Factorial Experimental Design to Study the Effects of Layers and Fiber Content on Concrete Flexural Behavior

Experimentation has come a long in helping researchers achieve breakthroughs in their different scientific areas and engineering happens to be one of those areas with the most impact from experimental advancement. The need for valid experimental results free from biases and confounding conclusions has prompted the development of new experimental techniques that takes consideration of all applicable factor and combinations in providing answers on a research topic, and the Factorial Experimental design credited to Sir Ronald Fisher is one technique yielding highly valid results. This paper uses the factorial design of experiments to research the flexural impact of polyvinyl acetate fiber and layered concrete in construction. The experiment considered two levels of fiber contents and two levels of layers, and prepared samples with all combinations of the variable factors. The samples were tested after 7 days from casting for flexural strength and an advance statistical analysis was performed on the flexural responses of the samples using R-program. The results from the analyses revealed the significance of the variables to the flexural strength of the samples, as well as their interactions. The experiment concluded that based on the number of layers and fiber content used for the experiment, casting concrete in layers does have a significant negative effect on the flexural strength of concrete, and the failure pattern of concrete members under flexural load in evidently influenced by the material composition of the concrete, and that it can be evidently influenced by casting the concrete in layers.

Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities

In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.

Periodic, Irrational and Transcendental Numbers in the Factorial Series

The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for ri after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.

Removal of Copper Ions from Acid Mine Drainage Wastewater Using Ion Exchange Technique: Factorial Design Analysis

A factorial experimental design method was used to examine the “Cu2+” removal from acid mine drainage wastewater by ion exchange technique. Ion Exchange technique is preferred because of reduced sludge generation compared to conventional treatment techniques and better decontamination efficiency from highly diluted solutions. Factorial design of experiments is employed to study the effect of four factors pH (3, 5, and 6), flow rate (5, 10, 15 L/hr), resin bed height (20, 40 and 60 cm) and initial concentration of the metal (100, 150 and 200 mgl-1) at three levels. The efficiency of metal removal was determined after 100 min of treatment. Main effects and interaction effects of the four factors were analyzed using statistical techniques. A regression model was recommended and it was found to fit the experimental data very well. The results were analyzed statistically using the Student’s t-test, analysis of variance, F-test and lack of fit to define most important process variables affecting the percentage “Cu2+” removal. In this study , pH was thus found to be the most important variable.

Cronbach's a reliability, concurrent validity, and factorial structure of the Death Depression Scale in an Iranian hospital staff sample

Objective: Death depression is an important component in the process of death and dying. Death depression is the second element of death. Depression is one of the important features in death distress. The aim of this study was to explore the performance of the Farsi version of the Death Depression Scale with an Iranian convenience sample of nurses (n =106).Methods: Nurses were selected using a convenience sampling method, and completed the Death Depression Scale (DDS), Death Concern Scale (DCS), Collett-Lester Fear of Death Scale (CLFDS), Reasons for Death Fear Scale (RDFS), Templer's Death Anxiety Scale (DAS), and Death Obsession Scale (DOS). Results: The results of exploratory factor analysis on DDS identified 4 factors (56.16%of variance). Factor 1 labeled"Death sadness", Factor 2 labeled"Death finality/end and Death dread/fear", Factor 3 labeled"Death despair and Death depression", and Factor 4 labeled"Death loneliness". Cronbach's a coefficient was 0.84, Spearman-Brown coefficient 0.85, and Guttman Split-Half coefficient 0.81 The DDS correlated 0.40 with the DCS, 0.39 with the CLFDS, 0.50 with the DAS, 0.35 with the RDFS, and 0.44 with the DOS, indicating good construct and criterion-related validity. Concurrent validity for the DDS with the other scales were significant. Conclusions: The DDS has good validity and reliability, and it can use in clinical and research settings.

Parameters studies for rail wear in high-speed railway turnouts by unreplicated saturated factorial design

Rail wear is one of the main reasons for reducing the service life of high-speed railway turnouts in China. The rail wear characteristics of high-speed railway turnouts are influenced by a large number of input parameters of the complex train-turnout system. To reproduce the actual operation conditions of railway turnouts, random distributions of these inputs need to be considered in rail wear simulation. For a given nominal layout of the high-speed railway turnout, 19 input parameters for rail wear simulation in high-speed railway turnouts are investigated based on orthogonal design of experiment. Three dynamic responses(wheel-rail friction work, normal contact force and size of contact patch) are defined as observed values and the significant factors(direction of passage, axle load, running speed, friction coefficient, and wheel and rail profiles) are determined by two unreplicated saturated factorial design methods, including the half-normal probability plot method and Dong 93 method. As part of the associated rail wear simulation, the influence of the wear models and the local elastic deformation on the rail wear was separately investigated. The calculation results for the wear models are quite different, especially for large creep mode. The local elastic deformation has a large effect on the sliding speed and rail wear and needs to be considered in the rail wear simulation.

Factorial analysis on forest canopy density restoration in the burned area of northern Great Xing＇an Mountains, China

The restoration of forest landscape has drawn much attention since thecatastrophic fire took place on the northern slope of Great Xing'an Mountains in 1987. Forest canopydensity, which has close relation to forest productivity, was selected as a key factor to find howmuch the forest quality was changed 13 years after fire, and how fire severity, regeneration way andterrain factors influenced the restoration of forest canopy density, based on forest inventory datain China, and using Kendall Bivariate Correlation Analysis, and Distances Correlation Analysis. Theresults showed that fire severity which was inversely correlated with forest canopy density gradewas an initial factor among all that selected. Regeneration way which did not remarkably affectforest canopy density restoration in short period, may shorten the cycle of forest succession andpromote the forest productivity of conophorium in the future. Among the three terrain factors, theeffect of slope was the strongest, the position on slope was the second and the aspect was the last.

Optimization of hydrothermal synthesis of H-ZSM-5 zeolite for dehydration of methanol to dimethyl ether using full factorial design

H-ZSM-5 zeolite was synthesized by hydrothermal method. The effects of different synthesis parameters, such as hydrothermal crystallization temperature （170-190 ℃） and Si/A1 molar ratio （100-150）, on the catalytic performance of the dehydration of methanol to dimethyl ether （DME） over the synthesized H-ZSM-5 zeolite were studied. The catalysts were characterized by N2 adsorption-desorption, XRD, NH3-TPD, TGA/DTA, and SEM techniques. The full factorial design of experiments was applied to the synthesis of H-ZSM-5 zeolite and the effects of synthesis conditions and their interaction on the yield of DME as the response variable were determined. Analysis of variance showed that two variables and their interaction significantly affected the response. According to the experimental results, the optimized catalyst prepared at 170℃ with the Si/A1 molar ratio of 100 showed the best catalytic performance among the tested H-ZSM-5 zeolite.

Multiple Factorial Analysis of Symbolic Data

This document presents an extension of the multiple factorial analysis to symbolic data and especially to space data. The analysis makes use of the characteristic coding method to obtain active individuals and the reconstitutive coding method for additional individuals in order to conserve the variability of assertion objects. Traditional analysis methods of the main components are applied to coded objects. Certain interpretation aids are presented after the coding process. This method was applied to poverty data.

Study on seismic performance enhancement in bridges based on factorial analysis

The seismic performance of bridges depends on the ductile behavior of its column, as the deck and other substructural components except pile foundations are normally designed to be elastic to facilitate bridge retrofitting. Codes such as AASHTO, Caltrans, IRC： 112 etc. give guidelines for the seismic performance enhancement of columns through ductile detailing. In the present study, a methodology for the seismic performance enhancement of bridges is discussed by using a ＂Parameter-Based Influence Factor＂ （PIF） developed from factorial analysis. The parameters considered in the factorial analysis are： percentage of longitudinal reinforcement （Pt）, compressive strength of concrete （f＇c）, yield strength of steel （fy）, spacing of lateral ties （5） and column height （/4）. The influence of each parameter and their combination on the limit states considered is estimated. Pushover analysis is used to evaluate the capacity of columns, considering shear failure criteria. A total of 243 （35 combinations） analysis results are compiled to develop ＇PIF＇ used in the performance enhancement process. The study also encompasses other sub-objectives such as evaluating the discrepancies in using the Importance Factor （/） in designing bridges of varied functional importance; and estimating the aspect ratio and slenderness ratio values of bridge columns for its initial sizing.

Evaluation of the Factorial Method for Determination of Energy Expenditure in 16 Young Adult Women Living in China

Objective The present study aimed to evaluate the accuracy of the factorial method for estimating energy needs in individuals living in China.Methods Sixteen healthy female adults aged 22.1±1.2 years with a body mass index （kg/m 2） of 20.4±1.7 were selected as subjects.In free-living conditions,energy expenditure （EE） was determined by using the factorial method.At the same time,the doubly labeled water method （DLW） was also used to measure energy expenditure of the subjects and served as the criterion method.EE predicted by the factorial method （EE factorial） was compared with the simultaneous measurement of EE by the validated DLW method （EE DLW）.Results There was excellent agreement between EE factorial （7.46±0.59 MJ/d） and EE DLW （7.64 ± 0.49 MJ/d）,with a difference of-2.6±4.9% （-0.18±0.36 MJ/d）.No significant differences were found between the two methods.EE factorial was highly correlated with EE DLW （r=0.795,P0.001） and a good agreement for individuals was found by using the Bland and Altman test.Conclusion The factorial method gives satisfactory estimates of EE for both groups and individuals living in China.

Methodology of factorial design deriving guidelines for simulation of growth curve and production of sugars by Spirulina (Arthrospira) maxima

It is practical, economic and sometimes essential to derive rules or conclusions by performing lesser runs of experiments. In this part, a methodology based on 2 f factorial design was brought up to derive guidelines to simulate growth curve and production of sugars by Spirulina (Arthrospira) maxima . The growth curve or accumulation process of sugars was idealized by sets of straight lines limited by phase transfers of growth or accumulation of sugars. Normal analyses of the critical values of the transfers were used to derive their linear relationships with the initial conditions of the experimental factors. These linear functions were called guidelines and were used to simulate the growth curve or accumulation of sugars. Generalization of the guideline technique was determined by the kinetic limitation of nutrient nitrogen or sulfur that was dependent upon their stoichiometric deficiency directly derived from their initial values in the medium. This method uses the initial conditions of culture and does not need measurements of concentrations of nitrate, sulfate and pigments during cultivation. It is a practical and useful alternative way to trace and predict approximately the growth curve and production of sugars by S. maxima .

The spatial multiscale variability of heavy metals based on factorial kriging analysis: A case study in the northeastern Beibu Gulf

Factorial kriging analysis is applied to the research on the spatial multiscale variability of heavy metals in submarine. It is used to analyze the multiscale spatial structures of seven heavy metals, Ni, Cu, Zn, Pb, Cr, As and Cd in the surface sediment from the northeastern of Beibu Gulf, identify and separate spatial variations at different scales of heavy metals, and discuss the provenance of heavy metals and the influencing factors. The results show that the existence of three-scale spatial variations those consist of nugget effect, a spherical structure with range of 30 km（short-range scale） and a spherical structure with range of 140 km（long-range scale） in the linear model of coregionalization fitted. The spatial distribution features of seven heavy metals at short-range scale reflect ＂spot-like＂ or ＂stripe-like＂ local-scale spatial variations; the spatial distribution features of the seven heavy metals at long-range scale represent ＂slice-like＂ regional-scale spatial variations. At local scale, Zn, Cr, Ni,Cu, Pb and Cd are derived primarily from parent materials of Hainan Island, Leizhou Peninsula and Guangxi land, whose spatial distribution characteristics are controlled by granularity of sediments, while As is influenced dominantly by human pollution components from Hainan Island and Leizhou Peninsula. At regional scale, Zn,Cr, Ni and Cu originate primarily from parent rock materials of Leizhou Peninsula and Hainan Island, secondly from Guangxi land; As originated primarily from parent rock materials from Hainan Island, secondly from Leizhou Peninsula and Guangxi land. These metals are transported and migrated with sediments dominated by the anticlockwise circulation of Beibu Gulf year-round, deposited in ＂convergence center＂, forming the whole sedimentary pattern in direction of NWW-NNW at regional scale. The difference in distribution type between As and other metals at regional scale is mainly due to their different geochemical behavior.

Artificial Neural Network and Full Factorial Design Assisted AT-MRAM on Fe Oxides, Organic Materials, and Fe/Mn Oxides in Surficial Sediments

Artificial neural network（ANN） and full factorial design assisted atrazine（AT） multiple regression adsorption model（AT-MRAM） were developed to analyze the adsorption capability of the main components in the surficial sediments（SSs）. Artificial neural network was used to build a model（the determination coefficient square r2 is 0.9977） to describe the process of atrazine adsorption onto SSs, and then to predict responses of the full factorial design. Based on the results of the full factorial design, the interactions of the main components in SSs on AT adsorption were investigated through the analysis of variance（ANOVA）, F-test and t-test. The adsorption capability of the main components in SSs for AT was calculated via a multiple regression adsorption model（MRAM）. The results show that the greatest contribution to the adsorption of AT on a molar basis was attributed to Fe/Mn（–1.993 μmol/mol）. Organic materials（OMs） and Fe oxides in SSs are the important adsorption sites for AT, and the adsorption capabilities are 1.944 and 0.418 μmol/mol, respectively. The interaction among the non-residual components（Fe, Mn oxides and OMs） in SSs interferes in the adsorption of AT that shouldn’t be neglected, revealing the significant contribution of the interaction among non-residual components to controlling the behavior of AT in aquatic environments.

Abrasive resistance of metastable V–Cr–Mn–Ni spheroidal carbide cast irons using the factorial design method

Full factorial design was used to evaluate the two-body abrasive resistance of 3wt%C–4wt%Mn–1.5wt%Ni spheroidal carbide cast irons with varying vanadium（5.0wt%–10.0wt%） and chromium（up to 9.0wt%） contents. The alloys were quenched at 920℃. The regression equation of wear rate as a function of V and Cr contents was proposed. This regression equation shows that the wear rate decreases with increasing V content because of the growth of spheroidal VC carbide amount. Cr influences the overall response in a complex manner both by reducing the wear rate owing to eutectic carbides（M7C3） and by increasing the wear rate though stabilizing austenite to deformation-induced martensite transformation. This transformation is recognized as an important factor in increasing the abrasive response of the alloys. By analyzing the regression equation, the optimal content ranges are found to be 7.5wt%–10.0wt% for V and 2.5wt%–4.5wt% for Cr, which corresponds to the alloys containing 9vol%–15vol% spheroidal VC carbides, 8vol%–16vol% M7C3, and a metastable austenite/martensite matrix. The wear resistance is 1.9–2.3 times that of the traditional 12wt% V–13wt% Mn spheroidal carbide cast iron.

Generalized Central Factorial Numbers with Odd Arguments

In this paper, we consider r-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.

FACTORIAL ANALYSIS OF ANNUAL EROSION-ACCRETION CYCLES OF TIDAL FLATS IN THE FRONT AREA OF THE SOUTHERN CHANGJIANG RIVER DELTA

ＦＡＣＴＯＲＩＡＬＡＮＡＬＹＳＩＳＯＦＡＮＮＵＡＬＥＲＯＳＩＯＮＡＣＣＲＥＴＩＯＮＣＹＣＬＥＳＯＦＴＩＤＡＬＦＬＡＴＳＩＮＴＨＥＦＲＯＮＴＡＲＥＡＯＦＴＨＥＳＯＵＴＨＥＲＮＣＨＡＮＧＪＩＡＮＧＲＩＶＥＲＤＥＬＴＡＹａｎｇＳｈｉｌｕｎ（杨世伦）Ｃｈｅ...

Modeling of biodiesel production: Performance comparison of Box–Behnken, face central composite and full factorial design

The performances of the response surface methodology(RSM)in connection with the Box–Behnken,face central composite or full factorial design(BBD,FCCD or FFD,respectively)were compared for the use in modeling of the NaOH-catalyzed sunflower oil ethanolysis.The influence of temperature,catalyst loading,and ethanol-to-oil molar ratio(EOMR)on fatty acid ethyl esters(FAEE)content was evaluated.All three multivariate strategies were efficient in the statistical modeling and optimization of the influential process variables but BBD and FCCD realization involved less number of experiments,generating smaller costs,requiring less work and consuming shorter time than the corresponding FFD.All three designs resulted in the same optimal catalyst loading(1.25%of oil)and EOMR(12:1).The reduced two-factorinteraction(2 FI)models based on the BBD and FCCD defined a range of optimal reaction temperature(25℃–75℃)and 25℃,respectively while the same model based on the 33 FFD appointed 75℃.The predicted FAEE content of about 97%–98.0%was close to the experimentally obtained FAEE content of about 97.0%–97.6%under the optimal reaction conditions.Therefore,the simpler BBD or FCCD might successfully be applied for statistical modeling of biodiesel production processes instead of the more extensive,more laborious and more expensive FFD.

Influence of parental sample sizes on the estimating genetic parameters in cultured clam Meretrix meretrix based on factorial mating designs

The precise and accurate knowledge of genetic parameters is a prerequisite for making efficient selection strategies in breeding programs.A number of estimators of heritability about important economic traits in many marine mollusks are available in the literature,however very few research have evaluated about the accuracy of genetic parameters estimated with different family structures.Thus,in the present study,the effect of parent sample size for estimating the precision of genetic parameters of four growth traits in clam M.meretrix by factorial designs were analyzed through restricted maximum likelihood（REML） and Bayesian.The results showed that the average estimated heritabilities of growth traits obtained from REML were 0.23-0.32 for 9 and 16 full-sib families and 0.19-0.22 for 25 full-sib families.When using Bayesian inference,the average estimated heritabilities were0.11-0.12 for 9 and 16 full-sib families and 0.13-0.16 for 25 full-sib families.Compared with REML,Bayesian got lower heritabilities,but still remained at a medium level.When the number of parents increased from 6 to 10,the estimated heritabilities were more closed to 0.20 in REML and 0.12 in Bayesian inference.Genetic correlations among traits were positive and high and had no significant difference between different sizes of designs.The accuracies of estimated breeding values from the 9 and 16 families were less precise than those from 25 families.Our results provide a basic genetic evaluation for growth traits and should be useful for the design and operation of a practical selective breeding program in the clam M.meretrix.

A Quantitative Factorial Component Analysis to Investigate the Recent Changes of Japan’s Weight-Based Food Self-Sufficiency Ratio

We investigate the weight-based food self-sufficiency ratio (WSSR) for Japan over a 50-year period (1961-2011) by applying factorial component analysis technique in order to measure the changes of the WSSR quantitatively. Quantitative data analysis is employed to determine the drivers of those changes. Numerical results show that Japan experienced a drastic decline in its food self-sufficiency ratio (FSSR) during the above period. The factorial component analysis shows that such a decline was caused by the changes in the FSSR of the food groups/items, not in the quantity of the food supply. A number of characteristics of those changes are presented and a list of major food groups that have major impacts on the changes is constructed. The findings in this paper reiterate the alarming food security problem in Japan and provide clear insight into the causes of this problem. The findings in this study pick up where previous studies have left off, aid the food-related policy-making process and identify new ideas for future food research.