Author: claimsbot

1. A pharmaceutical composition comprising a salt of a weak base compound of formula:
wherein X is hydrogen, halogen, alkyl of less than 7 carbon atoms or alkoxy of less than 7 carbon atoms; n is a positive integer of less than 4; Y is hydrogen, chlorine, nitro, methyl, ethyl or oxychloro; R is hydrogen, alkylaminocarbonyl wherein the alkyl group has from 3 to 6 carbon atoms or an alkyl group having from I to 8 carbons and R2 is 4-thiazolyl, NHCOOR1 wherein R1 is aliphatic hydrocarbon of less than 7 carbon atoms, or an alkyl group of less than 7 carbon atoms;
one or more free acids; and
optional pharmaceutical additives, wherein the salt and one or more free acids are present in the composition at a ratio of 1:0.5 to 1:3 by weight.
2. The pharmaceutical composition of claim 1, wherein the salt is one or more selected from the group consisting of: chlorides, bromides, phosphates, sulfates, tosylates, benzoylates, nitrates, sulfonates, formates, tartrates, maleates, malates, citrates, benzoates, salicylates, ascorbates and mesylates.
3. The pharmaceutical composition of claim 2, wherein the salt is one or more selected from the group consisting of: chlorides, phosphates, sulfates, tosylates, benzoylates and mesylates.
4. The pharmaceutical composition of claim 1, wherein the salt and the free acid are present in the composition in a weight ratio of 1:1.
5. The pharmaceutical composition of claim 1, wherein the salt and the free acid are present in the composition in a weight ratio of 1:2.
6. The pharmaceutical composition of claim 1, wherein the salt is crystalline.
7. The pharmaceutical composition of claim 1, wherein the pH of an aqueous solution or suspension of the composition is 2 or less.
8. The pharmaceutical composition of claim 1, wherein the weak base compound is an imidazole derivative.
9. The pharmaceutical composition of claim 8, wherein the weak base compound is
where n is an integer from 1 to 3 and R is hydrogen, alkyl having from 1 to 7 carbon atoms, chloro, bromo, fluoro, oxychloro, hydroxy, sulfhydryl or alkoxy having the formula \u2014O(CH2)yCH3 wherein y is an integer from 0 to 6.
10. The pharmaceutical composition of claim 1, wherein the weak base compound is a benzimidazole derivative.
11. The pharmaceutical composition of claim 10, wherein the weak base compound is carbendazim.
12. The pharmaceutical composition of claim 1, wherein the weak base compound is a pyridine derivative.
13. The pharmaceutical composition of claim 1, wherein the weak base compound is an aniline derivative.
14. The pharmaceutical composition of claim 1, wherein the composition is used for oral, intravenous or infusion administration.
15. The pharmaceutical composition of claim 1, wherein the free acid has the same anion as the salt.
16. The pharmaceutical composition of claim 15, further comprising a free acid having a different anion as the salt.
17. The pharmaceutical composition of claim 1, wherein the free acid has a different anion as the salt.
18. A solution or suspension of the pharmaceutical composition of claim 1.
19. A crystalline salt of a weak base compound of formula:
wherein X is hydrogen, halogen, alkyl of less than 7 carbon atoms or alkoxy of less than 7 carbon atoms; n is a positive integer of less than 4; Y is hydrogen, chlorine, nitro, methyl, ethyl or oxychloro; R is hydrogen, alkylaminocarbonyl wherein the alkyl group has from 3 to 6 carbon atoms or an alkyl group having from 1 to 8 carbons, and R2 is 4-thiazolyl, NHCOOR1 wherein R1 is an aliphatic hydrocarbon of less than 7 carbon atoms, or an alkyl group of less than 7 carbon atoms;
wherein the salt is selected from the group consisting of: hydrochloride, phosphate, sulfate, tosylate, benzoylate and mesylate.
20. The crystalline salt of claim 19, further comprising one or more free acids.
21. A method of treating disease, comprising administering to a patient a pharmaceutically active amount of a pharmaceutical composition of claim 1.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. An organic electroluminescent display device, comprising:
first and second substrates facing and spaced apart from each other, the first and second substrates including at least one pixel region having first, second and third sub-pixel region;
a gate line and a data line on the first substrate, the gate line and the data line crossing each other to define the at least one pixel region;
a first electrode on the first substrate in each of the first, second and third sub-pixel regions;
first, second and third organic patterns on the first electrode in the first, second and third sub-pixel regions, respectively, the first, second and third sub-pixel regions disposed in a single row along a first direction parallel to the gate line, the first, second and third organic patterns having a zigzag shape along the first direction with respect to a virtual line passing through a central portion of each of the first, second and third sub-pixel regions; and
a second electrode on the first, second and third organic patterns;
wherein the virtual line divides each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion, and
wherein the first organic pattern is disposed in either the lower half portion or the upper half portion of the first sub-pixel region and is not disposed in the other half portion of the first sub-pixel region,
wherein the second organic pattern is disposed in the opposite half portion of the second sub-pixel region, opposite to that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the second sub-pixel region, and
wherein the third organic pattern is disposed in the same half portion of the third sub-pixel region as that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the third sub-pixel region.
2. The device according to claim 1, wherein the first and second organic patterns are spaced apart from each other by a distance for preventing a shadowing effect along a diagonal direction with respect to the first direction and a second direction perpendicular to the first direction, and the second and third organic patterns are spaced apart from each other by the distance for preventing the shadowing effect along the diagonal direction with respect to the first direction and the second direction.
3. The device according to claim 1, wherein the first, second and third organic patterns correspond to red, green and blue organic patterns, respectively.
4. The device according to claim 3, wherein the first, second and third organic patterns are alternately disposed along the first direction and each of the first, second and third organic patterns is straightly disposed along a second direction parallel to the data line.
5. The device according to claim 1, wherein the virtual line divides each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion, and wherein the first organic pattern is disposed in the lower half portion of the first sub-pixel region, the second organic pattern is disposed in the upper half portion of the second sub-pixel region, and the third organic pattern is disposed in the lower half portion of the third sub-pixel region.
6. The device according to claim 1, wherein the at least one pixel region includes first, second, third and fourth pixel regions in 2.times.2 matrix, wherein the first pixel region includes the first, second and third sub-pixel regions, the second pixel region includes fourth, fifth and sixth sub-pixel regions, the third pixel region includes seventh, eighth and ninth sub-pixel regions, and the fourth pixel region includes tenth, eleventh and twelfth sub-pixel regions, wherein the first organic pattern is disposed in each of the first, fourth, seventh and tenth sub-pixel regions, the second organic pattern is disposed in each of the second, fifth, eighth and eleventh sub-pixel regions, and the third organic pattern is disposed in each of the third, sixth, ninth and twelfth sub-pixel regions, and wherein the first, second and third organic patterns of the first and second pixel regions have the zigzag shape along the first direction with respect to the virtual line and the first, second and third organic patterns of the third and fourth pixel regions have the zigzag shape along the first direction with respect to the virtual line.
7. The device according to claim 6, wherein the virtual line divides each of the first to twelfth sub-pixel regions into an upper half portion and a lower half portion, wherein the first organic pattern is disposed in each of the lower half portion of the first sub-pixel region, the upper half portion of the fourth sub-pixel region, the upper half portion of the seventh sub-pixel region and the lower half portion of the tenth sub-pixel region, wherein the second organic pattern is disposed in each of the upper half portion of the second sub-pixel region, the lower half portion of the fifth sub-pixel region, the lower half portion of the eighth sub-pixel region and the upper half portion of the eleventh sub-pixel region, and wherein the third organic pattern is disposed in each of the lower half portion of the third sub-pixel region, the upper half portion of the sixth sub-pixel region, the upper half portion of the ninth sub-pixel region and the lower portion of the twelfth sub-pixel region.
8. The device according to claim 1, wherein each of the first, second and third organic patterns has one of a rectangular shape and a rectangular shape having two truncated corners.
9. The device according to claim 1, wherein the virtual line is parallel to the first direction and the gate line.
10. The device according to claim 1, further comprising:
a switching thin film transistor connected to the gate line and the data line;
a storage capacitor connected to the switching thin film transistor;
a power line connected to the storage capacitor; and
a driving thin film transistor connected to the switching thin film transistor and the power line.
11. A method of fabricating an organic electroluminescent display device, comprising:
forming a gate line and a data line on a first substrate, the gate line and the data line crossing each other to define at least one pixel region having first, second and third sub-pixel region;
forming a first electrode on the first substrate in each of the first, second and third sub-pixel regions;
forming first, second and third organic patterns on the first electrode in the first, second and third sub-pixel regions, respectively, using a shadow mask, the first, second and third sub-pixel regions disposed in a single row along a first direction parallel to the gate line, the first, second and third organic patterns having a zigzag shape along the first direction with respect to a virtual line passing through a central portion of each of the first, second and third sub-pixel regions;
forming a second electrode on the first, second and third organic patterns; and
attaching a second substrate to the first substrate with a seal pattern;
wherein the virtual line divides each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion, and
wherein the first organic pattern is disposed in either the lower half portion or the upper half portion of the first sub-pixel region and is not disposed in the other half portion of the first sub-pixel region,
wherein the second organic pattern is disposed in the opposite half portion of the second sub-pixel region, opposite to that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the second sub-pixel region, and
wherein the third organic pattern is disposed in the same half portion of the third sub-pixel region as that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the third sub-pixel region.
12. The method according to claim 11, wherein the shadow mask includes a plurality of open portions in matrix.
13. The method according to claim 12, wherein adjacent two of the first, second and third organic patterns along the second direction are formed by depositing an organic material through a single one of the plurality of open portions.
14. The method according to claim 13, wherein each of the plurality of open portions has one of a rectangular shape and a rectangular shape having four truncated corners.
15. An organic electroluminescent display device, comprising:
first and second substrates facing and spaced apart from each other, the first and second substrates including at least one pixel region having first, second and third sub-pixel region;
a gate line and a data line on the first substrate, the gate line and the data line crossing each other to define the at least one pixel region;
a first electrode on the first substrate in each of the first, second and third sub-pixel regions;
first, second and third organic patterns on the first electrode in the first, second and third sub-pixel regions, respectively, the first, second and third organic patterns having a zigzag shape along a first direction parallel to the gate line with respect to a virtual line passing through a central portion of each of the first, second and third sub-pixel regions and dividing each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion; and
a second electrode on the first, second and third organic patterns;
wherein the first organic pattern is disposed in either the lower half portion or the upper half portion of the first sub-pixel region and is not disposed in the other half portion of the first sub-pixel region,
wherein the second organic pattern is disposed in the opposite half portion of the second sub-pixel region, opposite to that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the second sub-pixel region, and
wherein the third organic pattern is disposed in the same half portion of the third sub-pixel region as that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the third sub-pixel region.
16. An organic electroluminescent display device, comprising:
first and second substrates facing and spaced apart from each other, the first and second substrates including at least one pixel region having first, second and third sub-pixel region;
a gate line and a data line on the first substrate, the gate line and the data line crossing each other to define the at least one pixel region;
a first electrode on the first substrate in each of the first, second and third sub-pixel regions;
first, second and third organic patterns on the first electrode in the first, second and third sub-pixel regions, respectively, the first, second and third organic patterns having a zigzag shape along a first direction parallel to the gate line with respect to a virtual line passing through a central portion of each of the first, second and third sub-pixel region; and
a second electrode on the first, second and third organic patterns,
wherein the virtual line divides each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion,
wherein the first organic pattern is disposed in the lower half portion of the first sub-pixel region and is not disposed in the upper half portion of the first sub-pixel region,
wherein the second organic pattern is disposed in the upper half portion of the second sub-pixel region and is not disposed in the lower half portion of the second sub-pixel region, and
wherein the third organic pattern is disposed in the lower half portion of the third sub-pixel region and is not disposed in the upper half portion of the third sub-pixel region.
17. A method of fabricating an organic electroluminescent display device, comprising:
forming a gate line and a data line on a first substrate, the gate line and the data line crossing each other to define at least one pixel region having first, second and third sub-pixel region;
forming a first electrode on the first substrate in each of the first, second and third sub-pixel regions;
forming first, second and third organic patterns on the first electrode in the first, second and third sub-pixel regions, respectively, using a shadow mask, the first, second and third organic patterns having a zigzag shape along a first direction parallel to the gate line with respect to a virtual line passing through a central portion of each of the first, second and third sub-pixel regions and dividing each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion;
forming a second electrode on the first, second and third organic patterns; and
attaching a second substrate to the first substrate with a seal pattern;
wherein the first organic pattern is disposed in either the lower half portion or the upper half portion of the first sub-pixel region and is not disposed in the other half portion of the first sub-pixel region,
wherein the second organic pattern is disposed in the opposite half portion of the second sub-pixel region, opposite to that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the second sub-pixel region, and
wherein the third organic pattern is disposed in the same half portion of the third sub-pixel region as that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the third sub-pixel region.
18. A method of fabricating an organic electroluminescent display device, comprising:
forming a gate line and a data line on a first substrate, the gate line and the data line crossing each other to define at least one pixel region having first, second and third sub-pixel region;
forming a first electrode on the first substrate in each of the first, second and third sub-pixel regions;
forming first, second and third organic patterns on the first electrode in the first, second and third sub-pixel regions, respectively, using a shadow mask, the first, second and third organic patterns having a zigzag shape along a first direction parallel to the gate line with respect to a virtual line passing through a central portion of each of the first, second and third sub-pixel regions;
forming a second electrode on the first, second and third organic patterns; and attaching a second substrate to the first substrate with a seal pattern,
wherein the virtual line divides each of the first, second and third sub-pixel regions into an upper half portion and a lower half portion,
wherein the first organic pattern is disposed in either the lower half portion or the upper half portion of the first sub-pixel region and is not disposed in the other half portion of the first sub-pixel region,
wherein the second organic pattern is disposed in the opposite half portion of the second sub-pixel region, opposite to that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the second sub-pixel region, and
wherein the third organic pattern is disposed in the same half portion of the third sub-pixel region as that half portion of the first sub-pixel region in which the first organic pattern is disposed, and is not disposed in the other half portion of the third sub-pixel region.

1. A method for correcting the optical aberrations beyond defocus and astigmatism of an eye fitted with an original contact lens having a known anterior surface shape by providing a modified or new contact lens which has its anterior surface reshaped from said original contact lens’s anterior surface, comprising the steps of:
a) measuring said optical aberrations of an eye fitted with an original contact lens,
b) performing a mathematical analysis of said eye’s optical aberrations when fitted with original contact lens to determine said modified anterior contact lens surface shape, and
c) fabricating said modified anterior contact lens surface by methods that remove, add or compress material or alter the surface chemistry.
2. A method as claimed in claim 1 wherein said measuring of the eye’s optical aberrations comprises the sub-steps of:
i) optically projecting the image of a small point of incoherent light onto the macular region of the eye’s retina,
ii) optically conveying the image of the eye’s pupil, through which light scattered back from the macular region emerges, onto a microlens array,
iii) optically conveying the multiple spot images formed by said microlens array onto the image plane of a photo-electronic imaging device,
iv) transforming by means of the photo-electronic imaging device the multiple spot images formed by said microlens array to an electronic signal which represents the images,
v) conveying said electronic signal to a computer for data processing,
vi) processing first the electronic signal with said computer in order to obtain the coordinate locations of the centroids of said multiple spot images formed by said microlens array, and
vii) processing next said coordinate locations with said computer in order to obtain the slopes of optical rays emerging from the subject’s pupil at said coordinate locations.
3. A method as claimed in claim 1 wherein said mathematical analysis comprises the sub-steps of:
i) determining mathematically the normal vectors of said original contact lens’s anterior surface,
ii) determining mathematically the directional derivatives of said modified or new contact lens’s anterior surface using data of said normal vectors of original contact lens’s anterior surface and data of said eye’s optical aberrations, and
iii) fitting mathematically by the method of least squares said directional derivatives to the corresponding directional derivatives of a polynomial expression that represents said modified or new contact lens’s anterior surface.
4. A method as claimed in claim 1 wherein said step of fabricating said modified or new contact lens’s anterior surface is chosen from the group of methods comprising diamond point machining, laser ablation, thermal molding, photo-lithographic etching, thin film deposition, and surface chemistry alteration.
5. A method for correcting the optical aberrations beyond defocus and astigmatism of an eye with an original anterior corneal surface of known shape by providing a modified anterior corneal surface shape, comprising the steps of:
a) measuring said eye’s optical aberrations,
b) performing a mathematical analysis of said eye’s optical aberrations to determine said modified anterior corneal surface shape,
c) fabricating said modified anterior corneal surface by laser ablation.
6. A method as claimed in claim 5 wherein said measuring of the eye’s optical aberrations comprises the sub-steps of:
i) optically projecting the image of a small point of incoherent light onto the macular region of the eye’s retina,
ii) optically conveying the image of the eye’s pupil, through which light scattered back from the macular region emerges, onto a microlens array,
iii) optically conveying the multiple spot images formed by said microlens array onto the image plane of a photo-electronic imaging device,
iv) transforming by means of the photo-electronic imaging device the multiple spot images formed by said microlens array to an electronic signal which represents the images,
v) conveying said electronic signal to a computer for data processmg,
vi) processing first the electronic signal with said computer in order to obtain the coordinate locations of the centroids of said multiple spot images formed by said microlens array, and
vii) processing next said coordinate locations with said computer in order to obtain the slopes of optical rays emerging from the subject’s pupil at said coordinate locations.
7. A method as claimed in claim 5 wherein said mathematical analysis comprises the sub-steps of:
i) determining mathematically the normal vectors of said original anterior corneal surface,
ii) determining mathematically the directional derivatives of said modified anterior corneal surface using data of said normal vectors of original anterior corneal surface and data of said eye’s optical aberrations, and
iii) fitting mathematically by the method of least squares said directional derivatives to the corresponding directional derivatives of a polynomial expression that represents said modified anterior corneal surface.
8. An ophthalmic device for measuring the eye’s optical aberrations either with or without a contact lens in place on the cornea, including;
a) an optical projection system for imaging a small point of light onto the macular region of the eye’s retina with an improvement provided by use of an incoherent light source chosen from the group comprising laser diodes operated below threshold, light emitting diodes, arc and plasma sources, and incandescent filament lamps,
b) an optical image acquisition system for conveying the image of the eye’s pupil, through which light scattered back from the macular region emerges, onto a microlens array,
c) a microlens array to form multiple spot images onto the image plane of a photo-electronic imaging device,
d) a photo-electronic imaging device for transforming said multiple spot images formed by said microlens array to an electronic signal which represents the images,
e) a computer for processing the electronic signal in order, first, to obtain the coordinate locations of the centroids of said multiple spot images formed by said microlens array and, second, to obtain the slopes of optical rays emerging from the subject’s pupil at said coordinate locations, and
f) an optical alignment system allowing the entering beam to be accurately centered with respect to the subject’s pupil.
9. An ophthalmic device as claimed in claim 8 wherein said optical projection system includes an optical isolator consisting of a quarter-wave plate and polarizer.
10. An ophthalmic device as claimed in claim 8 wherein said optical projection system includes a field stop placed at a location that is optically conjugate to the eye’s retina.
11. An ophthalmic device as claimed in claim 8 wherein said optical projection system includes both an optical isolator consisting of a quarter-wave plate and polarizer, and a field stop placed at a location that is optically conjugate to the eye’s retina.
12. An ophthalmic device as claimed in claim 8 wherein said photo-electronic imaging device is chosen from the group comprising vidicons, charge-coupled devices, and charge-injection devices.
13. A device for thermally forming surfaces on thermoplastic contact lens blanks that correct eyes’ optical aberrations beyond defocus and astigmatism consisting of a die with an adjustable surface shape (either continuous or discontinuous) formed by computer-controlled electromechanical actuators or electromechanical fingers which are known in the field of adaptive optics.
14. A lathe device for machining surfaces on contact lens blanks that correct eyes’ optical aberrations beyond defocus and astigmatism consisting of a rotating spindle onto which a contact lens blank is fastened, translation slides for precisely positioning a diamond point cutting tool with respect to the surface of the contact lens blank, and a programmed computer that controls the movement of the translation slides synchronously with the rotational location of the spindle.
15. A contour cutting device for machining surfaces on contact lens blanks that correct eyes’optical aberrations beyond defocus and astigmatism consisting of a means for supporting and holding stationary a contact lens blank, translation slides for precisely positioning in three dimensions a diamond point cutting tool with respect to the surface of the contact lens blank, and a programmed computer that controls the movement of the translation slides.
16. A method for correcting optical aberrations beyond defocus and astigmatism of an eye comprising:
a) fitting the eye with a first contact lens having a known anterior surface shape that is corrected for at least focus,
b) measuring the optical aberrations of the eye fitted with the first contact lens,
c) performing a mathematical analysis of the eye’s optical aberrations when fitted with the first contact lens to determine a modified anterior contact lens surface shape, and
d) fabricating a second contact lens having the modified anterior contact lens surface.
17. A method as claimed in claim 16 performing the mathematical analysis to at least the eye’s 4th order optical aberrations of the eye when fitted with the first contact lens to determine the second contact lens surface shape, and the anterior surface of the second contact lens to have the modified anterior surface that corrects the eye to at least the 4th order aberration.
18. A method as claimed in claim 17 wherein the measuring of the eye’s optical aberrations comprises the sub-steps of:
i) optically projecting the image of a small point of incoherent light onto the macular region of the eye’s retina,
ii) optically conveying the image of the eye’s pupil, through which light scattered back from the macular region emerges, onto a microlens array,
iii) optically conveying the multiple spot images formed by the microlens array onto the image plane of a photo-electronic imaging device,
iv) transforming by means of the photo-electronic imaging device the multiple spot images formed by the microlens array to an electronic signal which represents the images,
v) conveying the electronic signal to a computer for data processing,
vi) processing first the electronic signal with the computer in order to obtain the coordinate locations of the centroids of the multiple spot images formed by the microlens array, and
vii) processing next the coordinate locations with the computer in order to obtain the slopes of optical rays emerging from the subject’s pupil at the coordinate locations.
19. A method as claimed in claim 17 wherein the mathematical analysis comprises the sub-steps of:
i) determining mathematically the normal vectors of the first contact lens’s anterior surface,
ii) determining mathematically the directional derivatives of the second contact lens’s anterior surface using data of the normal vectors of the first contact lens’s surface and data of the eye’s optical aberrations, and
iii) fitting mathematically by the method of least squares the directional derivatives to the corresponding directional derivatives of a polynomial expression that represents the second contact lens’s anterior surface.
20. A method as claimed in claim 1 wherein the original contact lens’s anterior surface contour function z (x,y) and the eye’s optical aberrations, represented by optical rays emerging from the pupil given by vector function B (x,y), are used to find the surface contour function z\u2032 (x,y) of the modified or new contact lens by the following mathematical procedures:
a) z\u2032(x,y) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, aj\xb7gj(x,y), consists of an unknown constant coefficient aj and a known function gj(x,y) as shown in following Equation (1)
z
\u2032

\u2061

(

x
,
y

)
\u2261
\u2211
j

\u2062

\u2003

\u2062
a
j

\xb7
g
j

\u2061

(

x
,
y

)
(
1
)
b) following Equation (2) is obtained by taking vector gradients of both sides of Equation (1) where grad z\u2032 (x,y) is a two-dimensional vector having components
\u03b4
\u2062

\u2003

\u2062

z
\u2032

\u2062

\u2003

\u2062
(

x
,
y

)
\u03b4

\u2062

\u2003

\u2062
x

,

\u03b4
\u2062

\u2003

\u2062

z
\u2032

\u2062

\u2003

\u2062
(

x
,
y

)
\u03b4

\u2062

\u2003

\u2062
y
grad
\u2062

\u2003

\u2062
z
\u2032

(

x
,
y

)
=
\u2211
j

\u2062

\u2003

\u2062
a
j

\xb7
grad

\u2062

\u2003

\u2062
g
j

(

x
,
y

)
(
2
)
c) the normal vectors of the original contact lens’s anterior surface, given by vector function N(x,y), are found by taking the vector gradient of z(x,y) and normalizing it to unity as shown in the following Equations (3A) to (3D)
Nx
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
x
,
(

3
\u2062
A

)
Ny
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
y
,
(

3
\u2062
B

)
Nz
\u2261

1
MAG
(

3
\u2062
C

)
\u2003MAG\u22611+(\u03b4z(x,y)\u03b4x)2+(\u03b4z(x,y)\u03b4y)2 12 \u2003\u2003(3D)
d) the rays incident on the original contact lens coming from within the eye are given by vector function A(x,y) which is found by applying Snell’s law of refraction at the airlens interface which relates A(x,y) to known vector function B(x,y) representing the emerging rays, and vector function N(x,y) given by Equations (3A)-(3D),
e) the normal vectors of the modified or new contact len’s anterior surface, given by the vector function N\u2032, are found from the following Equation (4) where vector function B\u2032 is represented by unit vectors pointed along the positive z-axis, and n is the lens’s refractive index
N
\u2032

\u2261
(
n
\xb7
A

–

B
\u2032
)
\uf603
n
\xb7
A

–

B
\u2035
\uf604
(
4
)
f) the directional derivatives of the modified or new contact lens’s anterior surface are obtained from the following Equation (5) using the components of vector function N\u2032=N\u2032x, N\u2032y, N\u2032z found from Equation (4)
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
x
\u2261
–
N
x
\u2035
N
z
\u2035
\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
y
\u2261

–
N
y
\u2035
N
z
\u2035
(
5
)
g) apply the method of least squares to minimize the square the difference between the component values of grad z\u2032(x,y) found from Equation (5) and the component values of grad z\u2032(x,y) given by the approximation series, Equa. (2), in order to obtain matrix Equation (6)
M\xb7a\u2261b \u2003\u2003(6)
where
M

(

i
,
j

)
\u2261
\u2211

x
,
y
\u2062

\u2003

\u2062
(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

g
j
)

\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062

b
i
\u2261
\u2211

x
,
y
\u2062

\u2003

\u2062

(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

z
\u2035
)
(
7
)
h) obtain the inverse of matrix M, and then find the a-coefficients from matrix Equation (8)
a\u2261M\u22121\xb7b \u2003\u2003(8)
i) the a-coefficients determined from Equation (8) are used in Equation (1) which defines the modified or new contact lens’s anterior surface, z\u2032 (x,y) when it is represented, for example, by a 5th order Taylor series.
21. A methdo as claimed in claim 19 wherein the first Contact lens’s anterior surface contour function z(x,y) and the eye’s optical aberrations, represented by optical rays emerging from the pupil given by vector function B(x,y), are used to find the surface contour function z\u2032(x\u2212y) of the second contact lens by the following mathematical procedures:
a) z\u2032 (x,y) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, aj\xb7gj(x,y), consists of an unknown constant coefficient aj and a known function gj(x,y) as shown in following Equation (1)
z
\u2032

\u2062

\u2003

\u2062

(

x
,
y

)
\u2261
\u2211
j

\u2062

\u2003

\u2062
a
j

\xb7
g
j

\u2061

(

x
,
y

)
(
1
)
b) following Equation (2) is obtained by taking vector gradients of both sides of Equation (1) where grad z\u2032 (x,y) is a two-dimensional vector having components
\u03b4
\u2062

\u2003

\u2062

z
\u2032

\u2062

\u2003

\u2062
(

x
,
y

)
\u03b4

\u2062

\u2003

\u2062
x

,

\u03b4
\u2062

\u2003

\u2062

z
\u2032

\u2062

\u2003

\u2062
(

x
,
y

)
\u03b4

\u2062

\u2003

\u2062
y
grad
\u2062

\u2003

\u2062
z
\u2032

(

x
,
y

)
=
\u2211
j

\u2062

\u2003

\u2062
a
j

\xb7
grad

\u2062

\u2003

\u2062
g
j

(

x
,
y

)
(
2
)
c) the normal vectors of the first contact lens’s anterior surface, given by vector function N(x,y), are found by taking the vector gradient of z(x,y) and normalizing it to unity as shown in the following Equations (3A) to (3D)
Nx
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
x
,
(

3
\u2062
A

)
Ny
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
y
,
(

3
\u2062
B

)
Nz
\u2261

1
MAG
(

3
\u2062
C

)
\u2003MAG\u22611+(\u03b4z(x,y)\u03b4x)2+(\u03b4z(x,y)\u03b4y)2 12 \u2003\u2003(3D)
d) the rays incident on the first contact lens coming from within the eye are given by vector function A(x,y) which is found by applying Snell’s law of refraction at the airlens interface which relates A(x,y) to known vector function B(x,y) representing the emerging rays, and vector function N(x,y) given by Equations (3A)-(3B),
e) the normal vectors of the second contact lens’s anterior surface, given by the vector function N\u2032, are found from the following Equation (4) where vector function B\u2032 is represented by unit vectors pointing along the positive z-axis, and n is the lens’s refractive index
N
\u2032

=
(
n
\xb7
A

–

B
\u2032
)
\uf603
n
\xb7
A

–

B
\u2035
\uf604
(
4
)
f) the directional derivatives of the second contact lens’s anterior surface are obtained from the following Equation (5) using the components of vector function N\u2032=N\u2032x,N\u2032y,N\u2032z found from Equation (4)
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
x
\u2261
–
N
x
\u2035
N
z
\u2035
\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
y
\u2261

–
N
y
\u2035
N
z
\u2035
(
5
)
g) apply the method of at least squares to minimize the square the difference between the component values of grad z\u2032 (x,y) found from Equation (5) and the component values of grad z\u2032 (x,y) given by the approximation series, Equa. (2), in order to obtain matrix Equation (6)
M\xb7a\u2261b \u2003\u2003(6)
where
M

(

i
,
j

)
\u2261
\u2211

x
,
y
\u2062

\u2003

\u2062
(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

g
j
)

\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062

b
i
=
\u2211

x
,
y
\u2062

\u2003

\u2062

(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

z
\u2035
)
(
7
)
h) obtain the inverse of matrix M, and then find the a-coefficient from matrix Equation (8)
a\u2261M\u22121\xb7b \u2003\u2003(8)
i) the a-coefficients determined from Equation (8) are used in Equation (1) which defines the second contact lens’s anterior surface, z\u2032 (x,y) when it is represented, for example, by a 5th order Taylor series.
22. A method as claimed in claim 5 wherein the original cornea’s anterior surface contour function z(x,y) and the eye’s optical aberrations, represented by optical rays emerging from the pupil given by vector function B(x,y), are used to find the surface contour function z\u2032(x,y) of the modified cornea by the following mathematical procedures:
a) z\u2032 (x,y) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, aj\xb7gj(x,y), consists of an unknown constant coefficient aj and a known function gj(x,y) as shown in following Equation (1)
z
\u2032

\u2062

\u2003

\u2062

(

x
,
y

)
\u2261
\u2211
j

\u2062

\u2003

\u2062
a
j

\xb7
g
j

\u2061

(

x
,
y

)
(
1
)
b) following Equation (2) is obtained by taking vector gradients of both sides of Equation (1) where grad z\u2032 (x,y) is a two-dimensional vector having components
\u03b4
\u2062

\u2003

\u2062

z
\u2032

\u2062

\u2003

\u2062
(

x
,
y

)
\u03b4

\u2062

\u2003

\u2062
x

,

\u03b4
\u2062

\u2003

\u2062

z
\u2032

\u2062

\u2003

\u2062
(

x
,
y

)
\u03b4

\u2062

\u2003

\u2062
y
grad
\u2062

\u2003

\u2062
z
\u2032

(

x
,
y

)
=
\u2211
j

\u2062

\u2003

\u2062
a
j

\xb7
grad

\u2062

\u2003

\u2062
g
j

(

x
,
y

)
(
2
)
c) the normal vectors of the original cornea’s anterior surface, given by vector function N(x,y), are found by taking the vector gradient of z(x,y) and normalizing it to unity as shown in the following Equations (3A) to (3D)
Nx
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
x
,
(

3
\u2062
A

)
Ny
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
y
,
(

3
\u2062
B

)
Nz
\u2261

1
MAG
(

3
\u2062
C

)
\u2003MAG\u22611+(\u03b4z(x,y)\u03b4x)2+(\u03b4z(x,y)\u03b4y)2 12 \u2003\u2003(30)
d) the rays incident on the original cornea coming from within the eye are given by vector function A(x,y) which is found by applying Snell’s law of reflection at the aircornea interface which relates A(x,y) to known vector function B(x,y) representing the emerging rays, and vector function N(x,y) given by Equations (3A)-(3B),
e) the normal vectors of the modified cornea’s anterior surface, given by the vector function N\u2032, are found from the following Equation (4) where vector function B\u2032 is represented by unit vectors pointing along the positive z-axis, and n is the cornea’s refractive index
N
\u2032

\u2261
(
n
\xb7
A

–

B
\u2032
)
\uf603
n
\xb7
A

–

B
\u2035
\uf604
(
4
)
f) the directional derivatives of the modified cornea’s anterior surface are obtained from the following Equation (5) using the components of vector function N\u2032=N\u2032x, N\u2032y, N\u2032z found from Equation (4)
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
x
\u2261
–
N
x
\u2035
N
z
\u2035
\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
y
\u2261

–
N
y
\u2035
N
z
\u2035
(
5
)
g) apply the method of least squares to minimize the square the difference between the component values of grad z\u2032(x,y) found the Equation (5) and the component values of grad z\u2032 (x,y) given by the approximation series, Equa. (2), in order to obtain matrix Equation (6)
M\xb7a\u2261b \u2003\u2003(6)
where
M

(

i
,
j

)
\u2261
\u2211

x
,
y
\u2062
(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

g
j
)

\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062

b
i
=
\u2211

x
,
y
\u2062

(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

z
\u2035
)
(
7
)
h) obtain the inverse of matrix M, and then find the a-coefficients from matrix Equation (8)
a\u2261M\u22121\xb7b
i) the a-coefficient determined from Equation (8) are used in Equation (1) which defines the modified cornea’s anterior surface, z\u2032 (x,y) when it is represented, for example, by a 5th order Taylor series.
23. A contact lens comprising an anterior surface which is fabricated to correct the optical aberration to at least 4th order of a person’s eye.
24. The contact lens of claim 23 wherein the measuring of the eye’s optical aberrations is by steps of:
(i) optically projecting the image of a small point of incoherent light onto the macular region of the eye’s retina,
(ii) optically conveying the image of the eye’s pupil, through which light scattered back from the macular region emerges onto a microlens array,
(iii) optically conveying the multiple spot images formed by the microlens array onto the image plane of a photo-electronic imaging device,
(iv) transforming by means of the photo-electronic imaging device the multiple spot images formed by the microlens array to an electronic signal which represents the images;
(v) conveying the electronic signal to a computer for data processing,
(vi) processing first the electronic signal with the computer in order to obtain the coordinate locations of the centroids of the multiple spot images formed by the microlens array, and
(vii) processing next the coordinate locations with the computer in order to obtain the slopes of optical rays emerging from the subject’s pupil at the coordinate locations.
25. The contact lens of claim 23 wherein the mathematical analysis comprises the sub-steps of:
(a) determining mathematically the normal vectors of a first contact lens anterior surface;
(b) determining mathematically the directional derivatives of the a second contact lens anterior surface using data of the normal vectors of the first contact lens anterior surface and data of the eye’s optical aberrations; and
(c) fitting mathematically by the method of least squares the directional derivatives to the corresponding directional derivatives of a polynomial expression that represents the second contact lens anterior surface.
26. The contact lens of claim 23 wherein the first contact lens anterior surface contour function z(x,y) and the eye’s optical aberrations, represented by optical rays emerging from the pupil given by vector function B(x,y), are used to find the surface contour function z\u2032(x,y) of the second contact lens by the following mathematical procedures:
(a) z\u2032(x,y) is approximated by the sum of a series of linearly independent terms in x & y with each term labeled by an index j wherein each term, aj\xb7gj(x,y), consists of an unknown constant coefficient aj and a known function gj (x,y) as shown in following Equation (1)
z
\u2032

\u2061

(

x
,
y

)
\u2261
\u2211
j

\u2062
a
j

\xb7
g

j
\u2062

\u2003
\u2061

(

x
,
y

)
(
1
)
b) following Equation (2) is obtained by taking vector gradients of both sides of Equation (1) where grad z\u2032 (x,y) is a two-dimensional vector having components \u03b4z\u2032(x,y)\u03b4x, \u03b4z\u2032(x,y)\u03b4y
grad
\u2062

\u2003

\u2062
z
\u2032

\u2061

(

x
,
y

)
=
\u2211
j

\u2062
a
j

\xb7
grad

\u2062

\u2003

\u2062
g
j

\u2061

(

x
,

\u2003

\u2062
y

)
(
2
)
c) the normal vectors of the first contact lens’s anterior surface, given by vector function N (x,y), are found by taking the vector gradient of z(x,y) and normalizing it to unity as shown in the following Equations (3A) to (3D)
Nx
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
x
,
(

3
\u2062
A

)
Ny
\u2261
1
MAG

\xb7
–
\u03b4

\u2062

\u2003

\u2062

z
\u2061

(

x
,
y

)
\u03b4
\u2062

\u2003

\u2062
y
,
(

3
\u2062
B

)
Nz
\u2261

1
MAG
(

3
\u2062
C

)
\u2003MAG\u22611+(\u03b4z(x,y)\u03b4x)2+(\u03b4z(x,y)\u03b4y)2\xbd\u2003\u2003(3D)
d) the rays incident on the first contact lens coming from within the eye are given by vector function A(x,y) which is found by applying Snell’s law of refraction at the airlens interface which relates A(x,y) to known vector function B(x,y) representing the emerging rays, and vector function N(x,y) given by Equations (3A)\u2212(3B),
e) the normal vectors of the second contact lens’s anterior surface, given by the vector function N\u2032, are found from the following Equation (4) where vector function B\u2032 is represented by unit vectors pointing along the positive z-axis, and n is the lens’s (or cornea’s) refractive index
N
\u2032

\u2261
(
n
\xb7
A

–

B
\u2032
)
\uf603
n
\xb7
A

–

B
\u2035
\uf604
(
4
)
f) the directional derivatives of the second contact lens’s anterior surface are obtained from the following Equation (5) using the components of vector function N\u2032=N\u2032x, N\u2032y, N\u2032z found from Equation (4)
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
x
\u2261
–
N
x
\u2035
N
z
\u2035
\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062
\u03b4
\u2062

\u2003

\u2062

z
\u2032
\u03b4
\u2062

\u2003

\u2062
y
\u2261

–
N
y
\u2035
N
z
\u2035
(
5
)
g) apply the method of least squares to minimize the square the difference between the component values of grad z\u2032 (x,y) found from Equation (5) and the component values of grad z\u2032(x,y) given by the approximation series, Equa. (2), in order to obtain matrix Equation (6)
M\xb7a\u2261b \u2003\u2003(6)
where
M

(

i
,
j

)
\u2261
\u2211

x
,
y
\u2062
(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

g
j
)

\u2062

\u2003

\u2062
and
\u2062

\u2003

\u2062

b
i
\u2261
\u2211

x
,
y
\u2062

(

grad
\u2062

\u2003

\u2062
g
i

\xb7
grad

\u2062

\u2003

\u2062

z
\u2035
)
(
7
)
h) obtain the inverse of matrix M, and then find the a-coefficients from matrix Equation (8)
a\u2261M\u2212\xb7b \u2003\u2003(8)
i) the a-coefficients determined from Equation (8) are used in Equation (1) which defines the second contact lens’s anterior surface, z\u2032 (x,y) when it is represented, for example, by a 5th order Taylor series.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A trailer comprising:
a chassis;
a trailer body connected to the chassis, said trailer body comprising:
left and right vertical side walls connected respectively to left and right bottom rails;
a cargo space located between the left and right vertical side walls;
a curved floor comprising a left edge connected to said left bottom rail and a right edge connected to said right bottom rail;
said left and right side walls each comprising a plurality of extruded panels each comprising an inner wall and an outer wall spaced from the inner wall, wherein said inner and outer walls of each extruded panel are parallel relative to each other;
wherein an inner surface of the curved floor follows a curved path as said inner surface extends from said left edge connected to said left bottom rail to said right edge connected to said right bottom rail, such that said inner surface of said floor is located a variable distance D from an imaginary reference plane that extends through the cargo space and that is oriented perpendicular to the left and right vertical side walls, wherein said distance D is maximized when measured at a centerline of said trailer body and wherein said distance D decreases progressively from said maximized value when measured at locations closer to the left and right side walls.
2. The trailer as set forth in claim 1, wherein said chassis comprises left and right chassis beams, said left chassis beam comprising a left saddle portion including a left curved saddle surface and said right chassis beam comprising a right saddle portion including a right curved saddle surface, wherein the left and right curved saddle surfaces are oriented inward toward a center of the cargo space and a curved outer surface of the floor is connected to the left and right curved saddle surfaces.