A Fast, Simpler Algorithm for the Matroid Parity Problem

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

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An augmenting path algorithm for linear matroid parity

COMBINATORICA ◽

10.1007/bf02579169 ◽

1986 ◽

Vol 6 (2) ◽

pp. 123-150 ◽

Cited By ~ 32

Author(s):

Harold N. Gabow ◽

Matthias Stallmann

Keyword(s):

Augmenting Path ◽

Matroid Parity

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Behavior of Radial Incompressible Flow in Pneumatic Dimensional Control Systems

Journal of Fluids Engineering ◽

10.1115/1.1598991 ◽

2003 ◽

Vol 125 (5) ◽

pp. 843-850 ◽

Cited By ~ 2

Author(s):

G. Roy ◽

D. Vo-Ngoc ◽

D. N. Nguyen ◽

P. Florent

Keyword(s):

Gas Flow ◽

Flow Behavior ◽

Pressure Gauge ◽

Axisymmetric Flow ◽

Low Pressure ◽

Industrial Applications ◽

Nozzle Geometry ◽

Machined Surface ◽

Flow Area ◽

Simpler Algorithm

The application of pneumatic metrology to control dimensional accuracy on machined parts is based on the measurement of gas flow resistance through a restricted section formed by a jet orifice placed at a small distance away from a machined surface. The backpressure, which is sensed and indicated by a pressure gauge, is calibrated to measure dimensional variations. It has been found that in some typical industrial applications, the nozzles are subject to fouling, e.g., dirt and oil deposits accumulate on their frontal areas, thus requiring more frequent calibration of the apparatus for reliable service. In this paper, a numerical and experimental analysis of the flow behavior in the region between an injection nozzle and a flat surface is presented. The analysis is based on the steady-state axisymmetric flow of an incompressible fluid. The governing equations, coupled with the appropriate boundary conditions, are solved using the SIMPLER algorithm. Results have shown that for the standard nozzle geometry used in industrial applications, an annular low-pressure separated flow area was found to exist near the frontal surface of the nozzle. The existence of this area is believed to be the cause of the nozzle fouling problem. A study of various alternate nozzle geometries has shown that this low-pressure recirculation area can be eliminated quite readily. Well-designed chamfered, rounded, and reduced frontal area nozzles have all reduced or eliminated the separated recirculation flow area. It has been noted, however, that rounded nozzles may adversely cause a reduction in apparatus sensitivity.

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Application of Through-Flow Calculation to Design and Performance Prediction of Centrifugal Compressor

International Journal of Rotating Machinery ◽

10.1155/s1023621x99000020 ◽

1999 ◽

Vol 5 (1) ◽

pp. 17-33 ◽

Cited By ~ 1

Author(s):

Y. S. Choi ◽

S. H. Kang

Keyword(s):

Centrifugal Compressor ◽

Performance Prediction ◽

Stokes Equations ◽

Control Volume ◽

Computer Code ◽

Secondary Flows ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Simpler Algorithm ◽

And Performance

A computer code predicting the flows through the centrifugal compressor with the radial vaneless diffuser was developed and applied to investigate the detailed flowfields, i.e., secondary flows and jet-wake type flow pattern in design and off-design conditions. Various parameters such as slip factors, aerodynamic blockages, entropy generation and two-zone modeling which are widely used in design and performance prediction, were discussed.A control volume method based on a general curvilinear coordinate system was used to solve the time-averaged Navier–Stokes equations and SIMPLER algorithm was used to solve the pressure linked continuity equation. The standardk-εturbulence model was used to obtain the eddy viscosity. Performance of the code was verified using the measured data for the Eckardt impeller.

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Step Pyramid Distribution for Prime Numbers

Journal of Mathematics Research ◽

10.5539/jmr.v14n1p55 ◽

2022 ◽

Vol 14 (1) ◽

pp. 55

Author(s):

Shaimaa said soltan

Keyword(s):

Number System ◽

Prime Numbers ◽

Classification Algorithm ◽

Algorithm Complexity ◽

Arithmetic Operations ◽

Simple Arithmetic ◽

Simpler Algorithm

In this document, we will present a new way to visualize the distribution of Prime Numbers in the number system to spot Prime numbers in a subset of numbers using a simpler algorithm. Then we will look throw a classification algorithm to check if a number is prime using only 7 simple arithmetic operations with an algorithm complexity less than or equal to O (7) operations for any number.

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The Influence of Combined Turbulators on the Hydraulic-Thermal Performance and Exergy Efficiency of MWCNT-Cu/Water Nanofluid in a Parabolic Solar Collector: A Numerical Approach

Frontiers in Energy Research ◽

10.3389/fenrg.2021.716549 ◽

2021 ◽

Vol 9 ◽

Author(s):

Yacine Khetib ◽

Ammar Melaibari ◽

Radi Alsulami

Keyword(s):

Solar Collector ◽

Volume Fraction ◽

Numerical Approach ◽

Exergy Efficiency ◽

Multiphase Model ◽

Two Phase ◽

Simpler Algorithm ◽

Fluent Software ◽

Parabolic Geometries ◽

Volume Method

The present research benefits from the finite volume method in investigating the influence of combined turbulators on the thermal and hydraulic exergy of a parabolic solar collector with two-phase hybrid MWCNT-Cu/water nanofluid. All parabolic geometries are produced using DesignModeler software. Furthermore, FLUENT software, equipped with a SIMPLER algorithm, is applied for analyzing the performance of thermal and hydraulic, and exergy efficiency. The Eulerian–Eulerian multiphase model and k-ε were opted for simulating the two-phase hybrid MWCNT-Cu/water nanofluid and turbulence model in the collector. The research was analyzed in torsion ratios from 1 to 4, Re numbers from 6,000 to 18,000 (turbulent flow), and the nanofluid volume fraction of 3%. The numerical outcomes confirm that the heat transfer and lowest pressure drop are relevant to the Re number of 18,000, nanofluid volume fraction of 3%, and torsion ratio of 4. Furthermore, in all torsion ratios, rising Re numbers and volume fraction lead to more exergy efficiency. The maximum value of 26.32% in the exergy efficiency was obtained at a volume fraction of 3% and a torsion ratio of 3, as the Re number goes from 60,000 to 18,000.

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