DETAILED ACTION
The Office Action is sent in response to Applicant’s Communication received on 07/03/2022 and 08/08/2022 for application number 17/810,603. The Office hereby acknowledges receipt of the following and placed of record in file: Specification, Abstract, Oath/declaration, IDS, and Claims.
Examiner notes that claims 14 and 15 has been cancelled, see Applicant response to Pre-Exam Formalities Notice on 08/08/2022, and on 03/28/2023, with respect to the Fee worksheet.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Specification
The abstract of the disclosure is objected to because of the use of Legal phraseology. The abstract refers to “said expression” at line 5. A corrected abstract of the disclosure is required and must be presented on a separate sheet, apart from any other text. See MPEP § 608.01(b).
Applicant is reminded of the proper language and format for an abstract of the disclosure.
The abstract should be in narrative form and generally limited to a single paragraph on a separate sheet within the range of 50 to 150 words in length. The abstract should describe the disclosure sufficiently to assist readers in deciding whether there is a need for consulting the full patent text for details.
The language should be clear and concise and should not repeat information given in the title. It should avoid using phrases which can be implied, such as, “The disclosure concerns,” “The disclosure defined by this invention,” “The disclosure describes,” etc.
Claim Objections
Claims 1, 4, 6, 8, 10, 11, 12, and 13 objected to because of the use of numerals within the parentheses. In claims, numbers within parentheses are only allowed for reference characters. Applicant’s claims use the numbers in parentheses to identify equations in the Specification. See MPEP 608.01(m). Examiner suggests looking at the Draft Amendment attached to this Office Action, wherein for at least claim 1, Examiner suggests amending ”of equ.(6) by using one of the expressions of equ.(32), equ.(38) or (41)” should read as “of equation 6, of the specification, by using one of the equations 32, 38, or 41, of the specification”. Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-13 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Claims 1-13 are unclear because they lack of a transitional phrase. It is therefore unclear whether the claims are open-ended or closed-ended, wherein “closed-ended” would refer to having ONLY the limitations listed in the claim and nothing else. Examiner suggests amending the independent claims to include transitional phases, wherein for example claim 1: “Method of calculating” should read as “A method comprising the step(s) of: calculating”. See MPEP 2111.03 and Draft Amendments for more details.
For purposes of examination the claims will be considered to be open-ended.
Examiner also suggests looking at 37 CFR 1.121(c) when amending the claims.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-13 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Under the Alice Framework Step 1, claim 1 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 1 recites:
Method of calculating the fourth column Vector (N3) of a local Frame (Ln) given in the form of equ.(6) by using one of the expressions of equ.(32), equ.(38) or (41).
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see equations on specification paragraphs 5, 23, 38, and 40). Additionally, the use of pure equations and expressions is purely mathematical calculations and can also be performed on pen and paper which falls under “mental steps” of abstract ideas. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 1, claims 2-6 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 2 recites:
Method of calculating the 4D-Frenet-Serret frame (**
L
-
η
, ***
L
-
η
) in four-dimensional Minkowski space of a timelike worldline by forming the product of another local frame
L
˘
η
,
L
˙
η
and one or more spatial rotations
R
˘
η
,
R
¨
η
,
R
˙
η
.
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see at least specification paragraphs 40, 42, 47, 48, 50, 55, 61). The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 2A prong 1, claims 3-6 recite further steps and details for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame and falls within the “mathematical Concepts” and/or “mental Processes” grouping of abstract ideas.
For claim 3, it is directed to mathematical relationship of the local frame, 4D-curvature, and worldline to be used in further mathematical operation with relation to spatial rotations. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
For claim 4, it is directed to the use of to 3 different formulas for the calculation of the local frame, rotation matrix and rotation angle which is pure mathematical equations and that can also be done with pen and paper. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
For claim 5, it is directed to mathematical relationship of the local frame and 4D-curvature to be used in to be used in further mathematical operation with relation to spatial rotations. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
For claim 6, it is directed to the use of to 9 different formulas for the calculation of the local frames, rotation matrices and rotation angles which is pure mathematical equations and that can also be done with pen and paper. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 1, claims 7-8 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 7 recites:
Method of calculating one of the three 4D-curvatures
p
1
,
p
2
,
p
3
of the 4-D Frenet-Serret frame in Minkowski space of a timelike worldline
r
τ
in terms of the 3D-curvature
ϰ
, the 3D-torsion
τ
and the magnitude
u
2
of the three-dimensional spatial part
u
of the four velocity
u
=
u
0
u
.
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see at least specification paragraphs 64-67, which also shows equations 74-77). The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 2A prong 1, claim 8 recite further steps and details for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model and falls within the “mathematical Concepts” and/or “mental Processes” grouping of abstract ideas. Claim 8 points to 3 different formulas for each of the three 4D-curvatures which is pure math and as an equation that can also be done with pen and paper. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 1, claims 9-10 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 9 recites:
Method of calculating the transport property of a local frame
L
'
η
=
L
η
R
η
, which is formed by multiplying another local frame
L
η
with a spatial rotation
R
η
using matrix partitioning.
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see at least specification paragraphs 12, 34, and 84-86, which also shows equations 13 and 33). The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 2A prong 1, claim 10 recite further steps and details to calculation of Fermi-Walker frame and falls within the “mathematical Concepts” and/or “mental Processes” grouping of abstract ideas. Claim 10 points to the formula used for the calculation of the transport property for the local frame which is pure math and as an equation that can also be done with pen and paper. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 1, claim 11 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 11 recites:
Method of constructing a general solution to the condition that the second 4D-curvature
p
2
, also known as first torsion, of the 4D-Frenet-Serret frame is zero by using equ.(81).
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see specification paragraphs 79 and 187-190, which also shows equation 81). Additionally, the use of pure equations and expressions is purely mathematical calculations and can also be performed on pen and paper which falls under “mental steps” of abstract ideas. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 1, claim 12 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 12 recites:
Method of constructing a general solution to the condition that the third 4D-curvature
p
3
, also known as second torsion, Hyper-torsion or bi-torsion, of the 4D-Frenet-Serret Frame is zero by using equ.(84).
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see specification paragraphs 75 and 200-206, which also shows equation 84). Additionally, the use of pure equations and expressions is purely mathematical calculations and can also be performed on pen and paper which falls under “mental steps” of abstract ideas. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Under the Alice Framework Step 1, claim 13 recite a method and, therefore, is a process.
Under the Alice Framework Step 2A prong 1, claim 13 recites:
Method of calculating a timelike worldline describing a circular movement with the second 4D-curvature
p
2
, also known as first torsion, of the 4D-Frenet-Serret frame being zero using one of the two formulas of equ.(82).
The above underlined limitations are related to field of relativity theory and/or physics for building the Frenet-Serret frames/curvatures in Minkowski space to produce a model to be further used for calculation of Fermi-Walker frame which amount to mathematical calculations and relationships that fall under “Mathematical concepts” of abstract ideas (see specification paragraphs 73 and 191-196, which also shows equation 82). Additionally, the use of pure equations and expressions is purely mathematical calculations and can also be performed on pen and paper which falls under “mental steps” of abstract ideas. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Allowable Subject Matter
Claims 1-13 would be allowable over the prior art of record if the outstanding rejections under 32 U.S.C. 101 and 112(b) are overcome.
The following is a statement of reasons for the indication of allowable subject matter:
Gourgoulhon (From IDS filed 07/03/2022 [hereinafter IDS]: “Special Relativity in General Frames) discloses Four-Velocity, first and second curvatures, First torsion and Second torsion of the worldline, Fermi-Walker and spatial rotation, and Fermi-Walker transport on pages 35-38, 59-62, and 83-94.
Gray et al. (IDS: “Modern Differential Geometry of Curves and Surfaces with Mathematica”) discloses Curves in 3D, with respect to curvature and torsion, see pages 203-204.
Maluf et al. (IDS: “On the construction of Fermi-Walker Transported frames”) discloses the use of producing the Transported frames using frame along a curve using Lorentz rotation and using angular velocity, see at least page 8-9 and sections 1 and 6.
For claim 1, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: a local Frame (Ln) given in the form of equ.(6) by using one of the expressions of equ.(32), equ.(38) or (41)
For claim 2, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: calculating the 4D-Frenet-Serret frame (**
L
-
η
, ***
L
-
η
) in four-dimensional Minkowski space of a timelike worldline by forming the product of another local frame
L
˘
η
,
L
˙
η
and one or more spatial rotations
R
˘
η
,
R
¨
η
,
R
˙
η
.
For claims 3-6, each claim effectively depends on claim 2 and would be allowable based on the reasons given for claim 2, after overcoming related rejections.
For claim 7, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: calculating one of the three 4D-curvatures
p
1
,
p
2
,
p
3
of the 4-D Frenet-Serret frame in Minkowski space of a timelike worldline
r
τ
in terms of the 3D-curvature
ϰ
, the 3D-torsion
τ
and the magnitude
u
2
of the three-dimensional spatial part
u
of the four velocity
u
=
u
0
u
.
For claim 8, it depends on claim 7 and would be allowable based on the reasons given for claim 7, after overcoming related rejections.
For claim 9, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: calculating the transport property of a local frame
L
'
η
=
L
η
R
η
, which is formed by multiplying another local frame
L
η
with a spatial rotation
R
η
using matrix partitioning.
For claim 10, it depends on claim 9 and would be allowable based on the reasons given for claim 9, after overcoming related rejections.
For claim 11, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: constructing a general solution to the condition that the second 4D-curvature
p
2
, also known as first torsion, of the 4D-Frenet-Serret frame is zero by using equ.(81).
For claim 12, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: constructing a general solution to the condition that the third 4D-curvature
p
3
, also known as second torsion, Hyper-torsion or bi-torsion, of the 4D-Frenet-Serret Frame is zero by using equ.(84).
For claim 13, the prior art above alone or in combination with any other reference(s) fails to disclose or provide motivation for the following limitations in combination with the rest of the claim limitations: calculating a timelike worldline describing a circular movement with the second 4D-curvature
p
2
, also known as first torsion, of the 4D-Frenet-Serret frame being zero using one of the two formulas of equ.(82).
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Kenny K. Bui whose telephone number is (571)270-0604. The examiner can normally be reached 9:00 am to 2:00 pm on Monday, 8:00 am to 5:00 pm on Tuesday to Thursday, and 8:00 am to 4:00pm on Friday ET.
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If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Andrew T Caldwell can be reached at (571)272-3702. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
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/KENNY K. BUI/Patent Examiner, Art Unit 2182 (571)270-0604
/ANDREW CALDWELL/Supervisory Patent Examiner, Art Unit 2182