Refer to the congruence commission for standard value of the Japanese Society for Pediatric Endocrinology and the Japanese Society for auxology in 0-17 years old. Refer to the National Health and Nutrition Examination Survey in 2010 and 2011 in 18 years old or elder.
Gender
Male
Female
Age
Reference height (cm)
Reference weight (kg)
Reference height (cm)
Reference weight (kg)
0-5 M
61.5
6.3
60.1
5.9
6-11 M
71.6
8.8
70.2
8.1
6-8 M
69.8
8.4
68.3
7.8
9-11 M
73.2
9.1
71.9
8.4
1-2
85.8
11.5
84.6
11.0
3-5
103.6
16.5
103.2
16.1
6-7
119.5
22.2
118.3
21.9
8-9
130.4
28.0
130.4
27.4
10-11
142.0
35.6
144.0
36.3
12-14
160.5
49.0
155.1
47.5
15-17
170.1
59.7
157.7
51.9
18-29
170.3
68.5
158.0
53.1
30-49
170.7
68.5
158.0
53.1
50-69
166.6
65.3
153.5
53.0
70-
160.8
60.0
148.0
49.5
Standard physique in 2010 edition
Refer to the National Health and Nutrition Examination Survey in 2005 and 2006 in 1 year old or elder. Refer to the Infant Physical Development Research in 2000 in less than 1 year old.
If the equation of a curve C in the plane is given as , the line integral (14) is evaluated by placing in the integrand to obtain the definite integral
which is then evaluated in the usual manner.
Similarly if C is given as , then and the line integral becomes
If C is given in parametric form , the line integral becomes
where and denote the values of corresponding to points and respectively.
Combination of the above methods may be used in the evaluation.
Similar methods are used for evaluating line integrals along space curve.
It is often convenient to express a line integral in vector form as an aid in physical or geometric understanding as well as for brevity of notation. For example, we can express the line integral (15) in the form
where and . The line integral (14) is a special case of this with .
If at each point (x, y, z) we associate a force F acting on an object (i.e. if a force field is defined), then
represents physically the total work done in moving the object along the curve C.
Let C be a curve in the xy plane which connects points and , (see Fig. 6-2). Let and be single-valued functions defined at all points of C. Subdivide C into n parts by choosing n – 1 points on it given by . Call and and suppose that points are chosen so that they are situated on C between points and . Form the sum
The limit of this sum as in such a way that all quantities approaches zero, if such limit exists, is called a line integral along C and is denoted by
or
The limit does exist if P and Q are continuous (or piecewise continuous) at all points of C. The value of the integral depends in general on P, Q, the particular curve C, and on the limits and .
In an exactly analogous manner one may define a line integral along a curve C in three dimensional space as
where , and are functions of , and .
Other types of line integrals, depending on particular curves, can be defined. For example, if denotes the arc length along curve C in the above figure between points and , then
is called the line integral of along curve C. Extensions to three (or higher) dimensions are possible.
You may fit honeycomb grid on the diffuser of soft box or light bank.
Soft box and light bank convert point light of speedlight into diffused surface light. Then the hard shade of the subject with speed light alone is converted into soft shade and the sharp shadow falling on the background is converted into mild shadow, respectively.
Honeycomb grid converts a surface light into convergent light with adding directivity, smooth a shade of subject and make the border of shadow unclear, respectively. As the ratio of the height of the grid to the area of the grid is greater, the light more converges with directivity. As the ratio is smaller, the directivity weaken and the light quality approaches to the diffused light.
The beam of the light from each grid diffuses on the subject. As the grids are arrayed offset each other, the beam with shifted optical axis reaches to the subject. As a result, the amount of light overlapped on the center of the surface becomes almost uniform, but on the peripheral area around it becomes gradually dark.
As the distance of the subject from the light source is longer, the shade becomes unclear and diffused and the area of diffuser becomes small from the point of view of the subject, the light quality approaches to point light.
Since the aperture of the honeycomb grid with straw is circular, you can’t use enough light. In this article, I’d like to describe how to cut out the honeycomb grid from a sheet of paper.
Spec
Materials
Assenbly
1.Spec
Since the guide number of Hikaru-Komachi is only 13, you can’t use in the field. I’d like to describe about honeycomb grid, it’s assumed to use of speed light with larger guide number and to attach to handmade soft-box. You should take care of flame with overheat because it’s made with paper.
In order to cut out a regular hexagonal grid from a sheet of paper, you have to draw a developed view as following;
Regardless of the length of hexagon, the length of the long side would be three quarters of the original. The length of the short side depends on the thickness of the grid. Irradiation angle depends on the ratio of the thickness of the grid and the length of the sides of the hexagon.
2. Materials
Materials are bellow;
Black Kent paper (A4)
Adhesive
Although you can purchase black Kent paper in Amazon, it’s too many to use with individual. You should purchase it in art supply store.
3. Assembly
Put the cut with a cutter knife and ruler and crease with ruler. Be careful because valley fold and mountain fold would visit alternatively.
Glue the opposite sides of the valley fold. You would understand the side to glue when you crease.
In evaluating a multiple integral over a region , it is often convenient to use coordinates other than rectangular, such as the curvilinear coordinates considered in Chapter 5.
If we let be curvilinear coordinates of points in a plane, there will be a set of transformation equations mapping points of the xy plane into points of the uv plane. In such case the region of the xy plane is mapped into a region of the uv plane. We then have
where and
is the Jacobian of x and y with respect to u and v.
Similarly if are curvilinear coordinates in three dimensions, there will be a set of transformation equations , , and we can write
where and
is the Jacobian of x, y and z with respect to u, v and w.
The results (9) and (11) correspond to change of variables for double and triple integrals.
Generalizations to higher dimensions are easily made.
The Japanese Society for Dialysis Therapy (JSDT) recommends PCR as an indicator of protein intake. Otherwise K/DOQQI recommends nPNA. If you calculate Kt/V with Daugirdas’ method, you can also define nPNA.
The above results are easily generalized to closed regions in three dimensions. For example, consider a function defined in a closed three dimensional region . Subdivided the region into n subregions of volume . Letting be some point in each subregion, we form
where the number n of subdivisions approaches infinity in such a way that the largest linear dimension of each subregion approaches zero. If this limit exists we denote it by
called the triple integral of over . The limit dose exist if is continuous (or piecewise continuous) in .
If we construct a grid consisting of planes parallel to the xy, yz and xz planes, the region is subdivided into subregions which are rectangular parallelepipeds. In such case we can express the triple integral over given by (7) as an iterated integral of the form
(where the innermost integral is to be evaluated first) or the sum of such integrals. The integration can also be performed in any other order to give an equivalent result.
Extensions to higher dimensions are also possible.
In Japan, Shinzato’s fomula for calculating Kt/V, an indicator of efficiency of dialysis, is recommended by JSDT. Since integral equation is used to solve Shinzato’s method, you couldn’t solve algebraically. In K/DOQQI, it is usual to solve Kt/V with Daugirdas’ method. Shinzato has described that Daugirdas’ Kt/V is similar to Shinzato’s Kt/V.
![\displaystyle \int_C [P(x, y)dx + Q(x, y)dy] = \int_C P(x, y)dx + \int_C Q(x, y)dy](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_C+%5BP%28x%2C+y%29dx+%2B+Q%28x%2C+y%29dy%5D+%3D+%5Cint_C+P%28x%2C+y%29dx+%2B+%5Cint_C+Q%28x%2C+y%29dy&bg=T&fg=000000&s=0 "\displaystyle \int_C [P(x, y)dx + Q(x, y)dy] = \int_C P(x, y)dx + \int_C Q(x, y)dy")
![\displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)} [Pdx + Qdy] = - \int_{(a_2, b_2)}^{(a_1, b_1)}[Pdx + Qdy]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7B%28a_1%2C+b_1%29%7D%5E%7B%28a_2%2C+b_2%29%7D+%5BPdx+%2B+Qdy%5D+%3D+-+%5Cint_%7B%28a_2%2C+b_2%29%7D%5E%7B%28a_1%2C+b_1%29%7D%5BPdx+%2B+Qdy%5D&bg=T&fg=000000&s=0 "\displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)} [Pdx + Qdy] = - \int_{(a_2, b_2)}^{(a_1, b_1)}[Pdx + Qdy]")
![\displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)} [Pdx + Qdy] = \int_{(a_1, b_1)}^{(a_3, b_3)} [Pdx + Qdy] + \int_{(a_3, b_3)}^{(a_2, b_2)} [Pdx + Qdy]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7B%28a_1%2C+b_1%29%7D%5E%7B%28a_2%2C+b_2%29%7D+%5BPdx+%2B+Qdy%5D+%3D+%5Cint_%7B%28a_1%2C+b_1%29%7D%5E%7B%28a_3%2C+b_3%29%7D+%5BPdx+%2B+Qdy%5D+%2B+%5Cint_%7B%28a_3%2C+b_3%29%7D%5E%7B%28a_2%2C+b_2%29%7D+%5BPdx+%2B+Qdy%5D+&bg=T&fg=000000&s=0 "\displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)} [Pdx + Qdy] = \int_{(a_1, b_1)}^{(a_3, b_3)} [Pdx + Qdy] + \int_{(a_3, b_3)}^{(a_2, b_2)} [Pdx + Qdy]")
is given as
, the line integral (14) is evaluated by placing
in the integrand to obtain the definite integral
![\displaystyle \int_{a_1}^{a_2}[P\{x, f(x)\}dx + Q\{x, f(x)\}f'(x)dx] \cdots(19)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7Ba_1%7D%5E%7Ba_2%7D%5BP%5C%7Bx%2C+f%28x%29%5C%7Ddx+%2B+Q%5C%7Bx%2C+f%28x%29%5C%7Df%27%28x%29dx%5D+%5Ccdots%2819%29&bg=T&fg=000000&s=0 "\displaystyle \int_{a_1}^{a_2}[P\{x, f(x)\}dx + Q\{x, f(x)\}f'(x)dx] \cdots(19)")
, then
and the line integral becomes
![\displaystyle \int_{b_1}^{b_2}[P\{g(y), y\}g'(y)dy + Q\{g(y), y\}dy]\cdots(20)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7Bb_1%7D%5E%7Bb_2%7D%5BP%5C%7Bg%28y%29%2C+y%5C%7Dg%27%28y%29dy+%2B+Q%5C%7Bg%28y%29%2C+y%5C%7Ddy%5D%5Ccdots%2820%29&bg=T&fg=000000&s=0 "\displaystyle \int_{b_1}^{b_2}[P\{g(y), y\}g'(y)dy + Q\{g(y), y\}dy]\cdots(20)")
, the line integral becomes
![\displaystyle \int_{t_1}^{t_2} [P\{ \phi(t),\ \psi(t) \}\phi'(t)dt + Q\{ \phi(t),\ \psi(t) \}\psi'(t)dt] \cdots (21)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%5BP%5C%7B+%5Cphi%28t%29%2C%5C+%5Cpsi%28t%29+%5C%7D%5Cphi%27%28t%29dt+%2B+Q%5C%7B+%5Cphi%28t%29%2C%5C+%5Cpsi%28t%29+%5C%7D%5Cpsi%27%28t%29dt%5D+%5Ccdots+%2821%29&bg=T&fg=000000&s=0 "\displaystyle \int_{t_1}^{t_2} [P\{ \phi(t),\ \psi(t) \}\phi'(t)dt + Q\{ \phi(t),\ \psi(t) \}\psi'(t)dt] \cdots (21)")
and
denote the values of
corresponding to points
and
respectively.
![\displaystyle \int_{C}[A_1dx + A_2dy + A_3dz] \\ = \int_{C} (A_1\bold{i} + A_2\bold{j} + A_3\bold{k}) \cdot (dx\bold{i} + dy\bold{j} + dz\bold{k})\\ = \int_{C} \bold{A}\cdot d\bold{r} \cdots (17)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7BC%7D%5BA_1dx+%2B+A_2dy+%2B+A_3dz%5D+%5C%5C++%3D+%5Cint_%7BC%7D+%28A_1%5Cbold%7Bi%7D+%2B+A_2%5Cbold%7Bj%7D+%2B+A_3%5Cbold%7Bk%7D%29+%5Ccdot+%28dx%5Cbold%7Bi%7D+%2B+dy%5Cbold%7Bj%7D+%2B+dz%5Cbold%7Bk%7D%29%5C%5C++%3D+%5Cint_%7BC%7D+%5Cbold%7BA%7D%5Ccdot+d%5Cbold%7Br%7D+%5Ccdots+%2817%29+&bg=T&fg=000000&s=0 "\displaystyle \int_{C}[A_1dx + A_2dy + A_3dz] \\ = \int_{C} (A_1\bold{i} + A_2\bold{j} + A_3\bold{k}) \cdot (dx\bold{i} + dy\bold{j} + dz\bold{k})\\ = \int_{C} \bold{A}\cdot d\bold{r} \cdots (17)")
and
. The line integral (14) is a special case of this with
.
and
, (see Fig. 6-2). Let
and
be single-valued functions defined at all points of C. Subdivide C into n parts by choosing n – 1 points on it given by
. Call
and
and suppose that points
are chosen so that they are situated on C between points
and
. Form the sum
in such a way that all quantities
approaches zero, if such limit exists, is called a line integral along C and is denoted by
or
and
.
![\displaystyle \lim\limits_{n \rightarrow\infty}\sum_{k=1}^{n}\left\{ A_1(\xi_k, \eta_k, \zeta_k)\Delta x_k + A_2(\xi_k, \eta_k, \zeta_k)\Delta y_k + A_3(\xi_k, \eta_k, \zeta_k)\Delta z_k \right\} \\ = \int_C \left[ A_1dx + A_2dy + A_3dz \right] \cdots(15)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Clim%5Climits_%7Bn+%5Crightarrow%5Cinfty%7D%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%5Cleft%5C%7B+A_1%28%5Cxi_k%2C+%5Ceta_k%2C+%5Czeta_k%29%5CDelta+x_k+%2B+A_2%28%5Cxi_k%2C+%5Ceta_k%2C+%5Czeta_k%29%5CDelta+y_k+%2B+A_3%28%5Cxi_k%2C+%5Ceta_k%2C+%5Czeta_k%29%5CDelta+z_k++%5Cright%5C%7D+%5C%5C+%3D+%5Cint_C+%5Cleft%5B+A_1dx+%2B+A_2dy+%2B+A_3dz+%5Cright%5D+%5Ccdots%2815%29&bg=T&fg=000000&s=0 "\displaystyle \lim\limits_{n \rightarrow\infty}\sum_{k=1}^{n}\left\{ A_1(\xi_k, \eta_k, \zeta_k)\Delta x_k + A_2(\xi_k, \eta_k, \zeta_k)\Delta y_k + A_3(\xi_k, \eta_k, \zeta_k)\Delta z_k \right\} \\ = \int_C \left[ A_1dx + A_2dy + A_3dz \right] \cdots(15)")
,
and
are functions of
,
and
.
denotes the arc length along curve C in the above figure between points
, then
along curve C. Extensions to three (or higher) dimensions are possible.
![\displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)}\left[ Pdx + Qdy \right]\cdots(14)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cint_%7B%28a_1%2C+b_1%29%7D%5E%7B%28a_2%2C+b_2%29%7D%5Cleft%5B+Pdx+%2B+Qdy+%5Cright%5D%5Ccdots%2814%29&bg=T&fg=000000&s=0 "\displaystyle \int_{(a_1, b_1)}^{(a_2, b_2)}\left[ Pdx + Qdy \right]\cdots(14)")
, it is often convenient to use coordinates other than rectangular, such as the curvilinear coordinates considered in Chapter 5.
be curvilinear coordinates of points in a plane, there will be a set of transformation equations
mapping points
of the xy plane into points
of the uv plane. We then have
and
are curvilinear coordinates in three dimensions, there will be a set of transformation equations
,
,
and we can write
and
defined in a closed three dimensional region
. Letting
be some point in each subregion, we form
![\displaystyle \int_{x=a}^{b}\int_{y=g_1(x)}^{g_2(x)}\int_{z=f_1(x,y)}^{f_2(x,y)}F(x, y, z)dxdydz = \\ \int_{x=a}^{b} \left [ \int_{y=g_1(x)}^{g_2(x)} \left \{ \int_{z=f_1(x,y)}^{f_2(x,y)} F(x, y, z)dz \right \} dy \right ] dx\cdots(8)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle++%5Cint_%7Bx%3Da%7D%5E%7Bb%7D%5Cint_%7By%3Dg_1%28x%29%7D%5E%7Bg_2%28x%29%7D%5Cint_%7Bz%3Df_1%28x%2Cy%29%7D%5E%7Bf_2%28x%2Cy%29%7DF%28x%2C+y%2C+z%29dxdydz+%3D+%5C%5C++%5Cint_%7Bx%3Da%7D%5E%7Bb%7D+%5Cleft+%5B+%5Cint_%7By%3Dg_1%28x%29%7D%5E%7Bg_2%28x%29%7D+%5Cleft+%5C%7B+%5Cint_%7Bz%3Df_1%28x%2Cy%29%7D%5E%7Bf_2%28x%2Cy%29%7D+F%28x%2C+y%2C+z%29dz+%5Cright+%5C%7D+dy+%5Cright+%5D+dx%5Ccdots%288%29&bg=T&fg=000000&s=0 "\displaystyle \int_{x=a}^{b}\int_{y=g_1(x)}^{g_2(x)}\int_{z=f_1(x,y)}^{f_2(x,y)}F(x, y, z)dxdydz = \\ \int_{x=a}^{b} \left [ \int_{y=g_1(x)}^{g_2(x)} \left \{ \int_{z=f_1(x,y)}^{f_2(x,y)} F(x, y, z)dz \right \} dy \right ] dx\cdots(8)")
![\displaystyle \mathrm{Kt/V} = - LN( R - 0.08 \times t ) + \left[ 4 - \left( 3.5 \times R \right) \right] \times\frac{\mathrm{UF}}{\mathrm{W}}\\ = - LN \left( \frac{\mathrm{postBUN}}{\mathrm{preBUN}} - 0.008 \times t \right) + \left[ 4 - \left( 3.5 \times \frac{\mathrm{postBUN}}{\mathrm{preBUN}} \right) \right] \times \frac{\mathrm{preWeight} - \mathrm{postWeight}}{\mathrm{postWeight}} \cdots(1)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cmathrm%7BKt%2FV%7D+%3D+-+LN%28+R+-+0.08+%5Ctimes+t+%29+%2B+%5Cleft%5B+4+-+%5Cleft%28+3.5+%5Ctimes+R+%5Cright%29+%5Cright%5D+%5Ctimes%5Cfrac%7B%5Cmathrm%7BUF%7D%7D%7B%5Cmathrm%7BW%7D%7D%5C%5C++%3D+-+LN+%5Cleft%28+%5Cfrac%7B%5Cmathrm%7BpostBUN%7D%7D%7B%5Cmathrm%7BpreBUN%7D%7D+-+0.008+%5Ctimes+t+%5Cright%29+%2B+%5Cleft%5B+4+-+%5Cleft%28+3.5+%5Ctimes+%5Cfrac%7B%5Cmathrm%7BpostBUN%7D%7D%7B%5Cmathrm%7BpreBUN%7D%7D+%5Cright%29+%5Cright%5D+%5Ctimes+%5Cfrac%7B%5Cmathrm%7BpreWeight%7D+-+%5Cmathrm%7BpostWeight%7D%7D%7B%5Cmathrm%7BpostWeight%7D%7D+%5Ccdots%281%29&bg=T&fg=000000&s=0 "\displaystyle \mathrm{Kt/V} = - LN( R - 0.08 \times t ) + \left[ 4 - \left( 3.5 \times R \right) \right] \times\frac{\mathrm{UF}}{\mathrm{W}}\\ = - LN \left( \frac{\mathrm{postBUN}}{\mathrm{preBUN}} - 0.008 \times t \right) + \left[ 4 - \left( 3.5 \times \frac{\mathrm{postBUN}}{\mathrm{preBUN}} \right) \right] \times \frac{\mathrm{preWeight} - \mathrm{postWeight}}{\mathrm{postWeight}} \cdots(1)")
![\displaystyle \mathrm{Ce} = \mathrm{Cs} Exp\left( - \frac{\mathrm{Kt}}{\mathrm{V}} \right) + \frac{\mathrm{G}}{\mathrm{K}}\left[ 1 - Exp\left( - \frac{\mathrm{Kt}}{\mathrm{V}} \right) \right] \cdots(3)](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Cmathrm%7BCe%7D+%3D+%5Cmathrm%7BCs%7D+Exp%5Cleft%28+-+%5Cfrac%7B%5Cmathrm%7BKt%7D%7D%7B%5Cmathrm%7BV%7D%7D+%5Cright%29+%2B+%5Cfrac%7B%5Cmathrm%7BG%7D%7D%7B%5Cmathrm%7BK%7D%7D%5Cleft%5B+1+-+Exp%5Cleft%28+-+%5Cfrac%7B%5Cmathrm%7BKt%7D%7D%7B%5Cmathrm%7BV%7D%7D+%5Cright%29+%5Cright%5D+%5Ccdots%283%29&bg=T&fg=000000&s=0 "\displaystyle \mathrm{Ce} = \mathrm{Cs} Exp\left( - \frac{\mathrm{Kt}}{\mathrm{V}} \right) + \frac{\mathrm{G}}{\mathrm{K}}\left[ 1 - Exp\left( - \frac{\mathrm{Kt}}{\mathrm{V}} \right) \right] \cdots(3)")