A multi-dimensional precise skin care method based on skin detection and formula design
By establishing a multi-dimensional skin detection system and combining multiple detection indicators for quantitative analysis, the problem of lack of objectivity and accuracy of skin care methods in the existing technology is solved, and accurate measurement of skin problems and targeted skin care solutions are achieved.
Patent Information
- Application Number
- CN202411857474.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-17
- Publication Date
- 2025-04-01
AI Technical Summary
The existing precise skin care methods in the cosmetics industry lack the objectivity and accuracy of detection, and the causes of skin problems are complex, so it is not accurate to judge by relying solely on one or two indicators.
By establishing a multi-dimensional skin detection system, including skin optical dimension detection, functional dimension detection and structural dimension detection, combined with skin sensitivity index, wrinkle index, oil index and moisture index, multi-dimensional quantitative analysis is carried out to design accurate skin care solutions.
It realizes multi-dimensional accurate measurement and analysis of skin problems, provides targeted skin care solutions, and improves the accuracy and effectiveness of skin care.
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Abstract
Description
Technical Field
[0001] The present invention relates to the field of cosmetics, and in particular to a multi-dimensional precise skin care method and application based on skin detection and formula design. Background Art
[0002] The Outline of the 14th Five-Year Plan for National Economic and Social Development and the Long-Term Goals for 2035 proposes to launch a Chinese brand innovation campaign, enhance the influence and competitiveness of independent brands, promote the construction of Chinese cosmetics brands, and promote the high-quality development of the cosmetics industry. The State Food and Drug Administration issued the "Notice on the Pilot of Personalized Cosmetics Services", encouraging companies to conduct pilot projects in skin testing, product tracking, and personalized skin care solutions for ordinary cosmetics such as makeup and skin care. It is necessary to ensure the quality and safety of cosmetics while meeting the personalized needs of consumers for makeup. Consumers' needs are becoming more diversified and refined, and popular products can no longer meet them. Breaking the homogeneity of the cosmetics industry and providing consumers with precise skin care solutions has become a gap that needs to be filled urgently.
[0003] The existing precise skin care concepts in the cosmetics industry mainly rely on AI algorithms, consumer feedback questionnaires, mobile phone skin testing software and other means. They lack objectivity and accuracy in testing and are easily affected by environmental factors such as light, temperature and humidity, as well as mobile phone models. In addition, the causes of skin problems are complex, and it is not accurate to judge based on one or two indicators alone. Summary of the invention
[0004] The technical problem to be solved by the present invention is to provide a multi-dimensional precise skin care method and application based on skin detection and formula design. The present invention is based on systematic skin detection, integrates and analyzes the skin's original state data, locks in skin problems through 4 indicators, and combines product formula design to provide consumers with precise skin care solutions to deal with different skin problems in a targeted manner.
[0005] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention comprises the following steps:
[0006] (1) Establishment of skin testing system: including skin optical dimension testing, skin functional dimension testing and skin structural dimension testing;
[0007] (2) Skin problem analysis: including skin sensitivity index (SSI), skin wrinkle index (SWI), skin oil index (SOI) and skin moisture index (SMI), and assigning different weight values to each detection index according to the degree of emphasis, and classifying, integrating and calculating the data;
[0008] (3) Formulate a precise skin care plan: Based on the results of step (1) and step (2), match them according to the quadrant diagram to obtain different skin problems, and then design a formula based on different skin problems to obtain a precise skin care plan.
[0009] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention, wherein the skin optical dimension detection in step (1) comprises the following steps:
[0010] The VISIA skin detector was used to take photos of the front face, left cheek and right cheek in seven different lighting modes, including standard light, oblique light, cross-polarized light, parallel polarized light, narrow-band blue light absorption, narrow-band blue light fluorescence and ultraviolet light. The red zone feature number, red zone score, hemoglobin content, wrinkle index, wrinkle feature count, wrinkle score, wrinkle percentage score, wrinkle grade, porphyrin feature count and porphyrin score of the analysis area were analyzed based on 3D PRIMOS software. The average of the test results was recorded as S7, S8, S9, W1, W2, W3, W4, W16, O3 and O4.
[0011] Antera 3D skin camera was used to take pictures of a 4cm×4cm skin area through 24 LED lights and 7 color channels. The hemoglobin score, hemoglobin average value, hemoglobin change value, total wrinkle length, average wrinkle width, average wrinkle depth, wrinkle score, wrinkle dent index, total fine line length, average fine line width, average fine line depth, fine line count, fine line score, fine line dent index and a* average value were analyzed based on the built-in computing system of Antera 3D skin camera. The average value of the test results was taken and recorded as S4, S5, S6, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15 and S3.
[0012] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention, wherein the skin function dimension detection comprises the following steps:
[0013] The Corneometer CM 825 stratum corneum hydration test probe was used to test the skin moisture content at the zygomatic bone position of the left and right cheeks under the single parameter condition in the stratum corneum hydration test mode. The test results were recorded as M1 and M2.
[0014] Sebumeter SM 815 skin oil test probe was used to test the skin oil content of the forehead and cheeks under the parameter condition of measuring time of 30 seconds. The test results were recorded as O1 and O2.
[0015] Cutometer MPA580 skin elasticity test probe was used to test the skin elasticity values R0, R2, R5, R7, and F4 on the left and right cheeks, and the average of the test results was recorded as W17, W18, W19, W20, and W21. The parameters were set as follows: skin elasticity test mode: M1; target pressure: 450 mBar; pressurization time: 3 seconds; pressure release time: 3 seconds; number of repetitions: 4;
[0016] Tewameter TM Hex transepidermal water loss and heat loss test probe was used to detect the transepidermal water loss values of the skin at the left and right cheeks respectively. The results were recorded as S1 and S2. The parameter settings were as follows: number of measurements per shot: unlimited; average number of samples: 10; stop indicator: time; time threshold: 25 seconds.
[0017] The multi-dimensional precise skin care method based on skin detection and formula design described in the present invention, wherein the skin structure dimension detection comprises the following steps: using UltrascanUC 22 skin ultrasonic diagnostic instrument under the parameter condition of "100%" resolution, respectively detect the full skin layer and dermis skin thickness of the left and right cheeks, and take the average value of the results and record them as W22, W23, W24, and W25.
[0018] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention, wherein the calculation method of the skin sensitivity index SSI is as follows:
[0019] Skin Sensitivity Index (SSI) detection indicators and weight values
[0020]
[0021] Calculation formula:
[0022] Primary calculation formula: Skin Sensitivity Index SSI 1 =∑SiFi(n=7)
[0023] Secondary calculation formula: Skin Sensitivity Index SSI 2 =S8×F8×100
[0024] Three-level calculation formula: Skin Sensitivity Index SSI 3 =S9×F9÷10
[0025] Skin Sensitivity Index SSI = SSI 1 -SSI 2 +SSI 3 .
[0026] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention, wherein the calculation method of the skin wrinkle index SWI is as follows:
[0027] Skin wrinkle index SWI detection index and weight value
[0028]
[0029]
[0030] Calculation formula:
[0031] Primary calculation formula SWI 1 =W1F1+W2F2+W4F4+W5F5+W8F8+W9F9+W10F10+W13F13+W14F14+W15F15+W16F16+W18F18+W19F19+W20F20+W22F22+W23F23+W24F24+W25F25
[0032] Secondary calculation formula SWI 2 =W3F3×100
[0033] Three-level calculation formula SWI 3 =(W6F6+W11F11)×10
[0034] Level 4 calculation formula SWI 4 =(W7F7+W12F12)×1000
[0035] Five-level calculation formula SWI 5 =W17F17+W21F21
[0036] Skin wrinkle index SWI = SWI 1 +SWI 2 +SWI 3 +SWI 4 -SWI 5 .
[0037] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention, wherein the calculation method of the skin oil index SOI is as follows:
[0038] Skin oil index SOI detection index and weight value
[0039]
[0040] Calculation formula: Skin oil index SOI = ∑OiFi;
[0041] The calculation method of the skin moisture index SMI is as follows:
[0042] Skin Moisture Index (SMI) detection index and weight value
[0043]
[0044] Calculation formula: Skin moisture index SMI = ∑MiFi.
[0045] The multi-dimensional precise skin care method based on skin detection and formula design described in the present invention, wherein, in step (3), different skin conditions are divided into 16 types through skin detection data analysis, and different skin care plans are matched.
[0046] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention is different from the prior art in that:
[0047] This invention is based on the test data of skin optics, skin function and skin structure, and combines the research of skin epiphysiology, skin beauty science, clinical dermatology and other fields to establish an evaluation and analysis system, and accurately mine the four major problems of skin wrinkles, sensitivity, oil secretion and moisture content. It solves the problem of accurate skin measurement, conducts multi-dimensional quantitative analysis of skin data, promotes the development of the field of accurate skin care in the cosmetics industry, and provides technical support for enterprises.
[0048] The present invention is based on cross-disciplinary subjects such as cosmetic raw materials, formulation science, and cosmetic efficacy evaluation, combined with targeted skin problem analysis and matching formula design, to propose a precise skin care solution to meet the needs of different consumers for skin care solutions and achieve the upgrade of precise skin care.
[0049] The present invention establishes a skin detection and evaluation analysis system through VISIA skin detector, Antera 3D skin camera, Corneometer CM 825 stratum corneum hydration test probe, Cutometer MPA 580 skin elasticity test probe, Tewameter TM Hex transepidermal water loss and heat loss test probe, skin ultrasonic diagnostic instrument Ultrascan UC 22 and skin wrinkle index (SWI), skin sensitivity index (SSI), skin oil index (SOI), skin moisture index (SWI), quantitatively analyzes skin problems in multiple dimensions, designs different formulas for different skin problems, and provides precise skin care solutions.
[0050] The present invention establishes a skin detection and analysis evaluation system to achieve rapid, non-invasive, quantifiable and precise skin analysis. It controls the skin detection process through labeling, eliminates the interference of external environmental factors and consumers' subjective wishes on the detection results, ensures the accuracy and scientificity of the data, improves the feasibility of current precise skin detection, and provides a reference paradigm for precise skin care.
[0051] The multi-dimensional precise skin care method based on skin detection and formula design of the present invention is further described below in conjunction with specific embodiments. DETAILED DESCRIPTION
[0052] Example 1
[0053] A multi-dimensional precise skin care method based on skin detection and formula design, comprising the following steps:
[0054] 1. Establishment of skin testing system: including skin optical dimension testing, skin functional dimension testing and skin structural dimension testing;
[0055] Skin optical dimension testing includes the following steps:
[0056] (1) Using a VISIA skin detector (VISIA CR Gen5 Canfield Scientific Inc / USA), seven different lighting modes, including standard light, oblique light, cross-polarized light, parallel polarized light, narrow-band blue light absorption (405±10nm), narrow-band blue light fluorescence, and ultraviolet light (365±40nm), were used to photograph and detect three areas: the front face, left cheek, and right cheek. Based on the 3D PRIMOS software, the red zone feature number, red zone score, hemoglobin content, wrinkle index, wrinkle feature count, wrinkle score, wrinkle percentage score, wrinkle grade, porphyrin feature count, and porphyrin score of the analysis area were analyzed (select the image to be analyzed, and the software will directly display the analysis results). The average of the test results was recorded as S7, S8, S9, W1, W2, W3, W4, W16, O3, and O4.
[0057] The detection indicators are detailed in the table below.
[0058] VISIA skin tester test indicators
[0059]
[0060]
[0061] (2) The Antera 3D skin camera was used to take pictures of a 4 cm × 4 cm skin area through 24 LED lights and 7 color channels (from red to blue, covering the entire visible spectrum). The hemoglobin score, hemoglobin average value, hemoglobin change value, total wrinkle length, average wrinkle width, average wrinkle depth, wrinkle score, wrinkle indentation index, total fine line length, average fine line width, average fine line depth, fine line count, fine line score, fine line indentation index and a* average value were analyzed based on the built-in computing system of the Antera 3D skin camera (select the picture to be analyzed and the software will directly display the analysis results). The average of the test results was taken and recorded as S4, S5, S6, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15 and S3.
[0062] The detection indicators are detailed in the table below.
[0063] Antera 3D Skin Camera Detection Indicators
[0064]
[0065]
[0066] Skin function dimension detection includes the following steps:
[0067] (1) Using Corneometer CM 825 stratum corneum hydration test probe (MDD4 CK), under the parameter condition of Measurement mode (stratum corneum hydration test mode): single, the stratum corneum skin moisture content at the zygomatic bone position of the left and right cheeks was measured respectively, and the obtained test results were recorded as M1 and M2.
[0068] Corneometer CM 825 stratum corneum hydration test probe detection indicators
[0069]
[0070] (2) Sebumeter SM 815 skin oil test probe (MPA4 CK) was used to test the skin oil content of the forehead and cheeks under the parameter condition of 30 seconds. The test results were recorded as O1 and O2;
[0071] Sebumeter SM 815 Skin Oil Test Probe Test Specifications
[0072]
[0073] (3) Using a Cutometer MPA 580 skin elasticity test probe (Cutometer Dual MPA580 CK) under the following parameters: Cutometer mode (skin elasticity test mode): M1; Target pressure (target pressure): 450 mBar; On time (pressurization time): 3 seconds (3 seconds); Off time (pressure release time): 3 seconds (3 seconds); repetitions per measureent (number of repetitions): 4 parameters, the skin elasticity values R0, R2, R5, R7, and F4 (which are common indicators in the cosmetics industry) of the left and right cheeks were tested respectively. The average value of the test results was taken and recorded as W17, W18, W19, W20, and W21.
[0074] Cutometer MPA 580 Skin Elasticity Test Probe Test Specifications
[0075]
[0076] (4) Tewameter TM Hex transepidermal water loss and heat loss test probe (MDD4 CK)
[0077] Under the parameter conditions of Number of measurements per take: No limit; Number of samples for average: 10; Stop event type: Time; time threshold: 25seccond, the transepidermal water loss values of the left and right cheeks were tested respectively, and the results were recorded as M1 and M2.
[0078] Tewameter TM Hex transepidermal water loss and heat loss test probe detection indicators
[0079]
[0080] Skin structure dimension detection:
[0081] Ultrascan UC 22 Skin Ultrasound Diagnostic System (U022 TBS0919E)
[0082] Under the parameter condition of "100%" resolution, the full-thickness skin thickness, full-thickness skin density, dermis skin thickness and dermis skin density of the left and right cheeks were tested respectively, and the average value of each result was taken and recorded as W22, W23, W24, and W25.
[0083] Ultrascan UC 22 Skin Ultrasonic Diagnostic Instrument Detection Indicators
[0084]
[0085] 2. Skin problem analysis: including skin sensitivity index SSI, skin wrinkle index SWI, skin oil index SOI and skin moisture index SMI, and assign different weight values to each detection index according to the degree of emphasis, and classify, integrate and calculate the data;
[0086] (1) The calculation method of skin sensitivity index (SSI) is as follows:
[0087] Skin Sensitivity Index (SSI) detection indicators and weight values
[0088]
[0089]
[0090] Calculation formula:
[0091] Primary calculation formula: Skin Sensitivity Index SSI 1 =∑SiFi(n=7) Secondary calculation formula: Skin Sensitivity Index SSI 2 =S8×F8×100
[0092] Three-level calculation formula: Skin Sensitivity Index SSI 3 =S9×F9÷10
[0093] Skin Sensitivity Index SSI = SSI 1 -SSI 2 +SSI 3 .
[0094] (2) The calculation method of skin wrinkle index (SWI) is as follows:
[0095] Skin wrinkle index SWI detection index and weight value
[0096]
[0097] Calculation formula:
[0098] Primary calculation formula SWI 1 =W1F1+W2F2+W4F4+W5F5+W8F8+W9F9+W10F10+W13F13+W14F14+W15F15+W16F16+W18F18+W19F19+W20F20+W22F22+W23F23+W24F24+W25F25
[0099] Secondary calculation formula SWI 2 =W3F3×100
[0100] Three-level calculation formula SWI 3 =(W6F6+W11F11)×10
[0101] Level 4 calculation formula SWI 4 =(W7F7+W12F12)×1000
[0102] Five-level calculation formula SWI 5 =W17F17+W21F21
[0103] Skin wrinkle index SWI = SWI 1 +SWI 2 +SWI 3 +SWI4 -SWI 5 .
[0104] (3) The calculation method of skin oil index SO1 is as follows:
[0105] Skin oil index SOI detection index and weight value
[0106]
[0107] Calculation formula: Skin oil index SOI = ∑OiFi;
[0108] (4) The calculation method of skin moisture index (SMI) is as follows:
[0109] Skin Moisture Index (SMI) detection index and weight value
[0110]
[0111] Calculation formula: Skin moisture index SMI = ∑MiFi.
[0112] 3. Formulate precise skin care solutions: Calculate based on skin test data, match the skin wrinkle index, skin sensitivity index, skin oil index and skin moisture index scores according to the quadrant diagram, and then get the corresponding skin problems. Then, according to different skin problems, design formulas to get precise skin care solutions.
[0113] Exact Matching Quadrant Diagram
[0114] Based on the integration of the test data of different dimensions of the skin, the above algorithm is used to obtain the values of skin sensitivity index, skin wrinkle index, skin oil index and skin moisture index, which correspond to one of the 16 skin types. See the table below for specific types.
[0115] Skin 16 classification matching table
[0116]
[0117] Through skin test data analysis, different skin conditions are divided into 16 types, and formulas are designed for different skin problems to obtain precise skin care solutions.
[0118]
[0119]
[0120]
[0121]
[0122] The skin test data ranges corresponding to the 16 skin types and the matching skin care formula solutions are shown in the table above.
[0123] Example 2
[0124] Skin testing:
[0125] (1) Antera 3D Skin Camera
[0126]
[0127]
[0128]
[0129] (2)VISIA Skin Detector
[0130]
[0131] (3) Corneometer CM 825 stratum corneum hydration test probe
[0132]
[0133] (4) Sebumeter SM 815 Skin Oil Test Probe
[0134]
[0135] (5) Cutometer MPA 580 Skin Elasticity Test Probe
[0136]
[0137] (6) Tewameter TM Hex transepidermal water loss and heat loss test probe
[0138]
[0139] (7) Ultrascan UC 22
[0140]
[0141] Skin problem type analysis
[0142]
[0143] The embodiments described above are merely descriptions of preferred implementation modes of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.
Claims
1. A multi-dimensional precise skin care method based on skin detection and formula design, characterized by: The steps include: (1) Establishment of skin testing system: including skin optical dimension testing, skin functional dimension testing and skin structural dimension testing; (2) Skin problem analysis: including skin sensitivity index (SSI), skin wrinkle index (SWI), skin oil index (SOI) and skin moisture index (SMI), and assigning different weight values to each detection index according to the degree of emphasis, and classifying, integrating and calculating the data; (3) Formulate a precise skin care plan: Based on the results of step (1) and step (2), match them according to the quadrant diagram to obtain different skin problems, and then design a formula based on different skin problems to obtain a precise skin care plan.
2. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 1, characterized in that: The skin optical dimension detection in step (1) comprises the following steps: The VISIA skin detector was used to take photos of the front face, left cheek and right cheek in seven different lighting modes, including standard light, oblique light, cross-polarized light, parallel polarized light, narrow-band blue light absorption, narrow-band blue light fluorescence and ultraviolet light. The red zone feature number, red zone score, hemoglobin content, wrinkle index, wrinkle feature count, wrinkle score, wrinkle percentage score, wrinkle grade, porphyrin feature count and porphyrin score of the analysis area were analyzed based on 3D PRIMOS software. The average of the test results was recorded as S7, S8, S9, W1, W2, W3, W4, W16, O3 and O4. Antera 3D skin camera was used to take pictures of a 4cm×4cm skin area through 24 LED lights and 7 color channels. The hemoglobin score, hemoglobin average value, hemoglobin change value, total wrinkle length, average wrinkle width, average wrinkle depth, wrinkle score, wrinkle dent index, total fine line length, average fine line width, average fine line depth, fine line count, fine line score, fine line dent index and a* average value were analyzed based on the built-in computing system of Antera 3D skin camera. The average value of the test results was taken and recorded as S4, S5, S6, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15 and S3.
3. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 2, characterized in that: The skin function dimension detection comprises the following steps: The Corneometer CM 825 stratum corneum hydration test probe was used to test the skin moisture content at the zygomatic bone position of the left and right cheeks under the single parameter condition in the stratum corneum hydration test mode. The test results were recorded as M1 and M2. Sebumeter SM 815 skin oil test probe was used to test the skin oil content of the forehead and cheeks under the parameter condition of measuring time of 30 seconds. The test results were recorded as O1 and O2. Cutometer MPA 580 skin elasticity test probe was used to test the skin elasticity values R0, R2, R5, R7, and F4 on the left and right cheeks respectively. The average of the test results was taken and recorded as W17, W18, W19, W20, and W21. The parameter settings were as follows: skin elasticity test mode: M1; target pressure: 450 mBar; pressurization time: 3 seconds; pressure release time: 3 seconds; number of repetitions: 4: Tewameter TM Hex transepidermal water loss and heat loss test probe was used to detect the transepidermal water loss values of the skin at the left and right cheeks respectively. The results were recorded as S1 and S2. The parameter settings were as follows: number of measurements per shot: unlimited; average number of samples: 10; stop indicator: time; time threshold: 25 seconds.
4. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 3, characterized in that: The skin structure dimension detection includes the following steps: using Ultrascan UC 22 skin ultrasound diagnostic instrument under the parameter condition of "100%" resolution, respectively detecting the thickness of the entire skin layer and dermis layer at the left and right cheeks, and taking the average value of the obtained results and recording them as W22, W23, W24, and W25.
5. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 4, characterized in that: The calculation method of the skin sensitivity index SSI is as follows: Skin Sensitivity Index (SSI) detection indicators and weight values Calculation formula: Primary calculation formula: Skin sensitivity index SSI1 = ∑SiFi (n = 7) Secondary calculation formula: Skin sensitivity index SSI2 = S8 × F8 × 100 Three-level calculation formula: Skin sensitivity index SSI3 = S 9 × F9 ÷ 10 Skin sensitivity index SSI = SSI1-SSI2+SSI3.
6. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 5, characterized in that: The calculation method of the skin wrinkle index SWI is as follows: Skin wrinkle index SwI detection index and weight value Calculation formula: First-level calculation formula SWI1=W1F1+W2F2+W4F4+W5F5+W8F8+W9F9+W10F10+W13F13+W14F14+W15F15+W16F16+W18F18+W19F19+W20F20+W22F22+W23F23+W24F24+W25F25 Secondary calculation formula SWI2=W3F3×100 The third-level calculation formula SWI3 = (W6F6 + W11F11) × 10 Level 4 calculation formula SWI4 = (W7F7 + W12F12) × 1000 Level 5 calculation formula SWI5=W17F17+W21F21 Skin wrinkle index SWI = SWI1 + SWI2 + SWI3 + SWI4-SWI5.
7. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 6, characterized in that: The calculation method of the skin oil index SOI is as follows: Skin oil index SOI detection index and weight value Calculation formula: Skin oil index SOI = ∑OiFi; The calculation method of the skin moisture index SMI is as follows: Skin Moisture Index (SMI) detection index and weight value Calculation formula: Skin moisture index SMI = ∑MiFi.
8. The multi-dimensional precise skin care method based on skin detection and formula design according to claim 7, characterized in that: In step (3), different skin conditions are divided into 16 types through skin detection data analysis, including: The skin test data ranges corresponding to the 16 skin types and the matching skin care formula solutions are shown in the table above.