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Music or other background sounds are often played in barns as environmental enrichment for animals on farms or to mask sudden disruptive noises. Previous studies looking at the effects of this practice on non-human animal well-being and productivity have found contradictory results. However, there is still a lack of discussion on whether piglets have the ability to distinguish different types of music. In this study, we exposed piglets to different music conditions to investigate whether the piglets preferred certain music types, in which case those types would have the potential to be used as environmental enrichment. In total, 30 piglets were tested for music type preference to determine whether growing pigs respond differently to different types of music. We used music from two families of instruments (S: string, W: wind) and with two tempos (S: slow, 65 beats/min (bpm); F: fast, 200 bpm), providing four music-type combinations (SS: string-slow; SF: string-fast; WS: wind-slow; WF: wind-fast). The piglets were given a choice between two chambers, one with no music and the other with one of the four types of music, and their behaviour was observed. The results showed that SS and WF music significantly increased residence time (P<0.01) compared with the other music conditions. Compared with the control group (with no music), the different music conditions led to different behavioural responses, where SS music significantly increased lying (P<0.01) and exploration behaviour (P<0.01); SF music significantly increased tail-wagging behaviour (P<0.01); WS music significantly increased exploration (P<0.01); and WF music significantly increased walking, lying, standing and exploration (all P<0.01). The results also showed that musical instruments and tempo had little effect on most of the behaviours. Fast-tempo music significantly increased walking (P=0.02), standing (P<0.01) and tail wagging (P=0.04) compared with slow-tempo music. In conclusion, the results of this experiment show that piglets are more sensitive to tempo than to musical instruments in their response to musical stimulation and seem to prefer SS and WF music to the other two types. The results also suggest a need for further research on the effect of music types on animals.
A multichannel calorimeter system is designed and constructed which is capable of delivering single-shot and broad-band spectral measurement of terahertz (THz) radiation generated in intense laser–plasma interactions. The generation mechanism of backward THz radiation (BTR) is studied by using the multichannel calorimeter system in an intense picosecond laser–solid interaction experiment. The dependence of the BTR energy and spectrum on laser energy, target thickness and pre-plasma scale length is obtained. These results indicate that coherent transition radiation is responsible for the low-frequency component (
1 THz) of BTR. It is also observed that a large-scale pre-plasma primarily enhances the high-frequency component (
3 THz) of BTR.
Heading date (HD) and flowering date (FD) are critical for yield potential and stability, so understanding their genetic foundation is of great significance in wheat breeding. Three related recombinant inbred line populations with a common female parent were developed to identify quantitative trait loci (QTL) for HD and FD in four environments. In total, 25 putative additive QTL and 20 pairwise epistatic effect QTL were detected in four environments. The additive QTL were distributed across 17 wheat chromosomes. Of these, QHd-1A, QHd-1D, QHd-2B, QHd-3B, QHd-4A, QHd-4B and QHd-6D were major and stable QTL for HD. QFd-1A, QFd-2B, QFd-4A and QFd-4B were major and stable QTL for FD. In addition, an epistatic interaction test showed that epistasis played important roles in controlling wheat HD and FD. Genetic relationships between HD/FD and five yield-related traits (YRTs) were characterized and ten QTL clusters (C1–C10) simultaneously controlling YRTs and HD/FD were identified. The present work laid a genetic foundation for improving yield potential in wheat molecular breeding programmes.
Muons produced by the Bethe–Heitler process from laser wakefield accelerated electrons interacting with high
materials have velocities close to the laser wakefield. It is possible to accelerate those muons with laser wakefield directly. Therefore for the first time we propose an all-optical ‘Generator and Booster’ scheme to accelerate the produced muons by another laser wakefield to supply a prompt, compact, low cost and controllable muon source in laser laboratories. The trapping and acceleration of muons are analyzed by one-dimensional analytic model and verified by two-dimensional particle-in-cell (PIC) simulation. It is shown that muons can be trapped in a broad energy range and accelerated to higher energy than that of electrons for longer dephasing length. We further extrapolate the dependence of the maximum acceleration energy of muons with the laser wakefield relativistic factor
and the relevant initial energy
. It is shown that a maximum energy up to 15.2 GeV is promising with
on the existing short pulse laser facilities.
Light colors may affect poultry behaviors, well-being and performance. However, preferences of layer pullets for light colors are not fully understood. This study was conducted to investigate the pullet preferences for four light-emitting diode colors, including white, red, green and blue, in a lighting preference test system. The system contained four identical compartments each provided with a respective light color. The pullets were able to move freely between the adjacent compartments. A total of three groups of 20 Chinese domestic Jingfen layer pullets (54 to 82 days of age) were used for the test. Pullet behaviors were continuously recorded and summarized for each light color/compartment into daily time spent (DTS), daily percentage of time spent (DPTS), daily times of visit (DTV), duration per visit, daily feed intake (DFI), daily feeding time (DFT), feeding rate (FR), distribution of pullet occupancy and hourly time spent. The results showed that the DTS (h/pullet·per day) were 3.9±0.4 under white, 1.4±0.3 under red, 2.2±0.3 under green and 4.5±0.4 under blue light, respectively. The DTS corresponded to 11.7% to 37.6% DPTS in 12-h lighting periods. The DTV (times/pullet·per day) were 84±5 under white, 48±10 under red, 88±10 under green and 94±8 under blue light. Each visit lasted 1.5 to 3.2 min. The DFI (g/pullet·per day) were 27.6±1.7 under white, 7.1±1.6 under red, 15.1±1.1 under green and 23.1±2.0 under blue light. The DFT was 0.18 to 0.65 h/pullet·per day and the FR was 0.57 to 0.75 g/min. For most of the time during the lighting periods, six to 10 birds stayed under white, and one to five birds stayed under red, green and blue light. Pullets preferred to stay under blue light when the light was on and under white light 4 h before the light off. Overall, pullets preferred blue light the most and red light the least. These findings substantiate the preferences of layer pullets for light colors, providing insights for use in the management of light-emitting diode colors to meet pullet needs.
Keratin-associated proteins (KAPs) are constituents of wool and hair fibres and are believed to play an important role in determining the characteristics of the fibres. In the current study, a polymerase chain reaction-single stranded conformational polymorphism (PCR-SSCP) approach was used to screen for variation in the ovine KAP15-1 gene (KRTAP15-1). Four PCR-SSCP banding patterns, representing four different variants (named A to D), were detected. Four single nucleotide polymorphisms were found within the coding region and three of these were non-synonymous. The effect of this genetic variation on wool traits was investigated in 396 Merino × Southdown-cross sheep. Of the three variants found in these sheep (A, B and C), the presence of B was found to be associated with decreased wool yield, while C was associated with increased wool yield and decreased fibre diameter standard deviation. Sheep of genotype AC had a higher wool yield than those of genotype AA or AB.
β-Casomorphin is an opioid-like bioactive peptide derived from β-casein of milk that plays a crucial role in modulating animal’s feed intake, growth, nutrient utilization and immunity. However, the effect of β-casomorphin on lipid metabolism in chickens and its mechanism remain unclear. The aim of this study was to investigate the effects of β-casomorphin on fat deposition in broiler chickens and explore its mechanism of action. A total of 120 21-day-old Arbor Acres male broilers (747.94±8.85 g) was chosen and randomly divided into four groups with six replicates of five birds per replicate. Three groups of broilers were injected with 0.1, 0.5 or 1.0 mg/kg BW of β-casomorphin in 1 ml saline for 7 days, whereas the control group received 1 ml saline only. The results showed that subcutaneous administration of β-casomorphin to broiler chickens increased average daily gain, average daily feed intake and fat deposition, and decreased feed : gain ratio (P<0.05). The activity of malate dehydrogenase in the pectoral muscle, liver and abdominal adipose tissue was also increased along with the concentrations of insulin, very-low-density lipoprotein and triglyceride in the plasma (P<0.05). The activity of hormone-sensitive lipase in the liver and abdominal adipose tissue and the concentration of glucagon in the plasma were decreased by injection with β-casomorphin (P<0.05). Affymetrix gene chip analysis revealed that administering 1.0 mg/kg BW β-casomorphin caused differential expression of 168 genes in the liver with a minimum of fourfold difference. Of those, 37 genes are directly involved in lipid metabolism with 18 up-regulated genes such as very low density lipoprotein receptor gene and fatty acid synthase gene, and 19 down-regulated genes such as lipoprotein lipase gene and low density lipoprotein receptor gene. In conclusion, β-casomorphin increased growth performance and fat deposition of broilers. Regulation of fat deposition by β-casomorphin appears to take place through changes in hormone secretion and enzyme activities by controlling the gene expression of lipid metabolism and feed intake, increasing fat synthesis and deposition.
Background: With advancements in technology, the use of video as a pedagogical method in medical education has gained in popularity, and may aid in teaching clinical skills. In the UBC MD program, videos have been used to assist in teaching the -neurological exam for several decades, but the currently available videos are outdated and not of contemporary quality. Methods: Drawing upon the cognitive theory of multimedia learning from Mayer and Moreno (2003) which describes methods to maximize learning by minimizing cognitive load, we developed a tool to systematically assess pedagogical videos. We inventoried twelve existing neurology videos and analyzed their use of methods such as weeding (removing extraneous information), signalling (visually highlighting important information), and chunking (grouping similar information together). Results: Generally, older videos had poor audiovisual quality that introduced extraneous load, while more current videos had higher production value, albeit inconsistent with the depth of their content. We therefore produced a new three-part neurological exam video series. We wrote storyboards, filmed with a focus on visually depicting the exam and findings, and edited to elucidate relevant physiological concepts. Conclusions: The end product has been adopted by the UBC MD program, and can be shared with other programs who may wish to adopt them.
Giant electromagnetic pulses (EMP) generated during the interaction of high-power lasers with solid targets can seriously degrade electrical measurements and equipment. EMP emission is caused by the acceleration of hot electrons inside the target, which produce radiation across a wide band from DC to terahertz frequencies. Improved understanding and control of EMP is vital as we enter a new era of high repetition rate, high intensity lasers (e.g. the Extreme Light Infrastructure). We present recent data from the VULCAN laser facility that demonstrates how EMP can be readily and effectively reduced. Characterization of the EMP was achieved using B-dot and D-dot probes that took measurements for a range of different target and laser parameters. We demonstrate that target stalk geometry, material composition, geodesic path length and foil surface area can all play a significant role in the reduction of EMP. A combination of electromagnetic wave and 3D particle-in-cell simulations is used to inform our conclusions about the effects of stalk geometry on EMP, providing an opportunity for comparison with existing charge separation models.
The present study evaluated the effects of isovalerate supplementation on the development of the small intestinal mucosa in dairy calves. Forty-eight Chinese Holstein bull calves at 15 days of age and 45.1 ± 0.36 kg of body weight were assigned randomly to four groups. The treatments were control, low-isovalerate, moderate-isovalerate and high-isovalerate with 0, 3, 6 and 9 g isovalerate per calf per day, respectively. The study comprised 75 days with a 15-day adaptation period followed by a 60-day sampling period. Calves were weaned at 60 days of age. Six calves were chosen from each treatment at random and slaughtered at 30 and 90 days of age. The small intestine morphology and activities of amylase and trypsin improved significantly with increasing age. No interaction between treatments and age was observed. The small intestine length, mucosa layer thickness, villus height and crypt depth increased linearly with increasing isovalerate supplementation. However, the ratio of villus height to crypt depth was not affected by treatment. Activities of amylase and trypsin increased linearly. The lactase activity increased linearly during the 75-day period and for pre-weaned calves but was unaltered for post-weaned calves. The relative mRNA expressions of growth hormone receptor, insulin-like growth factor-1 receptor and sodium-glucose co-transporter-1 in the small intestine mucosa increased linearly, and a similar pattern was observed for the expression of peptide transporter-1 in the duodenum and proximal jejunum. The results suggested that small intestine development was promoted by isovalerate in a dose-dependent manner.
Branched-chain volatile fatty acids (BCVFA) supplements could promote lactation performance and milk quality by improving ruminal fermentation and milk fatty acid synthesis. This study was conducted to evaluate the effects of BCVFA supplementation on milk performance, ruminal fermentation, nutrient digestibility and mRNA expression of genes related to fatty acid synthesis in mammary gland of dairy cows. A total of 36 multiparous Chinese Holstein cows averaging 606±4.7 kg of BW, 65±5.2 day in milk (DIM) with daily milk production of 30.6±0.72 kg were assigned to one of four groups blocked by lactation number, milk yield and DIM. The treatments were control, low-BCVFA (LBCVFA), medium-BCVFA (MBCVFA) and high-BCVFA (HBCVFA) with 0, 30, 60 and 90 g BCVFA per cow per day, respectively. Experimental periods were 105 days with 15 days of adaptation and 90 days of data collection. Dry matter (DM) intake tended to increase, but BW changes were similar among treatments. Yields of actual milk, 4% fat corrected milk, milk fat and true protein linearly increased, but feed conversion ratio (FCR) linearly decreased with increasing BCVFA supplementation. Milk fat content linearly increased, but true protein content tended to increase. Contents of C4:0, C6:0, C8:0, C10:0, C12:0, C14:0 and C15:0 fatty acids in milk fat linearly increased, whereas other fatty acids were not affected with increasing BCVFA supplementation. Ruminal pH, ammonia N concentration and propionate molar proportion linearly decreased, but total VFA production and molar proportions of acetate and butyrate linearly increased with increasing BCVFA supplementation. Consequently, acetate to propionate ratios linearly increased. Digestibilities of DM, organic matter, CP, NDF and ADF also linearly increased. In addition, mRNA expressions of peroxisome proliferator-activated receptor γ, sterol regulatory element-binding factor 1 and fatty acid-binding protein 3 linearly increased, mRNA expressions of acetyl-coenzyme A carboxylase-α, fatty acid synthase and stearoyl-CoA desaturase quadratically increased. However, lipoprotein lipase mRNA expression was not affected by treatments. The results indicated that lactation performance and milk fat synthesis increased with BCVFA supplementation by improving ruminal fermentation, nutrient digestibility and mRNA expressions of genes related to milk fat synthesis.
The mammalian target of rapamycin (mTOR) has been shown to be involved in lipopolysaccharide (LPS)-induced immune responses in many mammal cells. Here, we suggest that the mTOR pathway is involved in the intestinal inflammatory responses evoked by LPS treatment in chicken embryos. The intestinal tissue from Specific pathogen free chick embryos was cultured in the presence of LPS for 2 h. Secretory immunoglobulin A (sIgA) concentrations, messenger RNA (mRNA) expression of cytokines, and protein levels of nuclear factor-κB (NF-κB), mitogen-activated protein kinase (MAPK), mTOR and p70 ribosomal S6 kinase (p70S6K) were determined. The results showed that LPS treatment increased sIgA concentrations in a dose-dependent manner. The mRNA levels of interleukine (IL)-6, IL-8, IL-10, tumor necrosis factor-α and Toll-like receptor (TLR) 4 were upregulated by LPS treatment (P<0.05). Lipopolysaccharide increased the phosphorylation of Jun N-terminal kinase (JNK), p38 MAPK and NF-κB (P<0.05) while decreasing the phosphorylation level of mTOR (P<0.05). Supplementation of leucine at doses of 10, 20 and 40 mM dose-dependently decreased sIgA production. Leucine supplementation at 40 mM restored the phosphorylation level of mTOR and p70S6K while suppressing the phosphorylation levels of NF-κB (P<0.05) and partially down-regulating the phosphorylation of p38 MAPK and JNK. The transcription of IL-6 was significantly decreased by leucine supplementation. These results suggested that leucine could alleviate LPS-induced inflammatory responses by down-regulating NF-κB signaling pathway and evoking mTOR/p70S6K signaling pathway, which may involve in the regulation of the intestinal immune system in chicken embryos.
This study aims to investigate the climate–malaria associations in nine cities selected from malaria high-risk areas in China. Daily reports of malaria cases in Anhui, Henan, and Yunnan Provinces for 2005–2012 were obtained from the Chinese Center for Disease Control and Prevention. Generalized estimating equation models were used to quantify the city-specific climate–malaria associations. Multivariate random-effects meta-regression analyses were used to pool the city-specific effects. An inverted-U-shaped curve relationship was observed between temperatures, average relative humidity, and malaria. A 1 °C increase of maximum temperature (Tmax) resulted in 6·7% (95% CI 4·6–8·8%) to 15·8% (95% CI 14·1–17·4%) increase of malaria, with corresponding lags ranging from 7 to 45 days. For minimum temperature (Tmin), the effect estimates peaked at lag 0 to 40 days, ranging from 5·3% (95% CI 4·4–6·2%) to 17·9% (95% CI 15·6–20·1%). Malaria is more sensitive to Tmin in cool climates and Tmax in warm climates. The duration of lag effect in a cool climate zone is longer than that in a warm climate zone. Lagged effects did not vanish after an epidemic season but waned gradually in the following 2–3 warm seasons. A warming climate may potentially increase the risk of malaria resurgence in China.
Iron-deficiency anemia is a public health concern that frequently occurs in pregnant mammals and neonatal offspring. Ferrous N-carbamylglycinate chelate (Fe-CGly) is a newly designed iron fortifier with proven effects in iron-deficient rats and weanling piglets. However, the effects of this new compound on pregnant mammals are unknown. Therefore, this experiment was conducted to evaluate the effects of Fe-CGly on sow reproductive performance and iron status of both sows and neonatal piglets. A total of 40 large-white sows after second parity were randomly assigned to two groups (n=20). They were receiving a diet including 80 mg Fe/kg as FeSO4 or Fe-CGly, respectively, from day 85 of gestation to parturition. The serum (day 110 of pregnancy) and placentas of sows were sampled. Litter size, mean weight of live born piglets, birth (live) litter weight, number of live born piglets, and the number of still-born piglets, mummies, and weak-born piglets were recorded. Once delivered, eight litters were randomly selected from the 20 litters per treatment, and one new-born male piglet (1.503±0.142 kg) from each selected litter was slaughtered within 3 h after birth from the selected litters, without colostrum ingestion. The serum, longissimus muscle, liver and kidneys of the piglets were collected. The iron status of the serum samples and the messenger RNA level of iron-related genes in the placenta, liver and kidney were analyzed. The results showed that litter weight of live born piglets was higher (P=0.030) in the Fe-CGly group (19.86 kg) than in the FeSO4 group (17.34 kg). Fe-CGly significantly increased placental iron concentration (P<0.05) of sows. It also significantly increased iron saturation and reduced the total iron-binding capacity of piglets (P<0.05) at birth. However, the results revealed that supplementation of Fe-CGly in sows reduced liver and kidney iron concentration of neonatal piglets (P<0.05), indicating decreased iron storage. In addition, the concentration of iron in the colostrum was not significantly changed. Therefore, the present results suggested that replacement of maternal FeSO4 supplement with Fe-CGly in the late-gestating period for sows could improve litter birth weight, probably via enhanced iron transportation in the placenta.
Honeybee foraging can transfer exogenous genes from genetically modified (GM) oilseed rape (Brassica napus L.) to closely related plants, which not only induces potential ecological risks but also contaminates non-GM seeds or honey products with GM ingredients. These events may lead to international trade disputes. Chinese honeybees (Apis cerana cerana Fabricius) and a herbicide (glufosinate)-resistant GM strain of B. napus (Z7B10) were studied to examine the effects of honeybee short-range foraging on oilseed rape gene flow and honey ingredients. Results showed variable frequencies of gene flow between GM and non-GM oilseed rape cultivars, with the highest frequency under nylon net isolation with artificially stocked honeybees, the lowest frequency under nylon net isolation alone, and an intermediate frequency under natural pollination, suggesting the important role of honeybee foraging in gene flow frequency. Additionally, GM pollen grains were found in honey collected from honeybees foraging on both GM and non-GM oilseed rape cultivars. The phosphinothricin acetyltransferase protein was also detected in both unbroken pollen-containing and pollen-free honey by protein testing strips, suggesting that honeybee foraging on GM oilseed rape could lead to contamination with GM ingredients. Overall, the results provide a direct scientific basis for the ecological risk assessment and safety management of GM oilseed rape.
To explore the effects of maternal nutrition on offspring muscle characteristics, a total of 56 sows were assigned to one of the four dietary groups during gestation: control (CON), or control diets supplemented with methyl donor (MET), bisphenol A (BPA), and combined BPA and MET (BPA+MET). Compared with CON offspring, MET offspring showed a higher meat redness value, but lower glycogen content in the longissimus thoracis (LT). Moreover, compared with CON offspring, MET offspring showed lower LT glycogen synthase (GS) mRNA levels at birth and the finishing stage, and increased methylation at the GS promoter. Prenatal BPA exposure reduced the pH and redness value of meat, but increased the lightness value, lactate content, glycolytic potential and lactate dehydrogenase (LDH) enzyme activity in the LT muscle. Prenatal BPA exposure increased LDH mRNA levels in the LT muscle at birth and the finishing stage, and reduced methylation at the LDH promoter. Thus, maternal MET affects muscle GS and LDH expression via DNA methylation, thereby resulting in persistent effects on pork quality.
A liquid chromatography mass spectrometry method for determination of clothianidin in brown rice, straw, rice hull, paddy water and paddy sediment was developed and residue levels were determined in the different components. The limit of quantification was set at 0·01 mg/kg for the matrices studied. Clothianidin degradation in straw, paddy water and soil was studied, and clothianidin residues in brown rice, straw, hull and paddy soil were determined. Concurrent recoveries were between 85·6 and 92·5%, with relative standard deviations ranging from 1·3 to 6·8% at three fortification levels between 0·01 and 5·0 mg/kg. The half-lives in straw, paddy water and paddy sediment were found to be 1·9–4·9, 4·1–5·0 and 4·9–6·3 days, respectively. The maximum residues in brown rice, straw, hull and paddy soil samples were 0·38, 1·88, 1·38 and 0·14 mg/kg, respectively.
The current experiment was conducted to evaluate the effects of different dietary protein levels and rumen-protected folic acid (RPFA) supplementation on ruminal fermentation, microbial enzyme activity, bacterial populations and urinary excretion of purine derivatives (PD) in growing beef steers. Low-protein (LP) or high-protein (HP) diets were fed to eight ruminally cannulated first-generation cross-bred (Blonde d'Aquitaine × Simmental) beef steers with or without RPFA supplementation. Steers were fed a total mixed ration, and dietary concentrate to maize silage ratio was 50 : 50 (dry matter (DM) basis). No interaction between dietary crude protein (CP) levels and RPFA supplementation was observed during the experiment. Ruminal pH was unaffected by RPFA supplementation, but decreased with increasing dietary CP levels. Ruminal total volatile fatty acid concentration increased with increasing dietary CP levels or RPFA supplementation. Molar proportion of acetate increased with RPFA supplementation, but tended to decrease with increasing dietary CP levels. The proportion of propionate decreased with RPFA supplementation, but was unaffected by dietary CP levels. As a result, the acetate to propionate ratio increased with RPFA supplementation, but tended to be lower for the HP diets than the LP diets. Ammonia-nitrogen content decreased with RPFA supplementation, but increased with increasing dietary CP levels. In situ ruminal degradability of maize straw and concentrate increased with increasing dietary CP levels or RPFA supplementation. Microbial enzyme (carboxymethyl-cellulase, cellobiase, xylanase, pectinase, α-amylase and protease) activity, bacterial populations (Ruminococcus albus, Ruminococcus flavefaciens, Butyrivibrio fibrisolvens, Prevotella ruminicola, Fibrobacter succinogenes and Ruminobacter amylophilus) and urinary PD excretion increased with increasing dietary CP levels or RPFA supplementation. The current study showed that increasing dietary CP levels from 109·1 to 130·7 g/kg DM or supplementing 75 mg RPFA improved ruminal fermentation and microbial protein synthesis by increasing bacterial population and microbial enzyme activity.
We have suggested a scenario of fractal turbulence which might explain the origin of galaxies and the observed large scale structure of the universe (Liu and Deng, 1987). Under the condition of the early universe, the cosmic fluid can be regarded as incompressible. If we assume that the density perturbations in the early universe are adiabatic and have the scale-free Zeldovich spectrum, we may obtain the spectrum of the velocity perturbations. Perturbations with scales less than horizon will undergo dissipative process by Thomson scattering. So, the cosmic fluid can be considered as a viscous fluid (Peebles, 1971). We can find the largest and smallest scale of the perturbations in the cosmic fluid by taking account of the Reynold's number on given scale and the scale of horizon. Using the present values of Hubble constant and the mean density of matter, we have found that on the scale of horizon the Reynold's number is just the order of 102. This result shows that perturbations with scale a little smaller than horizon may produce Karman vortices before recombination and the vortices might form fractal turbulence due to Thomson drag.
In this work, we start from the definition of fractal dimension and by the number counting of galaxies to investigate that if the large scale distribution of galaxies has really a fractal structure. A fractal dimension in a distribution of objects is defined as
where N(R) is the number of objects within scale R. To find out D from number counting we have to pay attention to that the distribution of galaxies could not be a regular fractal map. The N(R) would understand as a statistical average. To avoid the edge effect appearing in the number counting we compare it with that obtained from an average by many times Monte Carlo sampling which is a uniform distribution and would have Dr = 3. From eq. (1) we get