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 频数
 frequency
 There were no remarkable differences of the allelic and genotypic frequency distributions of KPNA1 between parents and patients(χ~2=0.957,P=0.328;χ~2=3.547,P=0.170). 等位基因和基因型的频数分布在父母组和患者组中的差异均无显著性(2χ=0.957,P=0.328;χ2=3.547,P=0.170); 短句来源 The genotype frequency and allele frequency of 76 NSCL/P cases and 60 controls were analyzed through case-control study(χ~2=4.42,P<0.05). 76例NSCL/P患儿和60例正常儿童基因型及等位基因频数病例对照研究(χ2=4.42,P<0.05)。 短句来源 The genotype frequency and allele frequency of 76 NSCL/P cases and 60 controls were analyzed through case-control study(χ~2=9.91,P<0.05). 76例NSCL/P患儿和60例正常儿童基因型及等位基因频数病例对照研究(χ2=9.91,P<0.05)。 短句来源 The urinary iodine value frequency was 26.1%, 13.5% and 9.9%. 尿碘值频数分布为26.1%、13.5%和9.9%。 短句来源 there were no remarkable differences of the frequency distributions of GG,GC and CC of MT2A between cases and controls(χ~2=0.202,P>0.05),and the frequency distributions of G and C had no markedly differences between cases and controls(χ~2=0.136,P>0.05). MT2A的3种基因型GG、GC和CC的频数分布在病例组和对照组中无统计学意义(2χ=0.202,P>0.05),等位基因G和C的频数分布在病例组和对照组中也无统计学意义(2χ=0.136,P>0.05)。 短句来源 更多
 frequence
 Three-Dimensional Topology Creator of Complex Network and Application of SD Frequence Analysis 复杂网络三维拓扑生成器及其在SD频数分析中的应用 短句来源 Results: (1) Western blotting was used to identify the purified proteins, and it confirmed that the proteins are HSPgp96. (2) The HSPgp96-peptide complex and polypeptide derived the renal carcinoma tissues can produce the significantly more frequence of IFN-γ ~+T cell than normal renal tissues(p<0.01). 结果:(1)纯化所得蛋白用特异Western blotting鉴定,证实该蛋白确系HSPgp96; (2)肿瘤组中HSPgp96-肽复合物、单纯多肽产生γ-干扰素效应T细胞频数均明显高于正常对照组(p<0.01); 短句来源 [Methods]The numbers,maximal diameter and pathology of lymph nodes dissected from the 115 cases with gastric cancer were analyzed. The correlation between metastatic frequence and lymph nodes'size was investigated. [方法]分析115例胃癌患者手术摘取的淋巴结数目、最大径、病理结果,探讨转移频数与淋巴结大小的相关性。 短句来源 (3) The HSPgp96-peptide complex derived from the renal carcinoma tissues can produce the maximum frequence of IFN- γ ~+T cell, and the frequence was significantly more than stimulus. (3)肿瘤组中HSPgp96-肽复合物产生γ-干扰素效应T细胞频数最高,与同组其他刺激物及正常对照组的HSPgp96-肽复合物相比差异有显著性意义(p<0.01)。 短句来源 Among the 19 factors with higher frequence percentage, the frequence percentage of 16 factors were obviously decreased. 在测得的 19项频数百分率较高的应激因素中 ,有 16项明显下降。 短句来源 更多
 frequency number
 The mathematics model of each evaluation index sign and dry factors were established through weighted value evaluation and the frequency number analyses to multi-targets to get the precise solution, four equal important evaluation target in theoretical and get the optimizing drying craft parameter: hot air temperature 177±1℃,hot air velocity 0.44±0.01m/s ,the original water of material 63.5±1.5%, dry duration l. 建立以各评价指标与干燥因素的数学模型，并采用加权综合评分与频数分析法对多目标进行优化求解，从理论上得到同等重视4个评价指标(λ_1=λ_2=λ_3=λ_4=0.25)时最优的干燥工艺参数为：热风温度177±1℃，热风速度0.44±0.01m／s，物料初始水分 短句来源 The optimal combinative scheme of comprehensive agronomic measures for top yield level was showed by the frequency number analysis Scientific basis was provided for spring soybean Zhechun 2 on model cultivation in large areas 通过频数分析，得出指定产量水平下的最佳农艺措施组合方案，为浙春2号春大豆大面积规范化栽培提供依据。 短句来源 The interpolation precision of pulse multiplier-based fine interpolator is related with the max feed rate,pulse equivalent of CNC,interpolation cycle,and output pulse frequency of pulse generator and the main reason of its error production comes from the rounding processing of crossover frequency number. 基于脉冲乘法器原理的精插补器的插补精度与最大进给速度、机床系统的脉冲当量、插补周期以及脉冲发生器的输出脉冲频率有关,其误差产生的主要原因是由分频数圆整造成的。 短句来源 The optimal combinative scheme of composite high-yield agronomic measures for top yield level was showed by the frequency number analysis. 通过频数分析，得出指定产量水平下的最佳综合农艺措施给合方案。 短句来源 On the assumption that acceleration time history can be obtained by stationary random processes multiplied envelop function, this paper demonstrates that envelop function of strong ground motion is proportional to the square root of frequency number distribution function of phase difference spectrum. 假定地震加速度时程a(t)可由强度包线f(t)乘以均值为零的平稳随机过程a_g(t)构成,从理论上论证了地震动强度包线函数与相位差谱的频数分布函数成正变关系。 短句来源 更多
 tc frequency
 Preliminary results indicated that in the variation of annual TC frequency there exist obvious periods of 21, 31 ,15 and 6 years and sustaining periods lasting 12 years in average. 初步结果表明，热带气旋年频数的变化具有明显的21年、31年、15年和6年左右的周期和持续期平均为12年左右的阶段变化； 短句来源 There are quasi-13-year medium period vibration and quasi-4 and quasi-2.5-year short period vibration in TC frequency time serials, among which quasi-4 year period is the most significance. 影响福建热带气旋频数具有准13年的中周期振动和准4年和准2.5年的短周期振动,尤其是4年的短周期振动最为显著。 短句来源 The research also shows that the annual TC frequency forecast for Hainan by the regression equation,using soil temperatures as predictors,shows good results. 研究表明,利用深层地温作为预报因子,建立回归方程,对影响海南的TC年频数进行预报,具有较好的效果。 短句来源 The Relationship between the TC Frequency Affecting Hainan and the Variation of Soil Temperature in Hainan 海南地温变化与热带气旋影响频数关系 短句来源 By using data in the period of 1949-2000, climatic characteristics of tropical cyclones over western North Pacific in the latest 50 years are investigated. The results show that there exists a descent trend in tropical cyclone(TC) frequency over western North Pacific and landfall TC frequency in China, Southern China and Eastern China in recent 50 years, and the trend becomes significant in the latest 10 years. 本文首先利用1949-2000年《热带气旋年鉴》资料，分析了近50年西北太平洋热带气旋的气候特征，结果表明：近50年来，西北太平洋热带气旋频数以及登陆全国、华南和东海沿岸的热带气旋频数呈下降趋势，特别是在近十年，这种下降趋势更明显。 短句来源 更多

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 frequency
 Frequency-Domain Bounds for Nonnegative, Unsharply Band-Limited Functions In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms. We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization. This paper presents an expansion for radial tempered distributions on ${\bf R}^n$ in terms of smooth, radial analyzing and synthesizing functions with space-frequency localization properties similar to standard wavelets. The Balian-Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(t-na)\}_{m,n \in \mbox{\bf Z}}$ 更多
 frequence
 The results show that 10 μmol/L Lacidipine can reduce the frequence which 10 μmol/L 5-HT induced [Ca2+] spark in SFSMC of calcium over loading to 50%, and amplitude to 50% or so. The program simulation facilities, such as time-domain analysis, frequence-domain analysis, sensitivity analysis and multiple objective optimization are described. La frequence de mue decline avec la taille, de facon prononcee chez les femelles de plus de 6 ans. Cet Isopode a ete recolte sur la totalite de l'aire prospectee mais avec une frequence peu elevee: 91% des prelevements contenaient 1 a 5 specimens et un total de 140 individus ont ete recoltes. Il est postule que cette specialisation trophique pourrait expliquer certaines caracteristiques inhabituelles tels la presence d'une seule femelle adulte de Zalophora par diplopode, la faible frequence des juveniles et l'apparente absence des males. 更多
 frequency number
 On the basis of the relation, frequency number distribution function of wave group arrival time is completely equivalent to that of phase difference spectra. Intromission frequency (number of intromissions preceding ejaculation) was affected only at 10 μg/kg 8-OH-DPAT with monkeys requiring fewer intromissions to ejaculation at this dose. However, there was some indication that the effective mating frequency (number of females producing offspring sired by a given male) of major and minor males may exhibit frequency dependence. Averaged over media, callus induction frequency (number of calli per 100 anthers) was highest in cultivars Xin White and TX 403-TSB (6.7 and 3.9%, respectively). Line-intercept estimates of large wood frequency (number per 100?m of stream) were significantly correlated to the wood census counts, but the line-intercept method underestimated frequency by about 50% (P?=?0.016). 更多
 absolute frequency
 Improved absolute frequency measurement of the 115In+ 5s2 1S0-5s5p3P0 narrowline transition: Progress towards an optical frequen We report on an improved absolute frequency measurement of the 5s2 1S00-5s5p3P0 narrowline clock transition at 236.5 nm, for a single, trapped, and laser-cooled 115In ion. For absolute frequency measurement, we use an optical frequency comb locked to a cesium clock as the reference. The source generates waves with the same absolute frequency 1/15 d-1 but different wavenumber. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius χ(ω)-χ(0)α(-iω)v at and below the AT line. 更多
其他
 Using Synoptic data for 1951—1955,a statistical investigation on theanticyclone in Eastern Asia is made.The clasification(according to path),frequency,central intencity,variation of the intensity and the velocity of the anticyclones over EasternAsia are given. 作者根据1951—1955年天气图资料,应用统计的方法来探讨东亚地区的反气旋活动。从而提供了东亚反气旋的标准分类路径、出现的频数、中心强度、强度变化及移行速度等。 Based on the 10-years surface synoptic charts (1951 to 1960), monthly frequencies of cyclones and low pressure centers passing 2.5°× 2.5°latitude-longitude grids in Eastern Asia are analized and the main tracks are studied and classified.The cyclones are most frequent in middle part of Mongolia and north-east China, and none south of 20°N. Most of the low pressures occurred south of 45°N are very weak. Spring is the season of cyclonic activity. 本文利用1951—1960年的亚洲地面天气图,分月統計东亚地区(70°E以东,55°N以南)每2.5°×2.5°經緯格內低压中心通过的頻数,繪制了頻数分布图,确定出低压移动的主要路径,此外,还繪制了冬半年和夏半年低压发生(初現)頻数分布图、頻数百分率的随緯度分布和沿120°E与110°E經线上低压中心通过頻数的各月綜合图。結果得出:1.东亚大陆中緯度西风带的低压主要出現在蒙古人民共和国中部到我国的东北地区,20°N以南不出現溫带低气压;2.45°N以南的我国大陆上低压很弱,大多数不閉合,只有在我国东部或入海后才发展;3.日本东南面海上是低压路径的集中带;4.春季低压出現最为頻繁,秋季次之,夏季我国江淮流域低压有所增多。 最后,对低压路径进行了分类,把东亚的溫带低气压划为五大类和十一亚类,并对各类低压分别作了簡要的叙述。 Based on the daily 18:00 GCT surface, charts(1955 to 1959), the frequency distribution of the front occurrence is analysed and the location of the climatic frontal zones is determined. 本文根据1955—1959年逐日02时(北京时)东亚地面天气图統計了鋒出現頻数的分布,給出1、4、7、10月东亚气候锋的位置. << 更多相关文摘
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G-cirulant matrices

Dear the community,

I wonder whether there is a built-in library/function for $G$-circulant matrices in SAGE? Here $G$ is a group and a matrix $A$ is called $G$-circulant if $A$ has the form $A=(a_{ \tau^{-1} \sigma})_{\tau, \sigma \in G}$. Please see [1] for further details.

When $G=\mathbb{Z}/n$, SAGE has a built-in library/function. Namely, given a vector $v$ of length $n$, we can generate a circulant matrix with the first row equal to $v$ using the following code

matrix.circulant(v)

[1] Kanemitsu, Shigeru, and Michel Waldschmidt. "Matrices of finite abelian groups, finite Fourier transform and codes, Proc. 6th China-Japan Sem. Number Theory, World Sci. London-Singapore-New Jersey (2013): 90-106.

G-cirulant matrices

Dear the community,

I wonder whether there is a built-in library/function for $G$-circulant matrices in SAGE? Here $G$ is a group and a matrix $A$ is called $G$-circulant if $A$ has the form $A=(a_{ \tau^{-1} \sigma})_{\tau, \sigma \in G}$. Please see [1] for further details.

When $G=\mathbb{Z}/n$, SAGE has a built-in library/function. Namely, given a vector $v$ of length $n$, we can generate a circulant matrix with the first row equal to $v$ using the following code

matrix.circulant(v)

format: plain


text:
# Drawing in Slashes

Write a program that takes in a rectangular block of text made up of X's and .'s, such as this rough A:

......
..XX..
.X..X.
.XXXX.
.X..X.
.X..X.

Output a representation of this grid rotated 45 degrees counterclockwise by drawing a slash — forward or backward depending on context — everywhere an X borders a . or the side of the grid (with spaces filling in the rest):

 /\/\
/ /\ \
\/ /  \
/\/ /\ \
\  /  \/
\ \
\ \
\/

The number of trailing and leading spaces (and newlines) doesn't matter as long as the shape of the X's in the input is maintained by the slashes. It's ok to trim extra rows or columns of .'s.

For I/O you may use any combination of stdin/stdout/files/command line parameters. For example your script might take in a file name of the X. pattern and rewrite the file with the slash pattern. Or your script might take in the X. pattern from stdin line by line (pressing d when done) and output the result to stdout.

The input may be arbitrarily large, but you may assume it is always well formatted.

No characters besides / \ and newlines should be in any output.

# Scoring

The shortest code in bytes wins. Use https://mothereff.in/byte-counter as a byte counter if you use non-ASCII characters.

Bonus: Minus 50 bytes if you can change (replace, not remove) one character in your program so it outputs the slash grid rotated 45 degrees clockwise, e.g.:

   /\/\
/ /\ \
/  \ \/
/ /\ \/\
\/  \  /
/ /
/ /
\/

# Input Samples

XXXXXXXXX
X.......X
X.XXXXX.X
X.X...X.X
X.X.X.X.X
X.X...X.X
X.XXXXX.X
X.......X
XXXXXXXXX

XXX...XXX....XXX...XXX
X..X..X..X..X.....X...
XXX...XXX...X.....X.XX
X.....X.....X.....X..X
X.....X......XXX...XXX

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX...X
X...X...............X...............X...........X...................X...X
X...X...XXXXXXXXX...X...XXXXX...XXXXXXXXX...XXXXX...XXXXX...XXXXX...X...X
X...............X.......X...X...........X...........X...X...X.......X...X
XXXXXXXXX...X...XXXXXXXXX...XXXXXXXXX...XXXXX...X...X...X...XXXXXXXXX...X
X.......X...X...............X...........X...X...X...X...X...........X...X
X...X...XXXXXXXXXXXXX...X...X...XXXXXXXXX...XXXXX...X...XXXXXXXXX...X...X
X...X...............X...X...X.......X...........X...........X.......X...X
X...XXXXXXXXXXXXX...XXXXX...XXXXX...X...XXXXX...XXXXXXXXX...X...XXXXX...X
X...........X.......X...X.......X...X.......X...........X...X...........X
X...XXXXX...XXXXX...X...XXXXX...X...XXXXXXXXX...X...X...X...XXXXXXXXXXXXX
X.......X.......X...X...X.......X.......X.......X...X...X.......X.......X
XXXXXXXXXXXXX...X...X...X...XXXXXXXXX...X...XXXXX...X...XXXXX...XXXXX...X
X...........X...X...........X.......X...X.......X...X.......X...........X
X...XXXXX...X...XXXXXXXXX...XXXXX...X...XXXXX...XXXXX...XXXXXXXXXXXXX...X
X...X.......X...........X...........X.......X...X...X...............X...X
X...X...XXXXXXXXX...X...XXXXX...XXXXXXXXX...X...X...XXXXXXXXXXXXX...X...X
X...X...........X...X...X...X...X...........X...............X...X.......X
X...XXXXXXXXX...X...X...X...XXXXX...XXXXXXXXX...XXXXXXXXX...X...XXXXXXXXX
X...X.......X...X...X...........X...........X...X.......X...............X
X...X...XXXXX...XXXXX...XXXXX...XXXXXXXXX...XXXXX...X...XXXXXXXXX...X...X
X...X...................X...........X...............X...............X...X
X...XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

(maze source)

• Is replacing the single character with a whitespace character (or a whitespace to a symbol) acceptable? – nanofarad Sep 6 '14 at 16:39
• @hexafraction Sure – Calvin's Hobbies Sep 6 '14 at 16:40
• What we need is someone to answer this in itflabtijtslwi. Then we'd have "Drawing in Slashes in Slashes." – Justin Sep 6 '14 at 23:43

# Python 2 - 236, 228, 226, 221, 250, 248 246 - 50 = 196

s=input().split()
s=zip(*s[::-1])
X=len(s[0])+2
d=('.',)
B=[d*X]
s=B+[d+tuple(l)+d for l in s]+B
Y=len(s)
for x in range(X,-Y,-1):print' '*abs(x)+''.join(' \\'[s[y-1][x+y-1]!=s[y-1][x+y]]+' /'[s[y-1][x+y]!=s[y][x+y]]for y in range(1,Y)if 0<x+y<X)

I added the optional bonus feature that switches the direction from clockwise to counterclockwise. Basically, the second line simply rotates the input by 90 degrees. To switch between both options, replace s=zip(...) by something like S=zip(...) (i.e. assign to a variable that won't be used again).

.XX.X....X...XX.X.X
X...X...X.X.X...X.X
.X..X...XXX..X..XXX
..X.X...X.X...X.X.X
XX..XXX.X.X.XX..X.X

/\           /\/\
\ \          \/\ \
/\ \ \         /\ \/
\ \/  \     /\ \/   /\
/\ \  /\ \    \ \/\  / /
/ /  \ \ \/     \/\/ / /
\/    \ \           / /
/\/\/\ \/          / /
\/\/\/             \ \    /\/\
/\/\    /\              \ \  / /\/
\/\ \  / /               \/ /  \/\
/\/  \ \/                  / /\  /
\  /\ \                    \/ / / /\/\
\ \ \/                      / /  \/\ \
/\     \ \                        \/   /\ \/
\ \     \/                          /\ \/   /\
/\ \ \  /\                            \ \/\  / /
/ /  \ \/ /                             \/\/ / / /\
\/    \  /                                  /  \/ /
/\/\/\ \/                                  / /\  /
\/\/\/                                     \/ / /
/\                                       / /
/ /                                       \/
\/

• You could save 5bytes by sandwiching s with B by s=B+s+B. – BeetDemGuise Sep 7 '14 at 0:06
• @BeetDemGuise: Thanks! That's so much easier! :) – Falko Sep 7 '14 at 7:04

# MATLAB - 286 - 50 = 236

Minified:

S=input('');x=rot90(reshape(input('','s'),S),1);S=size(x);D=sum(S);[r,c]=ind2sub(S,find(x==88));A=zeros(D);f=@(o,p)sub2ind([D D],r+c+o-1,c-r+S(1)+p);A(f(1,1))=1;t=f(0,0);A(t)=A(t)+1;A(f(1,0))=3;t=f(0,1);A(t)=A(t)+3;fprintf('%s',char([(1-mod(A,2))*32+(A==1)*47+(A==3)*92,ones(D,1)*13]'))

Expanded:

S = input('');
x = rot90( reshape( input('','s'), S ), 1 );
S = size( x );
D = sum( S );
[r,c] = ind2sub( S, find( x==88 ) );
A = zeros( D );
f = @(o,p) sub2ind( [D D], r+c+o-1, c-r+S(1)+p );

A(f(1,1)) = 1;
t = f(0,0); A(t) = A(t)+1;
A(f(1,0)) = 3;
t = f(0,1); A(t) = A(t)+3;

fprintf( '%s', char( [(1-mod( A, 2 ))*32 + (A==1)*47 + (A==3)*92, ones( D, 1 )*13]' ) )

The code can be further reduced by 6 characters (to tie the current lead) by eliminating the cast to type char, but this results in a warning from MATLAB, and I wasn't sure if that was allowed.

It can be reduced by an additional 13 characters if the input is required to have a "marked up" format such as ['X..';'.X.';'..X'], but I didn't figure this was allowed either. Currently the script just accepts two numbers (row and column dimensions) and then reads in a single string of grid characters.

Bonus

By changing the 1 in the call x = rot90( ..., 1 ); to a 0, the transformation changes from a CCW 45° rotation to a CW 45° rotation. In fact, all possible 45° + n·90° rotations are possible by stepping this parameter from 0 to 3.

Sample Outputs:

XXX...XXX....XXX...XXX
X..X..X..X..X.....X...
XXX...XXX...X.....X.XX
X.....X.....X.....X..X
X.....X......XXX...XXX

/\
/ /
/ / /\
\/ /  \
/\ \/\ \
\ \  / /
/\   \ \/ /
/ /    \/\/
/ /
\/
/\    /\
\ \  / /
\ \/ /
/\/\   \/\/
/ /\/
/ / /\
\ \/ /
\  /
\ \
/\/\   \ \
/ /\/    \/
/ / /\
\ \/ /
\  /
\ \
\ \
\/

/\
/  \
/ /\ \
/  \ \/
/ /\ \/\
\/  \/\/
/\
/  \
/ /\ \
/  \ \/
/ /\ \/\
\/  \/\/

/\/\
/ /\ \
/ /  \ \
\/    \/
/\
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text:
# How to prove that the inverse of the given continuous function is not continuous

I have the following problem: Consider the identity map $id: C_{max} \rightarrow C_{int}$ where $C_{max}$ is the metric space $C([a,b],\mathbb{R})$ of continuous real valued function defined on $[a,b]$ equipped with the metric $d_{max}(f,g) = \max|f(x)-g(x)|$, and $C_{int}$ is $C([a,b],\mathbb{R})$ equipped with the integral metric, $d_{int}(f,g) = \int_{a}^b |f(x) - g(x)| dx$. Show that $id$ is a continuous linear bijection (an isomorphism) but its inverse is not continuous.

I proved continuity in the following manner: Note that it is trivially clear that the identity map $id$ is a bijection. We must then show that $id$ is continuous. For any given $\epsilon > 0$, suppose that $d_{max}(f,g) = \max|f - g| < \delta$ for $\delta < \frac{\epsilon}{b-a}$. Then we notice that

\begin{align} d_{int}(f,g) &= \int^a_b|f - g|dx \\ &< \int^a_b\delta \\ &= \delta(b - a) \\ &< \epsilon. \end{align}

However, I'm absolutely stuck on showing that the inverse of ${id}^{-1}$ is not continuous. My intuition says to us proof by contradiction, but I don't know what to do here. How would I begin going about proving that fact that ${id}^{-1}$ is not continuous?

• hint: $f_n(x) = x^n$ on $[0,1]$ – user251257 Sep 30 '15 at 1:42

The sequence of functions $$f_n(x) := \max(1 - n|x|,0)$$ $C_{\text{int}}([-1,1])$-converge to $0$, but $‖ f_n - 0 ‖_{C_{\text{max}}} = 1 \not\to0$.


text:
# Chapter 11 - Rational Expressions and Functions - 11-7 Graphing Rational Functions - Practice and Problem-Solving Exercises: 11

3

#### Work Step by Step

Since we cannot divide by zero, the excluded value will be the value that makes the denominator zero. For $h(x) = \frac{-3}{2x-6}$, we can set the denominator equal to zero in order to find the excluded value. $2x - 6 = 0$ When we solve for x, we find that $x \ne 3$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Fluid flow through porous media

In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media.

## Governing law

Symbol Description
${\displaystyle Q}$ Volumetric flow rate [m3/s]
${\displaystyle k}$ Permeability of porous medium [m2]. The permeability is a function of material type, and also varies with stress, temperature, etc.
${\displaystyle \mu }$ Fluid viscosity [Pa.s]
${\displaystyle A}$ Cross-sectional area of Porous medium [m2]
${\displaystyle (p_{b}-p_{a})}$ Pressure drop across medium [Pa]
${\displaystyle L}$ Length of sample [m]

The basic law governing the flow of fluids through porous media is Darcy's Law, which was formulated by the French civil engineer Henry Darcy in 1856 on the basis of his experiments on vertical water filtration through sand beds.[1]

 ${\displaystyle Q={\frac {-kA}{\mu }}{\frac {(p_{b}-p_{a})}{L}}}$

For transient processes in which the flux varies from point to-point, the following differential form of Darcy’s law is used.

 ${\displaystyle Q={\frac {-kA}{\mu }}\left({\frac {dp}{dx}}\right)}$

Darcy's law is valid for situation where the porous material is already saturated with the fluid. For the calculation of capillary imbibition speed of a liquid to an initially dry medium, Washburn's or Bosanquet's equations are used.

## Mass conservation

Mass conservation of fluid across the porous medium involves the basic principle that mass flux in minus mass flux out equals the increase in amount stored by a medium.[2] This means that total mass of the fluid is always conserved. In mathematical form, considering a time period from ${\displaystyle t}$ to ${\displaystyle \Delta t}$, length of porous medium from ${\displaystyle x}$ to ${\displaystyle \Delta x}$ and ${\displaystyle m}$ being the mass stored by the medium, we have

${\displaystyle [A\rho (x)q(x)-A\rho (x+\Delta x)q(x+\Delta x)]\Delta t=m(t+\Delta t)-m(t).}$

Furthermore, we have that ${\displaystyle m=\rho V_{p}}$, where ${\displaystyle V_{p}}$ is the pore volume of the medium between ${\displaystyle x}$ and ${\displaystyle x+\Delta x}$ and ${\displaystyle \rho }$ is the density. So ${\displaystyle m=\rho V_{p}=\rho \phi V=\rho \phi A\Delta x,}$ where ${\displaystyle \phi }$ is the porosity. Dividing both sides by ${\displaystyle A\Delta x}$, while ${\displaystyle \Delta x\rightarrow 0}$, we have for 1 dimensional linear flow in a porous medium the relation

${\displaystyle {\frac {-d(\rho q)}{dx}}={\frac {d(\rho \phi )}{dt}}~~~~(i)}$

In three dimensions, the equation can be written as

${\displaystyle {\frac {d(\rho q)}{dx}}+{\frac {d(\rho q)}{dy}}+{\frac {d(\rho q)}{dz}}={\frac {-d(\rho \phi )}{dt}}}$

The mathematical operation on the left-hand side of this equation is known as the divergence of ${\displaystyle \rho q}$, and represents the rate at which fluid diverges from a given region, per unit volume.

## Diffusion Equation

Material Type Compressibility (m2N−1 or Pa−1)[3]
Clay 10−6 - 10−8
Sand 10−7 - 10−9
Gravel 10−8 - 10−10
Jointed rock 10−8 - 10−10
Sound Rock 10−9 - 10−11
Water (beta) 4.4 x 10−10

Using product rule(and chain rule) on right hand side of the above mass conservation equation (i),

${\displaystyle {\frac {d(\rho \phi )}{dt}}=\rho {\frac {d\phi }{dt}}+\phi {\frac {d\rho }{dt}}=\rho {\frac {d\phi }{dP}}{\frac {dP}{dt}}+\phi {\frac {d\rho }{dP}}{\frac {dP}{dt}}=\rho \phi \left[{\frac {1}{\phi }}{\frac {d\phi }{dP}}+{\frac {1}{\rho }}{\frac {d\rho }{dP}}\right]\quad {\frac {dP}{dt}}=\rho \phi [c_{\phi }+c_{f}]{\frac {dP}{dt}}~~~~(ii)}$

Here, ${\displaystyle c_{f}}$ = compressibility of the fluid and ${\displaystyle c_{\phi }}$ = compressibility of porous medium.[4] Now considering the left hand side of the mass conservation equation, which is given by Darcy's Law as

${\displaystyle {\frac {-d(\rho q)}{dx}}={\frac {-d}{dx}}\left[{\frac {-\rho k}{\mu }}{\frac {dP}{dx}}\right]\quad ={\frac {k}{\mu }}\left[\rho {\frac {d^{2}P}{dx^{2}}}+{\frac {d\rho }{dP}}{\frac {dP}{dx}}{\frac {dP}{dx}}\right]\quad ={\frac {\rho k}{\mu }}\left[{\frac {d^{2}P}{dx^{2}}}+\left({\frac {1}{\rho }}{\frac {d\rho }{dP}}\right)\left({\frac {dP}{dx}}\right)^{2}\right]\quad ={\frac {\rho k}{\mu }}\left[{\frac {d^{2}P}{dx^{2}}}+c_{f}\left({\frac {dP}{dx}}\right)^{2}\right]\quad ~~~~(iii)}$

Equating the results obtained in ${\displaystyle (ii)}$ & ${\displaystyle (iii)}$, we get

${\displaystyle {\frac {d^{2}P}{dx^{2}}}+c_{f}\left({\frac {dP}{dx}}\right)^{2}={\frac {\phi \mu (c_{f}+c_{\phi })}{k}}{\frac {dP}{dt}}}$

The second term on the left side is usually negligible, and we obtain the diffusion equation in 1 dimension as

${\displaystyle {\frac {dP}{dt}}={\frac {k}{\phi \mu c_{t}}}{\frac {d^{2}P}{dx^{2}}}}$

where ${\displaystyle c_{t}=c_{f}+c_{\phi }}$.[5]

## References

1. ^ Whitaker, Stephen (1986). "Flow in porous media I: A theoretical derivation of Darcys law". Transport in Porous Media. 1: 3–25. doi:10.1007/BF01036523.
2. ^ Bear, Jacob (2013-02-26). Dynamics of fluids in Porous Media. ISBN 9780486131801.
3. ^ https://eng.ucmerced.edu/people/jfisher/.../EnveEss110_20081110.pdf
4. ^ Ohirhian, Peter. "Steady State Compressible Fluid Flow in Porous Media".
5. ^ Zimmerman, Dr. R.W. "Flow in porous media".


text: This results in a double bond. • Consider ethylene (also called ethene): C 2H 4. E = A +B -Tz(P + P3) Where A And B Are The Values Of The Coulomb And Resonance Integrals, Respectively. Each sp 1 hybrid orbital has s-character and The molecular orbital structure of ethylene: In ethene molecule, each carbon atom undergoes sp 2 … From the orbital diagram, we can write the electron configuration in an abbreviated form in which the occupied orbitals are identified by their principal quantum number n and their value of l (s, p, d, or f), with the number of electrons in the subshell indicated by a superscript. The atomic s- and p-orbitals in boron’s outer shell mix to form three equivalent hybrid orbitals. Structure (II) represents ethylene as possessing a double bond.Such a bond would prevent free rotation and would therefore explain geometrical isomerism. Different orbitals have different energy levels and different shapes s … Figl. In the formation of CH 2 = CH 2 each carbon atom in its excited state undergoes sp 2 hybridisation by intermixing one s-orbital (2s) and two p-orbitals (say 2p x, 2p y) … There is a nodal plane between the two nuclei of an antibonding molecular orbital i.e. This leads to the formation of three sp2 hybridized orbitals. H-atom to produce three sigma bond and the last overlaps with one Sp 3-orbital of other C-atom to produce a sigma bond between two C-atoms. It is widely used to control freshness in horticulture and fruits. SCH 102 Dr. Solomon Derese 147 Ethane (C 2 H 6)– sp3 Hybridization. Hence (II) was acceptable to the classical chemists. The helix with Fig2. Each sp 1 hybrid orbital has s-character and The molecular orbital structure of ethylene: In ethene molecule, each carbon atom undergoes sp 2 … When the coordinated ethylene molecule lies perpendicular to the molecular plane , the back bonding may take place either through d yz or d xz filled orbitals , but it may take place only through dxyfilled orbital. Valence Bond Model of the Double Bond (ethylene as the example) At right is a 3-D version of the Lewis structure of the ethylene molecule. Atomic orbitals are represented by s, p, d , the bonding molecular orbitals are represented by σ , π, δ and the corresponding antibonding molecular orbitals are represented by σ ∗, π ∗, δ ∗.. … 96 Chemical Bonding MODULE - 2 Atomic Structure and Chemical Bonding σ ∗ 2s σ ∗ 2s 2s 2s 2s 2s E N Notes E σ 2s σ 2s R G Y σ ∗ 1s σ ∗ 1s 1s 1s 1s 1s σ 1s σ 1s (a) (b) Fig. 39 Summary Organic chemistry – chemistry of carbon compounds Atom: positively charged nucleus surrounded by negatively charged electrons Electronic structure of an atom described by wave equation Electrons occupy orbitals around the nucleus. (1 is called a HOMO (Highest Occupied Molecular Orbital) and (2* is called a LUMO (Lowest Unoccupied Molecular Orbital). Geometry of ethane: Ethane molecule is arranged in tetrahedral geometry in which central carbon atoms are surrounded by H-atoms in three dimensions. The unhybridized 2p1 orbital lies perpendicular to the three hybridised orbitals. One 2s orbital and two 2p orbitals hybridized to form three #"sp"^2#orbitals. XII Organic Chemistry "Molecular Orbital Structure of Benzene" Lecture 6 #Benzene #OrganicChemistry Ethylene … [citation needed]Niche uses. In ethylene, each carbon combines with three other atoms rather than four. [15] Other uses are to hasten the ripening of fruit, … Problem 1.10 Draw a line-bond structure for propene, CH3CHPCH2. One 2pz orbital remains unchanged. sp2 orbitals are in a plane with120°angles Remaining p orbital is perpendicular to the plane 1.8 sp2 Orbitals and the Structure of Ethylene Ethene is built from hydrogen atoms (1s 1) and carbon atoms (1s 2 2s 2 2p x 1 2p y 1). An Approximate Valence MO Structure Of Formaldehyde Can Be Obtained By … Thus the main structure of ethylene is built. Indicate the hybridization of the orbitals on eachcarbon, and predict … Ethylene, H 2 C=CH 2 C SP2 - C SP2 C SP2-H 1S 152 103 1.33 1.076 33 Ethyne, HC≡CH C SP - C SP C SP-H 1S 200 125 1.20 1.06 50. ... the chemical behaviour of ethylene is … This is exactly the same as happens … sp 2 Hybridisation. Structure of Ethane. sp2 hybrid orbitals: 2s orbital combines with two 2p orbitals, giving 3 orbitals (s + pp = sp2). These particular orbitals are called sp 2 hybrids, meaning that this set of orbitals derives from one s- orbital and two p-orbitals of the free atom. Draw a Lewis structure, and use it to determine the geometry and hybridization of each of the carbon atoms. The σ bond is formed by the overlap of hybrid atomic orbitals, and the π bond is formed by the overlap of unhybridized p orbitals. Much of this production goes toward polyethylene, a widely used plastic containing polymer chains of ethylene units in various chain lengths. Click on any image above to view the optimized structure. –A valence bond is localized between two atoms. Representation of sp 2 hybridization sp 2 hybridization is also known as trigonal hybridisation. The un-hybridized p orbital overlaps laterally to form the π \pi π bond. The Hückel method or Hückel molecular orbital theory, proposed by Erich Hückel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals method for the determination of energies of molecular orbitals of π-electrons in π-delocalized molecules, such as ethylene, benzene, butadiene, and pyridine. Ethane, a two carbon molecule with a single-bond between the carbons, is the simplest alkane.. To understand the hybridization, start by thinking about the orbital diagram of the valence electrons of atomic, unhybridized carbon. Ethylene is also an important … What is the Hybridization of the Carbon atoms in Ethylene. 1. Chem. structure Electron-dot structure O C HH O C HH Like the carbon atoms in ethylene, the carbon atom in formaldehyde is in a double bond and its orbitals are therefore sp2-hybridized. One carbon atom overlaps the sp2 orbital of another carbon atom to form … The C-C pi (() bond in ethylene results from the side-to-side overlap of two 2p atomic orbitals producing two MO’s (one (1 bonding and one (2* antibonding). The helix with 3.7 residues per turn. The Lewis structure for etheneThe carbon atoms are sp 2 hybridized. It is the … One unpaired electron in the p orbital remains unchanged. An example of a niche use is as an anesthetic agent (in an 85% ethylene/15% oxygen ratio). In Zeise’s salt the metal ion , Pt(II) contains three π-type filled d-orbital which are d xy, d yz, and d xz. sp2 hybridization. P orbital and pi bonding of ethylene Orbital hybridization of ethylene –Covalent bonds are formed by the overlap of two atomic orbitals and the electron pair is shared by both atoms. 2s 2p 2p 2s sp2 Orbital Hybridization. There is a formation of a sigma bond and a pi bond between two carbon atoms. Ethylene | CH2=CH2 or (C2H4)n or C2H4 | CID 6325 - structure, chemical names, physical and chemical properties, classification, patents, literature, biological activities, safety/hazards/toxicity information, supplier lists, and more. • Molecular Orbital theory. 2p 2s ... Valence-Bond (Orbital Hybridization) provides more insight than Lewis model ability to connect structure and reactivity to hybridization develops with practice a plane on which electron density is zero. (c) A cutaway view of the combined σ and π system. It is #"sp"^2#hybridization. The overall structure of the ethene compound is linear but the molecular geometry around each carbon atom is trigonal planar. The entire structure is resistant to twisting around the carbon-carbon bond. –n atomic orbitals are combined to give a new set of n molecular orbitals (bonding and antibonding). The carbon atom doesn't have enough unpaired electrons to form the required number of bonds, so it needs to promote one of the 2s 2 pair into the empty 2p z orbital. The SPO (Split p ‐Orbital) Method and Its Application to Ethylene. classical structure theory of organic chemistry 1. The π \pi π bond is the site of reactivity. Question: Consider The Valence Molecular Orbital Diagram Of Ethene (ethylene) Obtained From Hückel MO Theory: E. =a-B --16-P) 188. An orbital view of the bonding in ethene. Representation of sp 2 hybridization sp 2 hybridization is also known as trigonal hybridisation. The π orbital has two regions of electron density extending above and below the plane of the molecule. 2s 2p Promote an electron from the 2s to the 2p orbital sp2 OrOrbbital Hybridization. For a given internuclear separation, this will result in the maximum overlap of the orbitals. In ethylene molecule, the electrons present in 2s and 2p orbitals are engaged in s p 2 sp^2 s p 2 hybridization leaving one un-hybridized p orbital. Ethylene is a hormone that affects the ripening and flowering of many plants. An Introduction to the Electronic Structure of Atoms and Molecules ... strongest possible bond when the hydrogen and oxygen nuclei lie on the axis which is defined by the direction of the 2p orbital. Calculations done at B3LYP/6-311G+(2d,p). The transition structure for the latter (Figure has a small Fermi contact integral as well (0.004 au), indicating 3b) is very similar to that found for addition to ethylene: 8,9 both 2.0 A, LHCC = 106', and a C C bond elongation zyxwvutsrq of have RX 0.04 relative = to the reactant olefin. 5.1 residues per turn. • Valence Orbital theory. DOI: 10.1063/1.1731723. The Rydberg orbital of the ethylene molecule is a 3d,7-orbital with its core at the center of the ethylene molecule. In ethylene molecule there are 3 σ \sigma σ bonds and 1 π \pi π bond. The Journal of Chemical Physics 1961 , 34 (4) , 1232-1236. Ethylene is widely used in the chemical industry, and its worldwide production (over 150 million tonnes in 2016) exceeds that of any other organic compound. Due to sp 2 hybridization, the bond angles are ethylene arc about 120° and all the atoms are on a plane. This orbital overlaps the 3d,7 orbital of the Cuion, and back-donation from the metal 129 3d~ orbital to the Rydberg 3d,7 orbital is then possible. You may rotate the molecule yourself by holding the mouse button down while dragging it around within the image frame. Trigonal … Figure 11: The shape of sp 2 hybrid orbitals and the structure of an ethylene molecule. Consider ethene (ethylene, CH 2 = CH 2) molecule as the example. How can we describe a double bond in terms of the overlap of orbitals? The unhybridized 2p1 orbital lies perpendicular to the three hybridised orbitals. ... structure of ethylene. As shown above, ethylene can be imagined to form when two -CH 2 fragments link together through overlap of the half-filled sp 2 hybrid orbitals on each. Structure of Ethylene. If we add four hydrogen atoms to each of the non-bonded sp 2 orbitals still unoccupied in the drawing above, we get ethylene. Here is a simplified drawing of ethylene, C 2 H 4, which has a C=C double bond with four hydrogen atoms bound to the other unpaired electrons (in sp 2 hybrid orbitals) of the carbon atoms. Page content is the responsibility of Prof. Kevin P. Gable kevin.gable@oregonstate.edu 153 Gilbert Hall Oregon State University Corvallis … C2H4 Molecular Geometry And … The modern theory of a double bond is that it consists of one – and one –bond or two ‘bent’ bonds. 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A plane B3LYP/6-311G+ ( 2d, p ) orbital has two regions of electron density above... Hybridized to form the π \pi π bond ( bonding and antibonding ) by H-atoms in three dimensions is. Hormone that affects the ripening and flowering of many plants the maximum overlap of the carbon atoms:... The plane of the overlap of orbitals leads to the 2p orbital OrOrbbital! Bonding and antibonding ) [ 15 ] other uses are to hasten the ripening of fruit …. Two 2p orbitals hybridized to form three # '' sp '' ^2 # orbitals trigonal … the unhybridized 2p1 lies! P ) holding the mouse button down while dragging it around within the image frame it to the... And two 2p orbitals hybridized to form the π \pi π bond the. Of this production goes toward polyethylene, a widely used to control in. There is a hormone that affects ethylene orbital structure ripening and flowering of many.... – and one –bond or two ‘ bent ’ bonds an 85 % ethylene/15 % ratio! 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text: There are now 191 companies in the S&P 500 that have net tangible book values below zero, up from 124 five years ago. Tangible items is a term used in business when appraising the overall value of a company. Net tangible book value per common share represents the amount of our total tangible assets less our total liabilities, excluding goodwill and other intangible assets, if any, and non-controlling interest, divided by 43,859,232, the total number of our common shares outstanding as … The tangible book value number is equal to the company’s total book value less than the value of any intangible assets. For assets, the value is based on the original cost of the asset less any depreciation, amortization or impairment costs made against the asset. Book value of equity per share (BVPS) measures a company's book value on a per-share basis. How to Find Negative Retained Earnings in a 10-k – Does it Indicate Distress? The gurus listed in this website are not affiliated with GuruFocus.com, LLC. In certain businesses, the carrying value is often a negative number. If total assets are less than total liabilities, the business has negative net assets. For instance, a truck with 100,000 miles on it isn't as valuable as a brand-new one. Stock 2 has a lower market cap than its book value of equity, so its Market to Book ratio is 0.9x. The information on this site, and in its related newsletters, is not intended to be, nor does it constitute, investment advice or recommendations. One must not only read it , but also study it . Book value is best viewed as a "quick and dirty" way to score value creation at Berkshire, as even Buffett admits it has its weaknesses. Gross cash recovery (GCR) is the gross cash collection expected over the remaining life of an asset. Reminds Investors That a Class Action Lawsuit Has Been Filed Against Zosano Pharma Corp. and Encourages Investors to Contact the Firm, SHAREHOLDER ALERT BY FORMER LOUISIANA ATTORNEY GENERAL: KSF REMINDS BSX, SPLK INVESTORS of Lead Plaintiff Deadline in Class Action Lawsuits, DEADLINE ALERT: Bragar Eagel & Squire, P.C. A DIY Guide on How to Invest Using Guru Strategies, a good blog to give you a taste of what I mean, an article about how free cash flow isn’t everything. Netflix’s streaming service is intangible good. The asset is the value of future tax savings. Usually a company's book value and Tangible Book per Share may not reflect its true value. A share repurchase can impact a company’s BVPS. Tangible book value (TBV) of a company is what common shareholders can expect to receive if a firm goes bankrupt—thereby forcing the liquidation of its assets at the book value price. Additional business equipment, such as computers and filing cabinets, may also be considered tangible assets for the purpose of valuation. Walmart Teams Up With FedEx to Challenge Amazon, With Alexion Off the Board, Amarin and Biomarin Are Attractive Acquisition Targets, A Trio of Stock Picks for the Value Investor, 3 Low Shiller Price-Earnings Ratio Stock Picks, DEADLINE ALERT: Bragar Eagel & Squire, P.C. Aside from assets related to the production of a product, any equipment used to create the product can be included as well. The historical September 30, 2011 net tangible book value was then divided by the 533,839 common shares outstanding at September 30, 2011, to arrive at $(174.18) historical net negative tangible book value per share at September 30, 2011. But plenty of well-known companies, whose competitive edge … Your selection and notes will be stored in your portfolio. An organization's tangible assets can include any physical products the company produces, as well as any materials used to produce them. Net Tangible Assets (NTA) is the value of all physical ("tangible") assets minus all liabilities in a business. Tangible Book Value is negative (by a wide margin) meaning that although they have decent revenues they have little cash and loads of debt. The book value of an individual tangible asset is calculated by subtracting accumulated depreciation from the initial cost of the asset, or its purchase price. This may underestimate the true economic values of the assets. I owned IMS Health before it was bought out. "The lack of tangible book value per share growth despite positive earnings at KEY is attributable to a rather significant reversal in unrealized gains on investment securities to … • Increasingly price is detached from book value. Very good article . “The price to tangible book value (PTBV) is a valuation ratio expressing the price of a security compared to its hard, or tangible, book value as reported in the company’s balance sheet. The company also recorded$15,000,000 of tangible book value last year. The value of tangible assets decrease over time. Tangible book value per share is calculated as the total tangible equity divided by .Total tangible equity is calculated as the Total Stockholders Equity minus Preferred Stock minus Intangible Assets.Citigroup's tangible book value per share for the quarter that ended in Mar. When you go shopping in a store, everything you place in your shopping cart would be tangible goods. And yet, incredibly, a “negative-value” fund, composed of the shares of companies with negative tangible book value, would have beaten the main U.S. … I found this article when I was searching for negative book value. For instance, a truck with 100,000 miles on it isn't as valuable as a brand-new one. The median price-to-book of S&P 500 stocks is 3.0. This was $738,450 MORE than investing in a simple low price to book value strategy, even though the net tangible assets portfolio edged out the low price to book value strategy by 3.3%. Since the company’s market value is greater than its book value, the market expects a return of 18%. The latest dip is not a new trend. It takes into account only the accounting valuation, which is not always an accurate reflection of the current market valuation, or of what could be received during a sale. If Price to tangible book value is greater than 1, then the share price is … Intangible assets, such as goodwill, are not included in the calculation of TBVPS. Book value per share (BVPS) refers to a company’s total shareholders’ equity divided by the total number of shares outstanding. For assets, the value is based on the original cost of the asset less any depreciation, amortization or impairment costs made against the asset. We estimate that a 100 basis-point increase in interest rates could negatively affect Wells Fargo's tangible book value by 5%, followed by Bank of America and PNC at a roughly 3% negative … Whether negative goodwill is more than, equal to, or less than the allocated asset value will determine how the negative goodwill will be accounted for in the acquirer's books. What the Price-To-Book Ratio (P/B Ratio) Tells You? The book value of an individual tangible asset is calculated by subtracting accumulated depreciation from the initial cost of the asset, or its purchase price. In no event shall GuruFocus.com be liable to any member, guest or third party for any damages of any kind arising out of the use of any content or other material published or available on GuruFocus.com, or relating to the use of, or inability to use, GuruFocus.com or any content, including, without limitation, any investment losses, lost profits, lost opportunity, special, incidental, indirect, consequential or punitive damages. Usually a company's book value and Tangible Book per Share may not reflect its true value. The price/earnings ratio of 3.32 is definitely low. Certain online databases and websites allow potential investors to examine the progress of a company’s TBVPS over time. In accounting, book value is the value of an asset according to its balance sheet account balance. The offers that appear in this table are from partnerships from which Investopedia receives compensation. Thank you very , very much ! The carrying value, or book value, of an item is related to business accounting. Bank of America was off 5.7%, to$21.38, above its tangible book value of … For example, let's assume that Company XYZ has 10,000,000 shares outstanding, which are trading at $3 per share. 4% for bondsAre too aggressive.Berkshire may be right to use 7% for their pension plan return assumptions. The information on this site, and in its related newsletters, is not intended to be, nor does it constitute, investment advice or recommendations. Q3 of 2018 was S&P 500’s best quarter since 2013 – signalling good times for corporate America. Stock quotes provided by InterActive Data. Let’s look at an example. Andy considers investing in a retail company. Once the value of the tangible assets is determined, that amount is divided by the number of the company’s current outstanding shares. Here is a firm with about 1.2 bil in assets and 1.9 bil in debt, giving it negative equity of 0.7 bil. Western Digital (NAS:WDC) Book Value per Share Explanation. The average expected return on pension assets is 7.8% at the 100 largest U.S. public companies. The information on this site is in no way guaranteed for completeness, accuracy or in any other way. The price to tangible book value (PTBV) is a valuation ratio expressing the price of a security compared to its hard, or tangible, book value as reported in the company's balance sheet. As of Sept. 30, Citigroup was the 11th-cheapest bank in the analysis by price to adjusted tangible book value. In this case it is prudent to subtract goodwill from book value, resulting in a "tangible book value." But, if it was up to me, I’d use 6%. Book value refers to the ratio of stockholder equity to the number of shares outstanding. We can then calculate the more meaningful "price-to-tangible-BV ratio." TBV excludes things like good will, ability to generate cash, and other 'intangibles' that can't be borrowed against or directly valued because an easily observable price doesn't exist. Book value per common share (BVPS) derives a company's book value on a per-share basis. Negative goodwill is an accounting gain that occurs when the price paid for an acquisition is less than the fair value of its net tangible assets. On average, companies have funded between 75% and 80% of their pension obligations.Here is a comparison of expect return and actual returns for the 100 public companies with the largest defined benefit plans: That's a long article for to answer one question. McDonald's (NYSE:MCD) Book Value per Share Explanation. The amount determined in this process is recognized as the company’s TBVPS. The origins of the value factor are generally attributed to the work on asset pricing and portfolio management by Fama and French 2 The classic paper often cited is ‘Common risk factors in the returns on stocks and bonds’. JPMorgan commands 1.5 times tangible book and Bank of America trades for 1.1 times tangible book. Of course, nobody uses 6%. Traditionally, a company's book value is its total assets [clarification needed] minus intangible assets and liabilities. Negative book equity can also occur with firms being involved with bad debts which have to be written off. JPMorgan shares were off 4.7%, to$91.50, against a tangible book value of about $61 a share. In accounting, book value is the value of an asset according to its balance sheet account balance. Using the Price to tangible book value ratio provides us with a relative valuation multiple for making such a comparison. The assets may be carried on the balance sheets at the original cost minus depreciation. I buy stocks all the time – most stocks I buy in fact – that have positive tangible equity in excess of my purchase price (that is, they trade below tangible book value). Seaboard is selling close to its mostly liquid, tangible book value, and a 19x P/E on depressed 2020 results. 2020 was$15.13.. Accordingly, the treatment of negative book ... firms who do not have substantial tangible assets but rich in patents or new ideas “eat” into their equity. This implies that if the company is liquidated today, the shareholders will profit from higher tangible book value. In other words, NTA are the total assets of a company minus intangible assets and total liabilities. … Usually a company's book value and Tangible Book per Share may not reflect its true value. In their original 3-factor model the expected return on equity assets is given by an extended form of the traditional CAPM asset pricing model. Book Value of Equity Per Share (BVPS) Definition. This was $738,450 MORE than investing in a simple low price to book value strategy, even though the net tangible assets portfolio edged out the low price to book value strategy by 3.3%. Intangible assets, such as goodwill, are not included in tangible book value because they cannot be sold during liquidation. A share repurchase can impact a company’s BVPS. But tangible book … What Is in the GuruFocus Premium Membership? We can then calculate the more meaningful "price-to-tangible-BV ratio." The value of tangible assets decrease over time. Well,$100,000 invested at 22.05% for 18 years would grow to $3,611,000. With a negative 15.7% total return in September, Citigroup Inc. was one of the worst market performers in the sector. BAC stock could get back to a near 2X tangible book value multiple in 2021. We estimate that a 100 basis-point increase in interest rates could negatively affect Wells Fargo's tangible book value by 5%, followed by Bank of America and PNC at a roughly 3% negative … Enter your name and email in … JPMorgan shares were off 4.7%, to$91.50, against a tangible book value … Should an organization be in the business of producing bicycles, for instance, then any completed bicycles, unused bicycle parts, or raw materials used during the process of fabricating bicycles would qualify as tangible assets. All Rights Reserved. Disclaimers: GuruFocus.com is not operated by a broker, a dealer, or a registered investment adviser. Under no circumstances does any information posted on GuruFocus.com represent a recommendation to buy or sell a security. Book value, in finance, also referred to as stockholders' equity or liquidation value, is calculated by subtracting liabilities from assets. Occidental Petroleum is at 70% of tangible book value even with ongoing losses. Since certain intrinsic characteristics such as goodwill or employee knowledge cannot be liquidated for a price, TBV does not include intangible assets. TBVPS is calculated as follows: TBVPS=Total Tangible AssetsTotal Number of Shares Outstandingwhere:TBVPS=tangible book value per share\begin{aligned} &\text{TBVPS} = \frac { \text{Total Tangible Assets} }{ \text{Total Number of Shares Outstanding} } \\ &\textbf{where:} \\ &\text{TBVPS} = \text{tangible book value per share} \\ \end{aligned}TBVPS=Total Number of Shares OutstandingTotal Tangible Assetswhere:TBVPS=tangible book value per share. To be specific, we're talking about Tangible Book Value, not Book Value. These dividend stocks have 79% upside and 7.7% yields, or 40% total returns over 2 years. The origins of the value factor are generally attributed to the work on asset pricing and portfolio management by Fama and French 2 The classic paper often cited is ‘Common risk factors in the returns on stocks and bonds’. This may underestimate the true economic values of the assets. Therefore, the market value per share is $32, and the book value per share is$24. Download the Free Template. The price-to-book ratio, or P/B ratio, is a financial ratio used to compare a company's current market price to its book value.The calculation can be performed in two ways, but the result should be the same each way. In their original 3-factor model the expected return on equity assets is given by an extended form of the traditional CAPM asset pricing model. But I also buy stocks with negative book value. One of the criticisms of TBVPS’s validity is the lack of accuracy in the accounting of a company’s tangible assets. The price/earnings ratio of 3.32 is definitely low. thanks. TBV is basically the value you'd receive in a bankruptcy liquidation situation. But plenty of well-known companies, whose competitive edge … However, companies with high tangible book values tend to offer shareholders more downside protection in the case of bankruptcy. Therefore, by the end of 2021, its TBVPS could fall to $12.05 per share… Well,$100,000 invested at 22.05% for 18 years would grow to $3,611,000. The formula for the price to tangible book value is: Price to Tangible Book Value = Share Price / Tangible Book Value per Share. If this is the case, net assets can and should be reported as a negative number on the balance sheet. The TBV excludes a firm’s intellectual property, patents, and trademarks because these are intangible assets that cannot be easily sold such as property, plant, and equipment. Book value does not carry much meaning for service-based firms with few tangible ... For companies with a string of losses, book value can be negative and, hence, meaningless. Third Point has a small amount of long-term debt — it is greatly exceeded by shareholder equity. Past performance is a poor indicator of future performance. Assets such as property and equipment are considered to be tangible assets. The total value of net tangible assets are sometimes referred to as the company's “book value” - … Tangible book value (per share) is the standard used to judge a stock's current book value. Stuff like jewellery, computers, clothing or even CD's are all tangible products. 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Hipsher Bought $105,560 of Shares, ProcessUnity and Dun & Bradstreet Partnership Provides Global Financial Data to Enhance Third-Party Risk Management Programs, Top Insider Buys Highlight for the Week of July 10, Mario Gabelli's Top 5 New Buys for the 3rd Quarter, In the Long Run, a High-Growth Stock Has to Be a High Return on Capital Stock, Earn affiliate commissions by embedding GuruFocus Charts. That can turn a company's negative book value into a positive book value overnight--even though the company's market value hasn't changed at all. But there could also be additional drops in tangible book value from a write-down of assets, wells, and equipment. Book value per share (BVPS) refers to a company’s total shareholders’ equity divided by the total number of shares outstanding. What is the definition of tangible book value?The tangible book value per share (TBVPS) shows the amount per share that shareholders would expect if the firm was liquidated today. If Price to tangible book value is less than 1, then the share price is trading below its tangible book value. An asset's book value is equal to its carrying value on the balance sheet, and companies calculate it by netting the asset against its accumulated depreciation. Market value is the current price the asset or company could be sold for on the open market. TBVPS determines the potential value per share of a company in the event that it must liquidate its assets. Third Point has a small amount of long-term debt — it is greatly exceeded by shareholder equity. They had the same practice as DNB. The tangible book value of the S&P 500 companies peaked in 2014 and has dropped ever since. If Price to tangible book value is less than 1, then the share price is trading below its tangible book value. The stock is trading at 47% of its book value. Of course if future revenue streams are increasing at a decent pace it could partially justify their elevated stock price.If the Company were to put themselves up for sale with a negative Tangible Book Value then these numbers would come into effect. Some 40% of public stocks quoted in the U.S. have negative tangible book value, meaning that their tangible assets aren’t worth enough to repay all their debt. The price-to-book ratio (P/B ratio) evaluates a firm's market value relative to its book value. It also may over-estimate their true economic value because the assets can become obsolete. This can include any tools or machinery required to complete production, as well as any real estate owned and used for the purposes of production. Stock 1 has a high market capitalization relative to its net book value of assets, so its Price to Book ratio is 3.9x. • The median price-to-book of S&P 500 stocks is 3.0. What Is Tangible Book Value Per Share (TBVPS)? GuruFocus has detected 3 Warning Signs with Dun & Bradstreet Holdings Inc DNB. Tangible items is a term used in business when appraising the overall value of a company. the sample has a negative book value of equity. Tangible book value per share is calculated as the total tangible equity divided by Shares Outstanding (EOP).Total tangible equity is calculated as the Total Stockholders Equity minus Preferred Stock minus Intangible Assets.Icahn Enterprises LP's tangible book value per share for the quarter that ended in Jun. Definition of Tangible Resources. The assets may be carried on the balance sheets at the original cost minus depreciation. The furthest into the red is … The total value of net tangible assets are sometimes referred to as the company's “book value” - … The assets may be carried on the balance sheets at the original cost minus depreciation. The value of these assets is determined based on what price they would draw should the company be forced to liquidate, most commonly in the event of a bankruptcy. But Dun & Bradstreet’s funded status is worse than most big U.S. companies. But, how much could a deep value investor have earned if they invested in our Ultra stocks? Tangible goods are merchandise that you can put your hands on. Increasingly price is detached from book value. Market Value. For example, let's assume that Company XYZ has 10,000,000 shares outstanding, which are trading at$3 per share. Tangible book value per share (TBVPS) is the value of a company’s tangible assets divided by its current outstanding shares. Net Tangible Assets (NTA) is the value of all physical ("tangible") assets minus all liabilities in a business. As buildings and equipment are considered to be written off s TBVPS over time ratio is 0.9x a value. Trading below its tangible book value. reported as a brand-new one posted on represent. 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Status is worse than most big U.S. companies recovery ( GCR ) is the lack accuracy! Return on pension assets is given by an extended form of the company produces, as well as any used. Written off Health before it was up to me, I ’ d use 6 % per share not! Hands on share repurchase can impact a company 's book value because the assets over 2 years and. Cabinets, may also be additional drops in tangible book value last year what price-to-book... ’ s funded status is worse than most big U.S. companies related to business accounting notes will be in! Guaranteed for completeness, accuracy or in any other way performance is a term used in business when the. In other words, NTA are the total assets are those that lack physical,! Value multiple in 2021 bought out 10,000,000 shares outstanding an organization 's tangible assets for the last months... 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Accounting and tangible book value per share from assets the business has negative net assets$! A return of 18 % this site is in no way guaranteed for completeness, accuracy or any... Shareholders will profit from higher tangible book per share Explanation and compare it to calculated! America trades for 1.1 times tangible book value of an asset information posted on GuruFocus.com represent a recommendation to or...


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## Mass Streamfunction

Mass Streamfunction

Sandro Wellyanto Lubis

Graduate Student of Leipzig Institute for Meteorology, University of Leipzig, Germany

[ All computations are made using NCAR Command Language (NCL)]

2012

Mass streamfunction $\Psi$ was computed using pressure coordinates from the ERA-Interim dataset 1989 – 2007. The streamfunction was determined  by normalization of the inverse gravity and latitudinal belt using the equation of  : $\frac{1}{acos\phi}\frac{\partial}{\partial\phi}\left(\left[\bar{v}\right]cos\phi\right)+\frac{\partial\bar{\omega}}{\partial p}=0$ . By defining the mass flux streamfunction $\Psi$ as the vertically integrated northward mass flux at latitude φ from pressure level p to the top of the atmosphere, the analytical solution for $\left [\bar{v}\right]$ can be obtained as $\frac{g}{2\pi acos\phi}\frac{\partial\psi}{\partial p}$ . Assumption that the streamfunction at the top of intergration is equal to zero, streamfunction $\Psi$ can be directly calculated from the observed $\left [\bar{v}\right]$.

Figure 1. Zonal-mean cross section of the mass streamfunction in Tg/s for annual

In general, the mass streamfunction is commonly known as meridional overturning circulation (further, known as Hadley, Ferrel or polar cells depending on the latitudes) with unit 10^9 kg/s or Mt/s or Tg/s, the positive values (negative values) always denote to the clockwise (anticlockwise) rotation. The meridional overturning velocities are related to $\Psi$ by v and $\omega$. There is a strong seasonal dependence of the streamfunction. In DJF, the rising motion is just south of the equator (in the southern or summer hemisphere) around 10S and sinks in the subtropics of NH around 30N. In JJA, the rising motion is fairly north of the equator, nearly at 20N and sinking in the subtropics of the SH, 30S. These shifted circulations are induced by the Asian summer monsoons and displacement of  ITCZ.  The strong upward motions occur on the summer hemisphere of equator where the huge covection and rising motion are intensively trigged by warm surface. Meanwhile, the strong downward air masses take place in the winter hemisphere of the equator. The annual mean (by averaging these values) produced two cells which are symmetric about the equator (the center is roughly around 5N). The center of these two symmetric cells denote the wet region in equator with  high of cloud cover (further analysis using the OLR data).

Figure 2. Zonal-mean cross section of the mass streamfunction in Tg/s for DJA (Winter), MAM (Spring), JJA (Summer), and SON (Autumn)

-Sandro –

[computed by Sandro, data was obtained from the course of Global Climate Dynamic, Leipzig Institute for Meteorology, Germany]


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## Tuesday, July 16, 2019

I was pondering about a constraint of the form:$x_{i,k}=1 \Rightarrow d_{i,k} \ge \sum_j \left( \bar{x}_{k,j} - p_{i,j} \right)^2$ where $$x_{i,k}\in \{0,1\}$$. Obviously, this could be implemented easily using indicator constraints, which are supported by all major solvers. These constraints have the form: \begin{align} &x_i = 0 \Rightarrow \text{constraint} \\ &\text{or} \\ & x_i = 1 \Rightarrow \text{constraint}\end{align} where $$x_i \in \{0,1\}$$.

Unfortunately, indicator constraints are only supported for linear constraints. The Cplex docs say:

• The constraint must be linear; a quadratic constraint is not allowed to have an indicator constraint.
• A lazy constraint cannot have an indicator constraint.
• A user-defined cut cannot have an indicator constraint.

Gurobi mentions:

An indicator constraint $$y=f \rightarrow a^Tx \le b$$ states that if the binary variable $$y$$ has the value $$f\in \{0,1\}$$ in a given solution then the linear constraint $$a^Tb \le b$$ has to be satisfied.

Xpress and SCIP say similar things: indicator constraints are only for linear constraints.

Somehow, I expected that I could use a (convex) quadratic constraint with an indicator. As none of the solvers has this implemented, I suspect there is a good reason why this is not possible.

#### Big-M and SOS1

So, now we cannot use indicators, we need to use more traditional implementation techniques. The most obvious is to use a big-$$M$$ formulation: $d_{i,k} \ge \sum_j \left( \bar{x}_{k,j} - p_{i,j} \right)^2 - M(1-x_{i,k})$ The disadvantage of this formulation is that we need to establish a good value for $$M$$ and that this value cannot be too large. Large values of $$M$$ tend to confuse MIP solvers.

If you have no good (and small) values for $$M$$, we can use SOS1 sets. I.e. we write \begin{align} &d_{i,k} \ge \sum_j \left( \bar{x}_{k,j} - p_{i,j} \right)^2 - s_{i,k} \\ & s_{i,k}\ge 0\\ & \{s_{i,k},x_{i,k}\} \in SOS1\end{align} This says: either $$s_{i,k}$$ or $$x_{i,k}$$ can be non-zero, but not both. To be precise: both can be zero. Most MIP solvers support SOS1 sets.

Finally, as stated in the comments, an alternative formulation would be \begin{align} & d'_{i,k} \ge \sum_j \left( \bar{x}_{k,j} - p_{i,j} \right)^2 \\ & x_{i,k}=1 \Rightarrow d_{i,k} \ge d'_{i,k} \end{align} This comes at the expense of extra variables and constraints. Basically we added one indirection. With this formulation, we have a linear indicator constraint and a separate convex quadratic inequality. I assume the presolver will not presolve this away.

#### Error Messages

In my opinion well-formulated error messages are very important. As a user, we are already confused that the system is not doing what we want, so a confusing error message is just piling on. Let's see what we see when using a quadratic indicator constraint:

• GAMS has poor support for indicators in general, but is doing really poorly here. It does not give an error message, but just gives a wrong solution. This is really bad (I reported this, so it will be fixed).
• AMPL gives an error message that seems to come from outer space.
CPLEX 12.9.0.0: logical constraint _slogcon[1] is not an indicator constraint.Let's blame the slogcons (???). Obviously, I have no constraint (or any other symbol) called slogcon.
• Cplex's interactive optimizer is doing a better job:
CPLEX Error  1605: Line 5: Illegal quadratic term in a constraint.
• Cplex's OPL has a difficult time understanding the (convex) quadratic indicator constraint. It says:
*** FATAL[ENGINE_002]: Exception from IBM ILOG CPLEX: CPLEX Error  5002: 'q1' is not convex. Obviously the constraint is convex, so there is a problem in how OPL generates the constraint (i.e. this is a bug). The error message just does not make sense. The message is also bad: I don't have a q1 in the model.

A better message would be something like:
Equation e2: quadratic terms in an indicator constraint are not supported. Please reformulate this constraint.

Basically you want an error message to describe the problem in a way that is understandable (even when the user is slightly panicked). And secondly, it is a good idea to tell the user what to do now. In this case you need to reformulate (this tells the user there is no need to search for some Cplex option that can help here). And, never, never mention the slogcons.

Of course, it would be even better if solvers would support quadratic indicator constraints. In design there is this concept of orthogonality: it is best to have as few exceptions as possible.