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Polynomial term structure models. Cheng, Tehranchi arxiv.org/abs/1504.03238 #q-fin

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Working Babbage machine. Fully mechanical machine used for computing results for high level polynomials up to seventh order.

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Check out here how to calculate zeros of polynomial equation using simple online calculator.

1. Fit polynomial in Excel or by Fourier

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"Polynomial dynamics: conjugacy and combinatorics"

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 1025 / length of data axis 1

NAXIS2 = 1480 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

MIPS-HI = 65535 / Lower visualization cutoff

MIPS-LO = 527 / Upper visualization cutoff

PROGRAM = 'Siril 1.4.0-beta3' / Software that created this HDU

FILENAME= 'Light_NGC 6888_20.0s_LP_20250728-231100.fit'

DATE = '2025-07-30T03:11:24' / UTC date that FITS file was created

DATE-OBS= '2025-07-29T04:10:36.490187' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light ' / Type of image

EXPTIME = 20. / [s] Exposure time duration

TELESCOP= 'S50_f1c10930' / Telescope used to acquire this image

FILTER = 'mixed ' / Active filter name

APERTURE= 5. / Aperture of the instrument

FOCALLEN= 251.885 / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.90000009536743 / [um] Pixel X axis size

YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size

INSTRUME= 'Seestar S50' / Instrument name

CCD-TEMP= 29.5625 / [degC] CCD temperature

GAIN = 80 / Sensor gain

FOCPOS = 1611 / [step] Focuser position

STACKCNT= 183 / Stack frames

LIVETIME= 3660. / [s] Exposure time after deadtime correction

EXPSTART= 2460885.67403345 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460885.72888051 / [JD] Exposure end time (standard Julian date)

OBJECT = 'NGC 6888' / Name of the object of interest

SITELAT = 41.7559 / [deg] Observation site latitude

SITELONG= -88.1817 / [deg] Observation site longitude

OBJCTRA = '20 13 9.981' / [H M S] Image center Right Ascension

OBJCTDEC= '+38 18 58.820' / [D M S] Image center Declination

RA = 303.291585618783 / [deg] Image center Right Ascension

DEC = 38.316338895816 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 512. / Axis1 reference pixel

CRPIX2 = 658.5 / Axis2 reference pixel

CRVAL1 = 303.291460830965 / [deg] Axis1 reference value

CRVAL2 = 38.2622414617112 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000659637298443911 / [deg] X pixel size

CDELT2 = 0.000659676036501389 / [deg] Y pixel size

PC1_1 = 0.999901889077021 / Linear transformation matrix (1, 1)

PC1_2 = -0.0140075772424854 / Linear transformation matrix (1, 2)

PC2_1 = 0.0144212544295453 / Linear transformation matrix (2, 1)

PC2_2 = 0.999896008303203 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -3.54660952464926E-08

A_1_1 = -1.06492931934894E-08

A_0_2 = 4.92193576270182E-08

A_3_0 = 9.74979757881843E-11

A_2_1 = 9.23412361528831E-11

A_1_2 = -3.86161022490911E-11

A_0_3 = -6.43471295887784E-11

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -1.81623121007492E-08

B_1_1 = -6.07628614360661E-08

B_0_2 = 3.13532550988818E-08

B_3_0 = -3.12167038535287E-10

B_2_1 = -1.09146453411891E-10

B_1_2 = 1.94576804568731E-11

B_0_3 = -3.15496678831747E-11

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = 7.20989472594576E-07

AP_1_0 = -7.15205461521151E-09

AP_0_1 = -3.02080367669585E-09

AP_2_0 = 3.54654294911883E-08

AP_1_1 = 1.06549366969563E-08

AP_0_2 = -4.92269218739494E-08

AP_3_0 = -9.74706495593266E-11

AP_2_1 = -9.23217310137704E-11

AP_1_2 = 3.86175478662565E-11

AP_0_3 = 6.4357601022277E-11

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = 2.56589862602273E-06

BP_1_0 = -1.860320048007E-09

BP_0_1 = -7.23457971307795E-09

BP_2_0 = 1.81624034350065E-08

BP_1_1 = 6.07705541620229E-08

BP_0_2 = -3.13643573956026E-08

BP_3_0 = 3.12158154059866E-10

BP_2_1 = 1.0915802357106E-10

BP_1_2 = -1.94485563690183E-11

BP_0_3 = 3.15661495061112E-11

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 1080 / length of data axis 1

NAXIS2 = 1920 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU

FILENAME= 'Light_M 8_20.0s_LP_20250623-004337.fit'

DATE = '2025-06-23T17:56:12' / UTC date that FITS file was created

DATE-OBS= '2025-06-23T05:43:13.684104' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light ' / Type of image

ROWORDER= 'BOTTOM-UP' / Order of the rows in image array

EXPTIME = 20. / [s] Exposure time duration

TELESCOP= 'S50_f1c10930' / Telescope used to acquire this image

FILTER = 'mixed ' / Active filter name

APERTURE= 5. / Aperture of the instrument

FOCALLEN= 251.933 / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.90000009536743 / [um] Pixel X axis size

YPIXSZ = 2.90000009536743 / [um] Pixel Y axis size

INSTRUME= 'Seestar S50' / Instrument name

CCD-TEMP= 34.3125 / [degC] CCD temperature

GAIN = 80 / Sensor gain

FOCPOS = 1624 / [step] Focuser position

STACKCNT= 78 / Stack frames

LIVETIME= 1560. / [s] Exposure time after deadtime correction

EXPSTART= 2460846.6366228 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460849.73961406 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M 8 ' / Name of the object of interest

SITELAT = 41.6816 / [deg] Observation site latitude

SITELONG= -88.2534 / [deg] Observation site longitude

OBJCTRA = '18 03 38.880' / [H M S] Image center Right Ascension

OBJCTDEC= '-24 24 14.314' / [D M S] Image center Declination

RA = 270.911998587708 / [deg] Image center Right Ascension

DEC = -24.4039761864265 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 540.5 / Axis1 reference pixel

CRPIX2 = 960.5 / Axis2 reference pixel

CRVAL1 = 270.911998587708 / [deg] Axis1 reference value

CRVAL2 = -24.4039761864265 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000659082468622788 / [deg] X pixel size

CDELT2 = 0.000659978400644474 / [deg] Y pixel size

PC1_1 = 0.999916305903843 / Linear transformation matrix (1, 1)

PC1_2 = -0.0129375881683126 / Linear transformation matrix (1, 2)

PC2_1 = 0.0130579518759834 / Linear transformation matrix (2, 1)

PC2_2 = 0.99991474131188 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -1.74663971740093E-07

A_1_1 = 1.1102370023928E-07

A_0_2 = 4.2642549292385E-09

A_3_0 = -4.65822780487741E-11

A_2_1 = -1.6234057826174E-10

A_1_2 = -4.72534137698903E-11

A_0_3 = 9.87666085858249E-12

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = 1.45464879076344E-07

B_1_1 = -1.19172611780262E-07

B_0_2 = 5.01691851105444E-08

B_3_0 = 1.24613186670743E-10

B_2_1 = 6.29865855314931E-11

B_1_2 = -1.17783226014919E-10

B_0_3 = 4.92090201518581E-11

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = 5.47377169669169E-07

AP_1_0 = -5.70332137073137E-09

AP_0_1 = -3.03896970252188E-09

AP_2_0 = 1.74662949168253E-07

AP_1_1 = -1.11016127716692E-07

AP_0_2 = -4.26486970419252E-09

AP_3_0 = 4.66856078214572E-11

AP_2_1 = 1.62295109644075E-10

AP_1_2 = 4.72772550885127E-11

AP_0_3 = -9.87098533893412E-12

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -3.54263523140669E-06

BP_1_0 = 2.6617236483243E-09

BP_0_1 = -4.00659450061625E-09

BP_2_0 = -1.45459455876847E-07

BP_1_1 = 1.19134279206738E-07

BP_0_2 = -5.01487203065079E-08

BP_3_0 = -1.24689018672938E-10

BP_2_1 = -6.2902158975274E-11

BP_1_2 = 1.17728825302614E-10

BP_0_3 = -4.91917511021709E-11

CREATOR = 'ZWO Seestar S50' / Capture software

PRODUCER= 'ZWO ' / Powered by ZWO

XORGSUBF= 0 / Subframe X position in binned pixels

YORGSUBF= 0 / Subframe Y position in binned pixels

EQMODE = 1 / Equatorial mode

CCDXBIN = 1 / Camera X Bin

CCDYBIN = 1 / Camera Y Bin

TOTALEXP= 20. / Total Exposure Time in seconds

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 6248 / length of data axis 1

NAXIS2 = 4176 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta2' / Software that created this HDU

DATE = '2025-06-20T16:14:50' / UTC date that FITS file was created

DATE-OBS= '2025-06-20T07:27:31.872214' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light ' / Type of image

ROWORDER= 'BOTTOM-UP' / Order of the rows in image array

EXPTIME = 180. / [s] Exposure time duration

TELESCOP= 'EQMod Mount' / Telescope used to acquire this image

FOCALLEN= 248.83 / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 3.76 / [um] Pixel X axis size

YPIXSZ = 3.76 / [um] Pixel Y axis size

INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name

CCD-TEMP= 0. / [degC] CCD temperature

SET-TEMP= 0. / [degC] CCD temperature setpoint

GAIN = 100 / Sensor gain

OFFSET = 50 / Sensor gain offset

CVF = 0.242862924933434 / [e-/ADU] Electrons per A/D unit

STACKCNT= 72 / Stack frames

LIVETIME= 12960. / [s] Exposure time after deadtime correction

EXPSTART= 2460843.81708572 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460846.81286889 / [JD] Exposure end time (standard Julian date)

OBJECT = 'NGC6604 ' / Name of the object of interest

SITELAT = 34.1986 / [deg] Observation site latitude

SITELONG= -118.919 / [deg] Observation site longitude

OBJCTRA = '18 19 20.276' / [H M S] Image center Right Ascension

OBJCTDEC= '-13 52 19.392' / [D M S] Image center Declination

RA = 274.83448499547 / [deg] Image center Right Ascension

DEC = -13.8720533573272 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 3124.5 / Axis1 reference pixel

CRPIX2 = 2088.5 / Axis2 reference pixel

CRVAL1 = 274.83448499547 / [deg] Axis1 reference value

CRVAL2 = -13.8720533573272 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000865650825984819 / [deg] X pixel size

CDELT2 = 0.000865911460066954 / [deg] Y pixel size

PC1_1 = 0.1714587540866 / Linear transformation matrix (1, 1)

PC1_2 = 0.985191299011045 / Linear transformation matrix (1, 2)

PC2_1 = -0.985151016018178 / Linear transformation matrix (2, 1)

PC2_2 = 0.171690056900079 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = 4.65233486830322E-08

A_1_1 = -1.20139337137873E-07

A_0_2 = 7.90186017407897E-09

A_3_0 = -8.71078819447912E-11

A_2_1 = -2.82743088028E-12

A_1_2 = -7.68826716416117E-11

A_0_3 = -5.30383728789426E-12

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -4.29988656374688E-09

B_1_1 = 3.70137104201147E-08

B_0_2 = -1.21206682426705E-07

B_3_0 = 1.01202277701665E-12

B_2_1 = -7.91997972035546E-11

B_1_2 = -2.1223146115746E-12

B_0_3 = -7.80337209565795E-11

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = 0.000366385691588379

AP_1_0 = -1.00380661594013E-06

AP_0_1 = -1.15737201301539E-07

AP_2_0 = -4.67636540331373E-08

AP_1_1 = 1.20576423245072E-07

AP_0_2 = -7.97526625029877E-09

AP_3_0 = 8.74485776160952E-11

AP_2_1 = 2.8400355967666E-12

AP_1_2 = 7.72068117366238E-11

AP_0_3 = 5.32817592859173E-12

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -0.000237111434434274

BP_1_0 = -5.48009758424604E-08

BP_0_1 = -5.42702147665608E-07

BP_2_0 = 4.35917362307412E-09

BP_1_1 = -3.71609981540702E-08

BP_0_2 = 1.2152028055963E-07

BP_3_0 = -1.01149257617419E-12

BP_2_1 = 7.94859028424784E-11

BP_1_2 = 2.142539348929E-12

BP_0_3 = 7.82478964437494E-11

PLTSOLVD= T / Siril internal solver

HISTORY GraXpert AI BGE: subtraction

HISTORY Background neutralization

HISTORY Plate Solve

HISTORY Photometric CC (algorithm: PCC)

HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)

HISTORY Histogram Transf. (mid=0.001, lo=0.001, hi=1.000)

CREATOR = 'ZWO ASIAIR Plus' / Capture software

XORGSUBF= 0 / Subframe X position in binned pixels

YORGSUBF= 0 / Subframe Y position in binned pixels

CCDXBIN = 1 / Camera X Bin

CCDYBIN = 1 / Camera Y Bin

GUIDECAM= 'ZWO ASI120MM Mini' / Guide camera model

IMAGEW = 6248 / Image width, in pixels.

IMAGEH = 4176 / Image height, in pixels.

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 4096 / length of data axis 1

NAXIS2 = 2855 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta3' / Software that created this HDU

DATE = '2025-09-11T15:41:41' / UTC date that FITS file was created

DATE-OBS= '2025-09-11T02:12:27.113710' / YYYY-MM-DDThh🇲🇲ss observation start,

ROWORDER= 'TOP-DOWN' / Order of the rows in image array

EXPTIME = 1800. / [s] Exposure time duration

OBSERVER= 'DaveMartin' / Observer name

FILTER = 'L_Enhance' / Active filter name

FOCALLEN= 958.072 / [mm] Focal length

CENTALT = 70.1227777777778 / [deg] Altitude of telescope

CENTAZ = 217.386666666667 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 3.75999999046326 / [um] Pixel X axis size

YPIXSZ = 3.75999999046326 / [um] Pixel Y axis size

INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name

CCD-TEMP= -10.1 / [degC] CCD temperature

SET-TEMP= -10. / [degC] CCD temperature setpoint

GAIN = 100 / Sensor gain

OFFSET = 12 / Sensor gain offset

CVF = 0.2636 / [e-/ADU] Electrons per A/D unit

FOCPOS = 19549 / [step] Focuser position

FOCTEMP = 16.4699993133545 / [degC] Focuser temperature

OBJECT = 'M27 (NGC 6853,Dumbbell Nebula)' / Name of the object of interest

AIRMASS = 1.06301618555987 / Airmass at frame center (Gueymard 1993)

SITELAT = 39.3488888888889 / [deg] Observation site latitude

SITELONG= -78.8116666666667 / [deg] Observation site longitude

OBJCTRA = '19 59 42.036' / [H M S] Image center Right Ascension

OBJCTDEC= '+22 38 52.905' / [D M S] Image center Declination

RA = 299.925148341019 / [deg] Image center Right Ascension

DEC = 22.6480291772483 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 2405.5 / Axis1 reference pixel

CRPIX2 = 1219.5 / Axis2 reference pixel

CRVAL1 = 299.908175341918 / [deg] Axis1 reference value

CRVAL2 = 22.739672427328 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000224841306895568 / [deg] X pixel size

CDELT2 = 0.000224879052039461 / [deg] Y pixel size

PC1_1 = -0.351561670851745 / Linear transformation matrix (1, 1)

PC1_2 = -0.936164724601354 / Linear transformation matrix (1, 2)

PC2_1 = 0.936122408820094 / Linear transformation matrix (2, 1)

PC2_2 = -0.351674331882305 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -1.95900331611686E-07

A_1_1 = -6.16054665622097E-08

A_0_2 = -9.08198210217208E-08

A_3_0 = -3.17094882817336E-10

A_2_1 = 2.38342474788276E-11

A_1_2 = -3.12200559109852E-10

A_0_3 = 1.00797895504647E-11

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -4.17644383671079E-08

B_1_1 = -9.84781512990151E-08

B_0_2 = -1.15014432546378E-07

B_3_0 = 4.65431034992503E-12

B_2_1 = -3.04938140200248E-10

B_1_2 = 2.14953446044965E-11

B_0_3 = -3.10357254487919E-10

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = -0.00377903891196342

AP_1_0 = -1.53665427859995E-05

AP_0_1 = 2.44777757819266E-06

AP_2_0 = 1.99292606812589E-07

AP_1_1 = 6.24484250354502E-08

AP_0_2 = 9.17615604693065E-08

AP_3_0 = 3.21869965708622E-10

AP_2_1 = -2.4600664659605E-11

AP_1_2 = 3.17304884885303E-10

AP_0_3 = -1.0687518137329E-11

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -0.00183650269545781

BP_1_0 = 1.34728244761553E-06

BP_0_1 = -1.05834921098058E-05

BP_2_0 = 4.24239116008558E-08

BP_1_1 = 9.98653688675327E-08

BP_0_2 = 1.16356847129521E-07

BP_3_0 = -4.82780184100781E-12

BP_2_1 = 3.09447378200046E-10

BP_1_2 = -2.2253344834573E-11

BP_0_3 = 3.13918801101728E-10

HISTORY Apply Signature

PIERSIDE= 'EAST' /

CAMID = '1E1E560D0B020900' /

ADCBITS = 16 / Bit depth of camera sensor ADC in current mode

BIASADU = 121.16593933105469 / ADU for bias level (no photons) at current sett

EGAINSAV= 0.26355 / Electrons per ADU at saved bit depth

RELGAIN = 2.964 / Multiplicative gain relative to minumum

RDNOISE = 1.77 / Read noise in electrons

SUBEXP = 30 /

COLORTYP= 'RGB' /

DATE-END= '2025-09-11T02:46:10.0667055' / System Clock:Est. Frame End

DATE-AVG= '2025-09-11T02:29:18.5902081' / System Clock:Est. Frame Mid Point

JD_UTC = 2460929.6036873865 / Julian Date at mid exposure

END

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 5476 / length of data axis 1

NAXIS2 = 3829 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta4' / Software that created this HDU

DATE = '2025-10-03T14:46:09' / UTC date that FITS file was created

DATE-OBS= '2025-10-02T00:03:51.750446' / YYYY-MM-DDThh🇲🇲ss observation start,

ROWORDER= 'TOP-DOWN' / Order of the rows in image array

EXPTIME = 1620. / [s] Exposure time duration

OBSERVER= 'DaveMartin' / Observer name

FILTER = 'Open ' / Active filter name

FOCALLEN= 958.351 / [mm] Focal length

CENTALT = 89.045 / [deg] Altitude of telescope

CENTAZ = 163.905277777778 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 3.76 / [um] Pixel X axis size

YPIXSZ = 3.76 / [um] Pixel Y axis size

INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name

CCD-TEMP= 0. / [degC] CCD temperature

SET-TEMP= 0. / [degC] CCD temperature setpoint

GAIN = 100 / Sensor gain

OFFSET = 12 / Sensor gain offset

CVF = 0.2636 / [e-/ADU] Electrons per A/D unit

FOCPOS = 19894 / [step] Focuser position

FOCTEMP = 15.1000003814697 / [degC] Focuser temperature

OBJECT = 'C27 (NGC 6888,Crescent Nebula)' / Name of the object of interest

AIRMASS = 1.00012788952518 / Airmass at frame center (Gueymard 1993)

SITELAT = 39.3488888888889 / [deg] Observation site latitude

SITELONG= -78.8116666666667 / [deg] Observation site longitude

OBJCTRA = '20 11 49.225' / [H M S] Image center Right Ascension

OBJCTDEC= '+38 18 38.723' / [D M S] Image center Declination

RA = 302.955105993462 / [deg] Image center Right Ascension

DEC = 38.310756355532 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 2512.5 / Axis1 reference pixel

CRPIX2 = 1842.5 / Axis2 reference pixel

CRVAL1 = 302.99693830452 / [deg] Axis1 reference value

CRVAL2 = 38.3528192243345 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000224785664728511 / [deg] X pixel size

CDELT2 = 0.000224803732880402 / [deg] Y pixel size

PC1_1 = 0.345064884988848 / Linear transformation matrix (1, 1)

PC1_2 = 0.938578832676101 / Linear transformation matrix (1, 2)

PC2_1 = -0.938541481435557 / Linear transformation matrix (2, 1)

PC2_2 = 0.345166463644356 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -1.33515070683457E-07

A_1_1 = -1.85753155144464E-08

A_0_2 = -6.96165946577253E-08

A_3_0 = -3.15530686133278E-10

A_2_1 = 3.61543320960793E-12

A_1_2 = -3.12243251827388E-10

A_0_3 = 2.3408577488978E-12

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -2.18299016474063E-08

B_1_1 = -6.18241175157028E-08

B_0_2 = -5.48863575115984E-08

B_3_0 = 1.36721019773087E-12

B_2_1 = -3.10309404002022E-10

B_1_2 = 4.46926528470426E-12

B_0_3 = -3.14868604350938E-10

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = -0.00247747675514094

AP_1_0 = -1.56112991080981E-05

AP_0_1 = 4.84918500750286E-07

AP_2_0 = 1.35781106151762E-07

AP_1_1 = 1.89932975392859E-08

AP_0_2 = 7.0457637242888E-08

AP_3_0 = 3.20238760091932E-10

AP_2_1 = -3.75367905351394E-12

AP_1_2 = 3.17586891385176E-10

AP_0_3 = -2.44990734207133E-12

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -0.000880871618802793

BP_1_0 = 4.34547820056161E-07

BP_0_1 = -1.11806676068582E-05

BP_2_0 = 2.21684065842865E-08

BP_1_1 = 6.26022469778019E-08

BP_0_2 = 5.55312447442106E-08

BP_3_0 = -1.41805563196242E-12

BP_2_1 = 3.1493469572289E-10

BP_1_2 = -4.69364845423484E-12

BP_0_3 = 3.18577071899455E-10

PLTSOLVD= T / Siril internal solver

HISTORY Plate Solve

HISTORY Crop (x=612, y=101, w=5476, h=3829)

HISTORY Background extraction (Correction: Subtraction)

HISTORY StatStretch: m=0.20 l=False n=False c=False b=0.00

HISTORY StatStretch: m=0.20 l=True n=False c=False b=0.00

HISTORY StatStretch: m=0.20 l=True n=True c=False b=0.00

HISTORY StatStretch: m=0.20 l=True n=True c=True b=0.00

HISTORY StatStretch: m=0.20 l=True n=True c=True b=0.10

HISTORY Cosmic Clarity denoise (luminance, str=0.5)

HISTORY Cosmic Clarity sharpen (Stellar Only)

HISTORY GHS pivot: 0.235, amount: 1.66, local: 0.00 [0.00 1.00]

HISTORY GHS LINEAR BP: 0.06

HISTORY GHS pivot: 0.213, amount: 3.50, local: -3.38 [0.00 1.00]

HISTORY GHS pivot: 0.341, amount: 0.90, local: 0.00 [0.00 1.00]

HISTORY GHS INV pivot: 0.168, amount: 0.86, local: 0.00 [0.00 1.00]

ADCBITS = 16 / Bit depth of camera sensor ADC in current mode

BIASADU = 121.16593933105469 / ADU for bias level (no photons) at current sett

CAMID = '1E1E560D0B020900' /

COLORTYP= 'RGB' /

DATE-AVG= '2025-10-02T00:19:18.5384346' / System Clock:Est. Frame Mid Point

DATE-END= '2025-10-02T00:34:45.3264224' / System Clock:Est. Frame End

EGAINSAV= 0.26355 / Electrons per ADU at saved bit depth

JD_UTC = 2460950.5134090097 / Julian Date at mid exposure

PIERSIDE= 'WEST' /

RADESYS = 'ICRS' /

RDNOISE = 1.77 / Read noise in electrons

RELGAIN = 2.964 / Multiplicative gain relative to minumum

SUBEXP = 30 /

END

SIMPLE = T / file does conform to FITS standard

BITPIX = 16 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 5609 / length of data axis 1

NAXIS2 = 3846 / length of data axis 2

NAXIS3 = 3 / length of data axis 3

EXTEND = T / FITS dataset may contain extensions

COMMENT FITS (Flexible Image Transport System) format is defined in 'Astronomy

COMMENT and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H

BZERO = 0. / Offset data range to that of unsigned short

BSCALE = 1. / Default scaling factor

PROGRAM = 'Siril 1.4.0-beta3' / Software that created this HDU

DATE = '2025-09-11T14:56:38' / UTC date that FITS file was created

DATE-OBS= '2025-09-11T01:24:47.985174' / YYYY-MM-DDThh🇲🇲ss observation start,

ROWORDER= 'TOP-DOWN' / Order of the rows in image array

EXPTIME = 1740. / [s] Exposure time duration

OBSERVER= 'DaveMartin' / Observer name

FILTER = 'L_Enhance' / Active filter name

FOCALLEN= 957.752 / [mm] Focal length

CENTALT = 28.4102777777778 / [deg] Altitude of telescope

CENTAZ = 211.461944444444 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 3.76 / [um] Pixel X axis size

YPIXSZ = 3.76 / [um] Pixel Y axis size

INSTRUME= 'ZWO ASI2600MC Pro' / Instrument name

CCD-TEMP= -10. / [degC] CCD temperature

SET-TEMP= -10. / [degC] CCD temperature setpoint

GAIN = 100 / Sensor gain

OFFSET = 12 / Sensor gain offset

CVF = 0.2636 / [e-/ADU] Electrons per A/D unit

FOCPOS = 19549 / [step] Focuser position

FOCTEMP = 17.5 / [degC] Focuser temperature

OBJECT = 'M17 (NGC 6618,Omega,Swan,Horseshoe Nebula)' / Name of the object of i

AIRMASS = 2.09318904147266 / Airmass at frame center (Gueymard 1993)

SITELAT = 39.3488888888889 / [deg] Observation site latitude

SITELONG= -78.8116666666667 / [deg] Observation site longitude

OBJCTRA = '18 20 46.744' / [H M S] Image center Right Ascension

OBJCTDEC= '-16 10 11.147' / [D M S] Image center Declination

RA = 275.194765291143 / [deg] Image center Right Ascension

DEC = -16.1697629615449 / [deg] Image center Declination

CTYPE1 = 'RA---TAN-SIP' / TAN (gnomic) projection + SIP distortions

CTYPE2 = 'DEC--TAN-SIP' / TAN (gnomic) projection + SIP distortions

CUNIT1 = 'deg ' / Unit of coordinates

CUNIT2 = 'deg ' / Unit of coordinates

EQUINOX = 2000. / Equatorial equinox

CRPIX1 = 2805. / Axis1 reference pixel

CRPIX2 = 1923.5 / Axis2 reference pixel

CRVAL1 = 275.194765291143 / [deg] Axis1 reference value

CRVAL2 = -16.1697629615449 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000224888425230204 / [deg] X pixel size

CDELT2 = 0.000224982118571145 / [deg] Y pixel size

PC1_1 = -0.352438328281194 / Linear transformation matrix (1, 1)

PC1_2 = -0.935835041424693 / Linear transformation matrix (1, 2)

PC2_1 = 0.935971808256997 / Linear transformation matrix (2, 1)

PC2_2 = -0.352074955298054 / Linear transformation matrix (2, 2)

A_ORDER = 3 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = -2.48631852600035E-07

A_1_1 = -6.2382581520478E-08

A_0_2 = -1.03385772643892E-07

A_3_0 = -3.21309904725447E-10

A_2_1 = 1.21273463791468E-11

A_1_2 = -3.15710758511071E-10

A_0_3 = 2.97036971111385E-12

B_ORDER = 3 / SIP polynomial degree, axis 2, pixel-to-sky

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -3.36573228505944E-08

B_1_1 = -1.28174087449613E-07

B_0_2 = -1.10067097532655E-07

B_3_0 = 4.57569104227693E-12

B_2_1 = -3.14455935262986E-10

B_1_2 = 1.0959542787778E-11

B_0_3 = -3.15196299628092E-10

AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = -0.00387538504595189

AP_1_0 = -1.02148802987312E-05

AP_0_1 = 8.95195348212583E-07

AP_2_0 = 2.52293713200998E-07

AP_1_1 = 6.32535441223069E-08

AP_0_2 = 1.047013596386E-07

AP_3_0 = 3.25306475619976E-10

AP_2_1 = -1.24368036124335E-11

AP_1_2 = 3.20035747504514E-10

AP_0_3 = -3.17349798746077E-12

BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel

BP_0_0 = -0.00110194118209101

BP_1_0 = 7.42384306986938E-07

BP_0_1 = -7.18489317730331E-06

BP_2_0 = 3.41130954977524E-08

BP_1_1 = 1.29843957811852E-07

BP_0_2 = 1.11125435305567E-07

BP_3_0 = -4.68999123635695E-12

BP_2_1 = 3.18292309543107E-10

BP_1_2 = -1.1377819498899E-11

BP_0_3 = 3.18165043023885E-10

PLTSOLVD= T / Siril internal solver

HISTORY Crop (x=367, y=191, w=5609, h=3846)

HISTORY Plate Solve

HISTORY Background extraction (Correction: Subtraction)

HISTORY Photometric CC (algorithm: PCC)

HISTORY Photometric CC (algorithm: PCC)

HISTORY Photometric CC (algorithm: SPCC)

HISTORY StatStretch: m=0.20 l=False n=False c=False b=0.00

HISTORY StatStretch: m=0.20 l=True n=False c=False b=0.00

HISTORY StatStretch: m=0.20 l=True n=True c=True b=0.00

HISTORY GHS LINEAR BP: 0.08

HISTORY GHS LINEAR BP: 0.02

HISTORY GHS INV pivot: 0.102, amount: 1.93, local: 0.00 [0.00 1.00]

HISTORY GHS pivot: 0.137, amount: 1.05, local: 0.00 [0.00 1.00]

HISTORY GHS pivot: 0.283, amount: 2.38, local: 0.00 [0.00 1.00]

HISTORY GHS INV pivot: 0.079, amount: 1.31, local: 0.00 [0.00 1.00]

HISTORY GraXpert AI denoise: strength 0.50

HISTORY GraXpert AI deconvolve: strength 0.50

HISTORY Trail Removal

HISTORY Trail Removal

HISTORY Cosmic Clarity sharpen (Both)

HISTORY Apply Signature

SUBEXP = 30 /

CAMID = '1E1E560D0B020900' /

PIERSIDE= 'EAST' /

ADCBITS = 16 / Bit depth of camera sensor ADC in current mode

BIASADU = 121.16593933105469 / ADU for bias level (no photons) at current sett

EGAINSAV= 0.26355 / Electrons per ADU at saved bit depth

RELGAIN = 2.964 / Multiplicative gain relative to minumum

RDNOISE = 1.77 / Read noise in electrons

COLORTYP= 'RGB' /

DATE-END= '2025-09-11T02:00:06.8357835' / System Clock:Est. Frame End

DATE-AVG= '2025-09-11T01:42:27.4104789' / System Clock:Est. Frame Mid Point

JD_UTC = 2460929.571150584 / Julian Date at mid exposure

END

"The protean chromatic polynomial"

You can get addition, subtraction, multiplication and division of polynomials, factoring polynomials and so on for free of cost.

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Statcon Energiaa’s SEOG Series Solar PCUs are built for harsh Indian weather conditions. The products are capable of handling extreme power grid variations with safety and smart management of renewable solar power, grid supply, and battery. They ensure maximum power extraction through the MPPT polynomial algorithm. SEOG Series PCUs boast proprietary technology that maximizes DC-AC conversion efficiency and provides a high level of energy storage.

 

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knitting projects - an ipod cover which I made too large so now it's a camera case, a polynomial camera bag (video camera), and the robot toy (in progress) for Amelie. plus my pattern book with notes

Download MCQs for Class 10 Polynomials for important topics for all chapters in Class 10 Polynomials based on CBSE and NCERT pattern. Multiple choice questions help to develop understanding of all key points of chapter. Download latest MCQs for Class 10 Polynomials in pdf free

 

www.studiestoday.com/multiple-choice-questions/165/polyno...

"Solving polynomial systems with Puiseux series"

knitting projects - an ipod cover which I made too large so now it's a camera case, a polynomial camera bag (video camera), and the robot toy (in progress) for Amelie. plus my pattern book with notes

Sunday 5/9/10

 

The newest addition to our apartment....Karly brought home Polynomial aka Polly.

Solving Polynomials Equations of Higher Degree

domain restrictions, polynomial, fraction, radical l... inverse functions asymptotes, holes, graphs

 

The Ultimate Cheat Sheet for STEM Majors

 

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Amplitude of charge injected versus ToT values. The curve corresponds to a second order polynomial fit to the data.

knitting projects - an ipod cover which I made too large so now it's a camera case, a polynomial camera bag (video camera), and the robot toy (in progress) for Amelie. plus my pattern book with notes

Solving Polynomials Equations of Higher Degree

Solving Polynomials Equations of Higher Degree

Solving Polynomials Equations of Higher Degree

Solving Polynomials Equations of Higher Degree

This little guy does polynomial equations!

Polynomial term structure models. Cheng, Tehranchi arxiv.org/abs/1504.03238 #q-fin

Polynomial term structure models. Cheng, Tehranchi arxiv.org/abs/1504.03238 #q-fin

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