pp. 225-246
Author(s):  
Serik Sagitov ◽  
Maria Conceição Serra
Keyword(s):  
Markov Chain ◽  
Asymptotic Analysis ◽  
Random Number ◽  
Asymptotic Structure ◽  
Limit Process ◽  
Stem Lineage ◽  
Mutation Event

In the framework of a multitype Bienaymé–Galton–Watson (BGW) process, the event that the daughter's type differs from the mother's type can be viewed as a mutation event. Assuming that mutations are rare, we study a situation where all types except one produce on average less than one offspring. We establish a neat asymptotic structure for the BGW process escaping extinction due to a sequence of mutations toward the supercritical type. Our asymptotic analysis is performed by letting mutation probabilities tend to 0. The limit process, conditional on escaping extinction, is another BGW process with an enriched set of types, allowing us to delineate a stem lineage of particles that leads toward the escape event. The stem lineage can be described by a simple Markov chain on the set of particle types. The total time to escape becomes a sum of a random number of independent, geometrically distributed times spent at intermediate types.

Sign in / Sign up

Export Citation Format

Share Document