Singular id filetype pdf

This value can be used to determine the eigenvector that can be placed in the columns of U. Thus we obtain the following equations:. Upon simplifying the first two equations we obtain a ratio which relates the value of x1 to x2. The values of x1 and x2 are chosen such that the elements of the S are the square roots of the eigenvalues. Substituting the other eigenvalue we obtain:. Combining these we obtain:. In that paper the values were computed and normalized such that the highest singular value was equal to 1.

U and V are orthogonal Where the columns of U are the left singular vectors gene coefficient vectors ; S the same dimensions as A has singular values and is diagonal mode amplitudes ; and V T has rows that are the right singular vectors expression level vectors.

Thus we obtain the following equations: Substituting the other eigenvalue we obtain: Combining these we obtain: Similarly A T A makes up the columns of V so we can do a similar analysis to find the value of V. Golub, G. Baltimore : Johns Hopkins University Press. Greenberg, M. Strang , G. This invention concerns methods for manufacturing Singular ID products as well as Singular ID products including a decorative article made from one or more separate die cut pieces wherein the die cut pieces that make up the Singular ID product can be simultaneously applied to a substrate surface.

Labels and decorations including a plurality of separated design elements are highly desired due in part to their uniqueness. The manufacture of such labels and designs in a form that can be easily applied to a substrate surface is difficult and expensive. Therefore, methods for reproducibly and inexpensively manufacturing the labels and designs are needed.

Still other aspects of this invention are Singular ID products comprising: a decorative portion comprising one or more die cut pieces, each die cut piece having a first surface and a second surface; a mask layer covering the one or more die cut pieces; and an adhesive material located between and in contact with the mask layer and with the one or more die cut pieces.

The present invention relates to methods and processes for manufacturing a Singular ID product and well as unique Singular ID products. The Singular ID product 5 includes a decorative portion 7 including one or more die cut pieces 8. For decorative portion 7 shown in FIG. The Singular ID product 5 further includes a carrier 30 and an adhesive layer The Singular ID product invention embodiments will all typically share a decorative portion 7 including one or more die cut pieces 8.

Carrier 30 including, for example paper sheet with a detachable adhesive on one side will be applied to decorative portion 7 to stabilize decorative portion 7 for shipping and so that it can be easily applied to a substrate surface. Decorative portion 7 may include many optional layers such as carriers, mask layers, removable adhesive layers, permanent adhesive layers, adhesive layer liners, and so forth.

The type of optional and additional layers used for a particular Singular ID product would be apparent to one skilled in the art depending upon the end application for the Singular ID product. For example, a Singular ID product that is applied to a computer housing might include a permanent adhesive layer on the undecorated side of decorative portion 7 that will bond the decorative portion to the computer housing and a carrier associated with the decorated side that is removed once decorative portion is attached to the computer housing.

Alternatively, the decorative side of the decorative portion can include a permanent adhesive that is used to attached the decorative portion to a clear substrate such as glass. In this example, a carrier can be applied to the undecorated side on the decorative portion to stabilize the Singular ID product. The methods and Singular ID products of this invention use or are fabricated from a sheet material 18 , an example of which is shown in FIGS. Sheet material 18 may be any material that is stiff enough and resilient enough to be cut with a die.

For example, sheet material 18 may be a metal sheet material such as aluminum, copper, brass, steel, alloys thereof and the like. Sheet material will have a first surface 20 that is used as the decorative face. The decorative face may be the natural color and or texture of the sheet material or a decorative material or surface texture may be applied to the first surface 20 of sheet material 18 to form a decorative surface.

For example paint or a thin decorative sheet may be applied to first surface 20 of sheet material 18 before or during the Singular ID manufacturing process. Alternatively, metal sheet materials can include buffed surfaces, painted surfaces, partially painted surfaces and so forth. Polymer sheets may have similarly decorated first surfaces An optional adhesive layer 32 can be applied to the second surface 22 of sheet material 18 —opposite the decorative surface—before sheet material 18 is processed in the methods discussed below.

Adhesive layer 32 can be any type of adhesive, such as a pressure sensitive adhesive or a heat sensitive adhesive that is capable of forming a permanent or near permanent bond between decorative portion 7 and a substrate surface. The choice of adhesive type for adhesive layer 32 will generally depend upon how the singular ID product will be applied to a substrate. One useful type of adhesives are acrylic-based adhesives such as or acrylic transfer tape sold by The 3M Corporation, St.

Paul Minn. In another optional embodiment, adhesive layer 32 can be applied to the second, non-decorative surface 22 of sheet material 18 during or at the end of the Singular ID manufacturing process. An optional liner layer 34 can then be applied to protect adhesive layer Liner layer 34 can optionally be applied to adhesive layer 32 before, during or following the manipulation of sheet material 18 in the manufacturing steps recited below. Examples of liner layers include paper, polymer coated or embedded paper, and polymer films such as polypropylene and polyester films.

Sheet material 18 may have any dimension or shape that can be processed in the manufacturing steps of this invention using the die s discussed below. For example sheet material 18 can be circular, square, and rectangular or it may have a shaped or irregular perimeter.

The factor that most limits the sizes of sheet material 18 are the dies and other equipment used to manufacture Singular ID products of this invention. The thickness of sheet materials 18 will generally range from about 0. The adhesive layer that is used to bond a decorative portion to a substrate will generally have a thickness of from about 0.

The sheet material may be pre-manufactured with registration holes 40 that are complementary to registration pins 42 in the dies used in the methods of the invention. Alternatively, registration holes 40 can be made in sheet material 18 during the processes of this invention or sheet materials 18 without registration holes can be processed in dies.

The methods of this invention may use an optional preliminary die station followed by or preceded by a process die station. In the die embodiments shown in FIGS. Die second half 14 includes a female die 14 that includes depression s 23 corresponding to each of the one or more decorative portion die cut pieces 8. Depression s 23 accept and momentarily retain the one or more die cut pieces 8 that are cut from sheet material 18 by the action of male punch The die halves further includes optional registration pin s 42 and die guide s In FIGS.

Also in the embodiment shown in FIGS. For this reason, registration pins 42 would preferably be located on die second half However, the location of optional die guide s 15 and optional registration pin s 42 is not critical so they can be located on either die first half 10 or die second half 14 regardless of which if either die half is stationary.

If the dies include die guide s 15 and registration pin s 42 , then corresponding die guide aperture s 17 and registration aperture s 43 will be located on the die half opposite the die half on which die guide s 15 and registration pin s 42 are placed.

In operation, a material sheet 18 including registration holes 40 is associated with die second half 14 such that registration pins 42 pass through registration holes 40 in sheet material When the two die halves are brought together, die guide s 15 and registration pin s 42 enter die guide aperture s 17 and registration aperture s 43 as the die halves approach one another. Die guide s 15 and registration pin s 42 thereby ensure that sheet material 18 and the two die halves remain in registration with one another during the die cutting step.

Process die station 55 includes a die first half 10 having a male punch 12 along with a die second half 14 including a female die 16 , registration pins 42 and die guides Process die station 55 further includes a first spring 56 for urging male punch 12 towards sheet material Die station 55 also includes a second spring 57 that urges a spring loaded knockout 19 towards depressions 23 formed in female die In operation, male punch 12 cuts sheet material 18 to form one or more die cut pieces 8.

Continued movement of male punch 12 towards female die 16 forces die cut pieces 8 into depressions 23 in female die When die first half 10 moves away from die second half 14 , the spring associated with spring loaded knockout 19 urges die cut pieces 8 back into registration with voids 21 formed in sheet material 18 during the die cutting procedure to form a die cut sheet material including a decorative portion having one or more die cut pieces.

There are several aspects of the die first half 10 and die second half 14 that can be optionally optimized in order to most efficiently manufacture Singular ID products. Die enter the clearance between the male punch 12 and female die 16 should be kept to minimum. That specification is not acceptable in the present method because dies with such large clearances would produce a decoration portion that could not be returned to registration with the scrap portion of the sheet material.

Therefore, dies of the present invention must have tighter clearances to be useful. The tolerated clearance will depend upon the sheet material thickness.

Preferred die clearances are reported in Table 1 below. A small taper can be added to die edges to ensure proper clearance between the male and female portions of the die. Registration holes 40 can be applied to material sheet 18 as discussed above in a separate die cutting process. Alternatively, registration holes 40 can be applied to material sheet 18 using the processing die station discussed immediately above.

As noted above, the orientation of the die first half 10 and die second half 14 which die halves move and which is located above the other is not critical. In FIG. In both embodiments shown in FIGS. The primary difference between the Singular ID products produced by these different dies might be the orientation of the decorative portion with respect to the die cut material sheet after the decorative portion is returned to registration with the die cut material sheet.

The steps of manufacturing a die cut sheet material including an embedded decorative portion will be discussed with reference in particular to FIGS. The process die station 55 is useful for cutting a sheet material 18 that may or may not include an optional adhesive layer 32 associated either the decorated or undecorated surface.

Sheet material 18 further includes a first surface 20 that is generally decorated. Registration holes 40 pass through sheet material 18 and adhesive layer Referring now to FIGS. Die first half 10 is then moved towards die second half 14 to cause male punch 12 to punch out a desired decorative portion 7 from sheet material As shown in FIGS.