From: Ka-In Yen on

Pmb wrote:
> >> l m<i,j,k> = <a,b,c> m
> >>
> >> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> >> and <i,j,k> is a unit vector which gives the direction of
> >> the vector.
>
> <i,j,k> is not a unit vector. It has a magnitude of sqrt(3)

Dear Pete,
Thank you for your comment. i=a/l, j=b/l, and k=c/l.
<i,j,k> is a unit vector.

>
> >> 2. Linear mass density is a vector.
> >>
> >> The mass of a string is M kg, and the length of the string
> >> is l m<i:3>. Where l m is the magnitude of the length, and
> >> <i:3> is a 3-D unit vector which gives the direction of the
> >> string. Then the linear mass density of the string is:
> >>
> >> M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> That doesn't mean that you can call mass a vector. Mass is a scalar which
> has a value at every point on the string. As you have it there are two
> vectors each of which are tangent to the string and point in opposite
> directions.

Vector of linear mass density and vector of surface mass
density are a long name; shortly I call them mass vector.
Sorry for the confussion. Please refer to:
http://www.geocities.com/redlorikee/mdb2.html

Ka-In Yen

From: Ka-In Yen on
Back to 1905, Einstein was lack of a fine tool to solve
the null result of MMX; STR was based on an incomplete
physical mathematics.

Ka-In Yen
Magnetic force: Drag nd Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee

Ka-In Yen wrote:
> The proof of mass vector.
>
> Introduction:
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
>
> 1. The unit of vector.
>
> In physics, The unit of three-dimensional cartesian coordinate
> systems is meter. In this paper, a point of 3-D coordinate
> system is written as
>
> (p1,p2,p3) m, or (p:3) m
>
> and a vector is written as
>
> <a,b,c> m, or <a:3> m
>
> or
>
> l m<i,j,k> = <a,b,c> m
>
> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> and <i,j,k> is a unit vector which gives the direction of
> the vector.
>
> For three reasons, a magnitude of a vector can not add to a
> scalar:
> i) The magnitude belongs to the set of vector; it's a
> portion of a vector. Scalar belongs to a field.
> ii) The magnitude is real non-negative number, but scalar
> is real number.
> iii) The unit of magnitude is meter, but scalar has no unit.
> This is a major difference between physics and mathematics.
> 5m+3 is meaningless.
>
>
> 2. Linear mass density is a vector.
>
> The mass of a string is M kg, and the length of the string
> is l m<i:3>. Where l m is the magnitude of the length, and
> <i:3> is a 3-D unit vector which gives the direction of the
> string. Then the linear mass density of the string is:
>
> M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> The direction, <i:3>, is not changed by "division", so we
> can move <i:3> from denominator to numerator. A direction
> is changed by -1 only. A proof is found in Clifford algebras:
>
> [Proof]
> k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
> =(k/l) <i,j,k>
> where l is the magnitude of <a,b,c>, and <i,j,k> is the
> unit vector of <a,b,c>.
> [Proof]
>
>
> 3. Surface mass density is a vector.
>
> A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
> and <j:3> are unit vectors. The area vector of the parallelogram
> is the cross product of these two vectors.
>
> l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
> = lh abs(sin(theta)) (m^2)<k:3>
>
> Where theta is the angle between <i:3> and <j:3>. <k:3> is
> a unit vector which is perpendicular to <i:3> and <j:3>.
> For AXB=-BXA, an area has two directions.
>
> We can divide the area vector by the length vector.
>
> lh*abs(sin(theta))<k:3>/[l<i:3>]
> =h<i:3>X<j:3>/<i:3>
> =h(<i:3>X<j:3>)X<i:3>
> (The direction, <i:3>, is not changed by "division", and
> the division is replaced by a cross product.)
> =-h<i:3>X(<i:3>X<j:3>)
> =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
> (where o is dot product.)
> =-h(cos(theta)<i:3>-<j:3>)
> =h(<j:3>-cos(theta)<i:3>) m
>
> The result is a rectangle, not the original parallelogram. We
> can test the result.
>
> h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>
>
> The magnitude of the area vector is conserved, but the direction
> is opposite.
>
> The mass of a round plate is M kg, and the area vector is
> A m^2<i:3>; then the surface mass density is
>
> M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>
>
>
> 4. Mass vector in physics.
>
> Mass vector has been found in two equations: 1) the velocity
> equation of string. 2) Bernoulli's equation.
>
> i) For waves on a string, we have the velocity equation:
>
> v=sqrt(tau/mu). v is velocity of wave, tau is tension
> applying to string, and mu is linear mass density of
> string. We can rewrite the equation:
>
> mu=tau/v^2.
>
> In the above equation, the mu is parallel to tau, and both
> of them are vector.
>
> ii) Bernoulli's equation is:
>
> P + k*v^2/2=C (P is pressure, k is volume density, and v is
> velocity. Here we neglect the gravitational term.)
>
> Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
> equation(where <i:3> is a unit vector),
>
> P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
> F<i:3> + L<i:3>*v^2/2=C*A<i:3>
> (where F is the magnitude of force, and L is the magnitude
> of linear mass density.)
>
> These two equations are well used in the theory "Magnetic force:
> Combining Drag force and Bernoulli force of ether dynamics."
> For detail, please refer to my site:
> http://www.geocities.com/redlorikee

From: Hexenmeister on

"Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message
news:1137987739.530029.300450(a)f14g2000cwb.googlegroups.com...
> Back to 1905, Einstein was lack of a fine tool to solve
> the null result of MMX;

No he wasn't. Georges Sagnac had it built by 1913.
http://www.androcles01.pwp.blueyonder.co.uk/Sagnac.JPG


> STR was based on an incomplete
> physical mathematics.

Wrong again.
STR was based on a deliberate hoax.
http://www.androcles01.pwp.blueyonder.co.uk/how_to_be_as_smart_as_einstein.htm

>
> Ka-In Yen
> Magnetic force: Drag nd Bernoulli force of ether dynamics.
> http://www.geocities.com/redlorikee


Wrong a third time. There is no aether.
http://www.androcles01.pwp.blueyonder.co.uk/RR_C7/RelativityRevealed.htm

Notice I'm using real data.
Hexenmeister.


From: Ka-In Yen on

Hexenmeister wrote:
> "Ka-In Yen" <yenkain(a)yahoo.com.tw> wrote in message
> news:1137987739.530029.300450(a)f14g2000cwb.googlegroups.com...
> > Back to 1905, Einstein was lack of a fine tool to solve
> > the null result of MMX;
>
> No he wasn't. Georges Sagnac had it built by 1913.
> http://www.androcles01.pwp.blueyonder.co.uk/Sagnac.JPG
>
>
> > STR was based on an incomplete
> > physical mathematics.
>
> Wrong again.
> STR was based on a deliberate hoax.
> http://www.androcles01.pwp.blueyonder.co.uk/how_to_be_as_smart_as_einstein.htm
>
> >
> > Ka-In Yen
> > Magnetic force: Drag nd Bernoulli force of ether dynamics.
> > http://www.geocities.com/redlorikee
>
>
> Wrong a third time. There is no aether.
> http://www.androcles01.pwp.blueyonder.co.uk/RR_C7/RelativityRevealed.htm
>
> Notice I'm using real data.

Dear Hexenmeister,

Thank you for your comment. It's a high probability that a flawless
derivation has some physical meaning. If you find any flaw of the
mathematic derivation of the theory, please kindly advise me; it's
grateful.

Ka-In Yen
Magnetic force: Drag nd Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee

From: Ka-In Yen on
Physicists need more training in vector algebra and logic,
especially logic. Leading by Einstein, they overthrew logic.
What a bunch of lunatic idiots!!!

Ka-In Yen
Magnetic force: Drag nd Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee

Ka-In Yen wrote:
> The proof of mass vector.
>
> Introduction:
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
>
> 1. The unit of vector.
>
> In physics, The unit of three-dimensional cartesian coordinate
> systems is meter. In this paper, a point of 3-D coordinate
> system is written as
>
> (p1,p2,p3) m, or (p:3) m
>
> and a vector is written as
>
> <a,b,c> m, or <a:3> m
>
> or
>
> l m<i,j,k> = <a,b,c> m
>
> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> and <i,j,k> is a unit vector which gives the direction of
> the vector.
>
> For three reasons, a magnitude of a vector can not add to a
> scalar:
> i) The magnitude belongs to the set of vector; it's a
> portion of a vector. Scalar belongs to a field.
> ii) The magnitude is real non-negative number, but scalar
> is real number.
> iii) The unit of magnitude is meter, but scalar has no unit.
> This is a major difference between physics and mathematics.
> 5m+3 is meaningless.
>
>
> 2. Linear mass density is a vector.
>
> The mass of a string is M kg, and the length of the string
> is l m<i:3>. Where l m is the magnitude of the length, and
> <i:3> is a 3-D unit vector which gives the direction of the
> string. Then the linear mass density of the string is:
>
> M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> The direction, <i:3>, is not changed by "division", so we
> can move <i:3> from denominator to numerator. A direction
> is changed by -1 only. A proof is found in Clifford algebras:
>
> [Proof]
> k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
> =(k/l) <i,j,k>
> where l is the magnitude of <a,b,c>, and <i,j,k> is the
> unit vector of <a,b,c>.
> [Proof]
>
>
> 3. Surface mass density is a vector.
>
> A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
> and <j:3> are unit vectors. The area vector of the parallelogram
> is the cross product of these two vectors.
>
> l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
> = lh abs(sin(theta)) (m^2)<k:3>
>
> Where theta is the angle between <i:3> and <j:3>. <k:3> is
> a unit vector which is perpendicular to <i:3> and <j:3>.
> For AXB=-BXA, an area has two directions.
>
> We can divide the area vector by the length vector.
>
> lh*abs(sin(theta))<k:3>/[l<i:3>]
> =h<i:3>X<j:3>/<i:3>
> =h(<i:3>X<j:3>)X<i:3>
> (The direction, <i:3>, is not changed by "division", and
> the division is replaced by a cross product.)
> =-h<i:3>X(<i:3>X<j:3>)
> =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
> (where o is dot product.)
> =-h(cos(theta)<i:3>-<j:3>)
> =h(<j:3>-cos(theta)<i:3>) m
>
> The result is a rectangle, not the original parallelogram. We
> can test the result.
>
> h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>
>
> The magnitude of the area vector is conserved, but the direction
> is opposite.
>
> The mass of a round plate is M kg, and the area vector is
> A m^2<i:3>; then the surface mass density is
>
> M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>
>
>
> 4. Mass vector in physics.
>
> Mass vector has been found in two equations: 1) the velocity
> equation of string. 2) Bernoulli's equation.
>
> i) For waves on a string, we have the velocity equation:
>
> v=sqrt(tau/mu). v is velocity of wave, tau is tension
> applying to string, and mu is linear mass density of
> string. We can rewrite the equation:
>
> mu=tau/v^2.
>
> In the above equation, the mu is parallel to tau, and both
> of them are vector.
>
> ii) Bernoulli's equation is:
>
> P + k*v^2/2=C (P is pressure, k is volume density, and v is
> velocity. Here we neglect the gravitational term.)
>
> Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
> equation(where <i:3> is a unit vector),
>
> P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
> F<i:3> + L<i:3>*v^2/2=C*A<i:3>
> (where F is the magnitude of force, and L is the magnitude
> of linear mass density.)
>
> These two equations are well used in the theory "Magnetic force:
> Combining Drag force and Bernoulli force of ether dynamics."
> For detail, please refer to my site:
> http://www.geocities.com/redlorikee

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