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Furthermore, two approximation algorithms are presented, and algorithms' performances are considered through the experiments with large amounts of data.
Proof: we use a reduction from the Partition problem which is known to be NP-hard.
It is clear that the reduction can be done in polynomial time.
We design several group data to test the performance of FFDA and SPTA.

These smaller, more manageable data sets are easier to compare quantitatively.
This approach was used because initial work had shown that Tchebichef moments cannot reliably describe the discontinuities in a strain distribution that are associated with complex shapes or boundary conditions; whereas the Fourier transform is ideally suited to such distributions but does not provide any dimensional reduction in the data.
For the experimental data set, this meant the data was reduced from almost 40,000 data points to only 50 Tchebichef moments.
It provides a dimensional reduction in the data from ten of thousands of data points to fifty which allows a practical and straightforward comparison of the data sets; and at the same time preserves the information.
The method was applied to an engineering component employing data from an experiment obtained using digital image correlation and numerical data obtained using finite element analysis.

The calculations suggested that the application of the US welded seams instead of sewn seams would allow the reduction of the costs for sewing threads during the manufacturing of the canopy to 50 % and the significant reduction of the labour requirement.
The strength of the welded seams P, N Sample style 56039 style 56023P style 56307krP Distance between the welding spots, cm 1 1.5 2 0.5 1 1.5 0.5 1 1.5 by the strip method 82.5 75 48.5 43 27 25 21.5 13.5 12.5 “in shear” 148 137 134.5 72.5 46 38.5 102.5 74.5 57 The represented data show that the strength of the welded seams depends on the strength of the materials themselves – the largest values are typical for the sample style 56039, then style 56023P and the smallest values – for the sample with the smallest breaking load and the surface weight – style 56307krP.
The draft of the nozzle-roll for the US welding of the parachute fabrics during the preliminary joint (tacking) of the parts The calculations showed that the application of the US welding instead of sewn joint would allow the reduction of the costs for sewing threads during the manufacturing of the canopy to 50%, the significant reduction of the labour requirement, which would reduce the manufacturing cost of the parachute systems.

In this paper, we propose a genetic algorithm (GA) based MCS for microarray data classification.
The design of GA-1 The design of Chromosome Filter feature selection methods are efficient techniques for the reduction of the dimension of microarray data.
The breast cancer data set contains missing values.
No further preprocessing is applied to the prostate data set.
(a).Breast cancer data set (b) Prostate cancer data set Fig. 2.

The XRD data for GO revealed a distinctive peak at 10.1°.
Additionally, the prominence of the D band at 1346 cm-1 indicates a reduction in the size of the in-plane sp2 domains, possibly due to extensive oxidation.
This change suggests a decrease in the average size of the sp2 domains following the reduction of exfoliated GO [14].
Therefore based on the result obtained, it can be inferred that GO did not undergo any reduction process during the reaction with chives extract.
Excess-reducing agents can cause rapid and uncontrolled reduction of Ag+, resulting in the creation of many AgNPs.

This paper chooses Shanghai Hangzhou Bay north shore as the study area, to analyze the change of landscape pattern from 1994 to 2007, the data adopts 1994 aerial image and remote sensing image with 5m resolution of 2003 and 2007, land is divided into 11 types: urban land, rural land, factory, farm land, undeveloped land, beach, forest, water, fish ponds, road and railway.
Data resources The data of this paper are aerial images and remote sensing images, the images select 3 different periods which are 1994, 2003 and 2007, the image in 1994 is aerial image (1 meter resolution) and the other two are remote sensing images which are SPOT5 images with 5 meters resolution.
Using RS images as the basic information source, with 1:100000 map, other related maps, Shanghai statistical yearbook and other document data, using graphic splicing and geometric correction, gets 3 RS images of Shanghai Hangzhou Bay in 1994, 2003 and 2007 as shown in Fig.1.
Conclusion (1) The dominant landscape type in study area is farmland which CA is in the most significantwith most prominent change CA from 44.88% to 34.61%, an reduction of 10.27.
Area reduction of beach land was because that speed of artificial land reclamation was faster than that of natural formation of beach.

China azhl@nepu.edu.cn, bssm@nepu.edu.cn, chechunbo@yahoo.cn, dfangxiaomeng123@126.com Keywords: geothermal resource; Oilfield produced water; energy saving and emission reduction; heat pump; Oilfield Abstract.
The development and utilization of oilfield produced water geothermal resource is very important for both oil field development of new energy industry and the strategically performance of energy saving and emission reduction.
Data indicates that only a Daqing oilfield, the average daily verification of oilfield produced water is 109.14×104m3 in 2006.
Using the hidden heat of oilfield produced water geothermal resource reasonably and scientifically can not only save a lot of energy, but also have an important meaning in energy saving and emission reduction.
Analysis of energy saving and emission reduction pathway of the oil and gas field industry.

From experimental data, the fatigue-life is usually described in terms of Basquin's law.
In our case, the fitted equation reads, (1) The coefficients of an approximate fit are situated in the Eq. 1, and their coherence with experimental data appears in Fig. 1 left.
The observed fracture for the sample m5 was coherent with the experimental data of fracture for these samples as shows the Fig. 1 left.
The minor increase of dissipate energy relates a local reduction of the SMA creep.
The effect of the SMA induces one reduction of the oscillation amplitude to “zero” in less than “ten” seconds.

The better results indicate that ECO using kriging approximation models can achieve a considerable reduction of computational expense while guaranteeing the accuracy of optimal solutions with efficient convergence.
When applied to MDO problems, this coordination mechanism and hierarchical design model can make a great deal of reduction of computational expense.
Subsequently, in response to the issue that the applicability of using polynomial response surface method to model deterministic computer simulation data, kriging approximation technique was proposed by statisticians to approximate the deterministic data in design and analysis of computer experiments (DACE) [4].
From the data in Table 1, it can be seen that the optimized objective function values solved by ECO using kriging approximation models are very adjacent to those solved by ECO approach, while the number of system iteration using the former method is significantly decreased, and sometimes the reduction is attractive.
As a result, ECO using kriging approximation models can achieve a considerable reduction of computational expense in MDO problems while guaranteeing the accuracy of optimal solutions with efficient convergence.

The Discussion About Improving the Bearing Capacity of Single Pile for Bored Pile in Sandy and Silt Layer Yuqin Feng1,a, Yinghao Wang1,b 1The school of Architecture and Civil Engineering , Inner Mongolia University of Science & Technology, Baotou 014010, China abtfyq@126.com, bwyh1978@sina.com Keywords: Bored pile, Construction technology, Bearing capacity, Pile end resistance, Reduction factor Abstract.
It also discusses the influence construction technology on pile-end ultimate resistance and the reasonable range of reduction factor of the ultimate resistance.
Single Pile Vertical Ultimate Bearing Capacity Standard Value of 2# Pile Number Soil Name Thickness (m) The Bearing Capacity of Bored Pile Parameter Provided by The Technical Code for Building Pile Foundations The Bearing Capacity of Bored Pile Parameter Provided by The Exploration Departments The Ultimate Bearing Capacity of Pile Foundation (Φ800) qsik (kPa) qpk (kPa) qsik (kPa) qpk (kPa) Qu (kN) 2-1 Miscellaneous Fill 0.5~1.1 2-2 Sandy Silt 3.0~3.8 24 650 25 2-3 Medium Sand 5.0~6.4 45 1500 45 2200 2-4 Clay Silt 5.1~6.7 56 750 55 930 The Bearing Capacity of Bored Pile Parameter Provided by The Technical Code for Building Pile Foundations up∑qsikli=866kN qpkAP=750kN 1616 The Bearing Capacity of Bored Pile Parameter Provided by The Exploration Departments up∑qsikli =867kN qpkAP=1100kN 1967 The Static Load Test Results 1390 According to the data of static load test drew the pile top load Q and settlement S relation curve(Q-S curve).
Bored Pile’S Optional Regrouping in The Supporting Layer and Substratum Number Soil Name Thickness (m) The Bearing Capacity of Bored Pile Parameter Provided by The Technical Code for Building Pile Foundations, pile: L=10m, Φ800 mm The Bearing Capacity of Bored Pile Parameter Provided by The Technical Code for Building Pile Foundations, pile: L=13 m, Φ600 mm up∑qsikli (kN) qpkAP (kN) Qu (kN) up∑qsikli (kN) qpkAP (kN) Qu (kN) 2-3 Medium Sand 5.0~6.4 866 750 1616 2-4 Clay Silt 5.1~6.7 1087 375 1462 Measured Data By Static Load Test 1390 1200 Explain: 1) The settlement of pile length10m is 38.1mm. 2) The settlement of pile length13m is 50.5mm.