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using a parabolic gradient for the blur and tweaked the polynomial for a narrrower band. Rendering too a long arse to generate this image..not sure why....

"Zeros of real random polynomials spanned by OPUC"

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

"Counting perfect polynomials"

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 = 1844 / 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 = 63538 / Lower visualization cutoff

MIPS-LO = 3739 / Upper visualization cutoff

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

FILENAME= 'Light_NGC 6960_20.0s_LP_20250615-031807.fit'

DATE = '2025-06-15T14:49:32' / UTC date that FITS file was created

DATE-OBS= '2025-06-15T08:17:44.199239' / 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= 251.973 / [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= 24.125 / [degC] CCD temperature

GAIN = 80 / Sensor gain

FOCPOS = 1609 / [step] Focuser position

STACKCNT= 353 / Stack frames

LIVETIME= 7060. / [s] Exposure time after deadtime correction

EXPSTART= 2460841.65368447 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460841.88803402 / [JD] Exposure end time (standard Julian date)

OBJECT = 'NGC 6960' / Name of the object of interest

SITELAT = 41.7559 / [deg] Observation site latitude

SITELONG= -88.1817 / [deg] Observation site longitude

OBJCTRA = '20 45 53.999' / [H M S] Image center Right Ascension

OBJCTDEC= '+30 42 34.755' / [D M S] Image center Declination

RA = 311.474996729012 / [deg] Image center Right Ascension

DEC = 30.7096540680233 / [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 = 311.474996729012 / [deg] Axis1 reference value

CRVAL2 = 30.7096540680233 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000659369714430329 / [deg] X pixel size

CDELT2 = 0.000659486369621355 / [deg] Y pixel size

PC1_1 = 0.999937182715875 / Linear transformation matrix (1, 1)

PC1_2 = -0.0112085066908687 / Linear transformation matrix (1, 2)

PC2_1 = 0.0109177171842403 / Linear transformation matrix (2, 1)

PC2_2 = 0.999940399949659 / 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 = -2.83969006169435E-07

A_1_1 = -6.32703072964155E-08

A_0_2 = -7.13563925467378E-08

A_3_0 = 5.80146732456915E-11

A_2_1 = 1.85636817844204E-11

A_1_2 = 7.85550780392795E-11

A_0_3 = -4.03360968243548E-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 = -3.49475775181142E-08

B_1_1 = -1.53924781281742E-07

B_0_2 = -2.55103928583899E-07

B_3_0 = 6.64412624288153E-11

B_2_1 = 1.76188447879581E-10

B_1_2 = 1.15009521367569E-11

B_0_3 = 1.13653024340474E-10

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

AP_0_0 = 6.99781748196637E-06

AP_1_0 = -4.85269324723703E-09

AP_0_1 = 5.08554449800355E-10

AP_2_0 = 2.83904240166767E-07

AP_1_1 = 6.32280469247762E-08

AP_0_2 = 7.13259186463274E-08

AP_3_0 = -5.78364504652274E-11

AP_2_1 = -1.84928190208594E-11

AP_1_2 = -7.84429088845412E-11

AP_0_3 = 4.07242923738454E-12

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

BP_0_0 = 2.06593714341602E-05

BP_1_0 = -1.16963724948547E-08

BP_0_1 = -2.28807578439572E-08

BP_2_0 = 3.48687015744228E-08

BP_1_1 = 1.53806743887991E-07

BP_0_2 = 2.54944845785798E-07

BP_3_0 = -6.63545827618531E-11

BP_2_1 = -1.75989922888107E-10

BP_1_2 = -1.13523328878445E-11

BP_0_3 = -1.13451859308692E-10

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

BG-EXTR = 'GraXpert'

CBG-1 = 0.16765243

CBG-2 = 0.16765243

CBG-3 = 0.16765243

INTP-OPT= 'RBF '

HIERARCH SMOOTHING = 0.9

HIERARCH CORR-TYPE = 'Subtraction'

HIERARCH SAMPLE-SIZE = 15

HIERARCH RBF-KERNEL = 'thin_plate'

HIERARCH SPLINE-ORDER = 3

BG-PTS = '[[555, 9, 1], [627, 9, 1], [699, 9, 1], [741, 9, 1], [813, 9, 1], &'

CONTINUE '[411, 111, 1], [555, 111, 1], [627, 111, 1], [699, 111, 1], [771, &'

CONTINUE '111, 1], [813, 111, 1], [885, 111, 1], [339, 183, 1], [381, 183, &'

CONTINUE '1], [453, 183, 1], [525, 183, 1], [597, 183, 1], [699, 183, 1], &'

CONTINUE '[771, 183, 1], [843, 153, 1], [885, 183, 1], [987, 183, 1], [1029, &'

CONTINUE '183, 1], [600.456026058632, 354.3973941368078, 1.0], &'

CONTINUE '[175.17915309446266, 178.2410423452769, 1.0], [396, 240, 1], [453, &'

CONTINUE '255, 1], [525, 255, 1], [597, 255, 1], [699, 255, 1], [771, 225, &'

CONTINUE '1], [828, 240, 1], [885, 255, 1], [987, 255, 1], [1044, 240, 1], &'

CONTINUE '[195, 297, 1], [98.04560260586322, 353.3550488599348, 1.0], &'

CONTINUE '[141.8241042345278, 356.48208469055373, 1.0], [503.5179153094464, &'

CONTINUE '300.19543973941364, 1.0], [453, 327, 1], [540, 312, 1], [597, 297, &'

CONTINUE '1], [699, 327, 1], [771, 297, 1], [843, 297, 1], [915, 327, 1], &'

CONTINUE '[972, 312, 1], [1029, 327, 1], [195, 399, 1], [675.5048859934855, &'

CONTINUE '410.6840390879479, 1.0], [259.6091205211726, 397.1335504885993, &'

CONTINUE '1.0], [501.4332247557004, 365.8631921824104, 1.0], &'

CONTINUE '[553.5504885993487, 429.4462540716612, 1.0], [555, 369, 1], [597, &'

CONTINUE '399, 1], [699, 369, 1], [756, 384, 1], [843, 399, 1], [915, 399, &'

CONTINUE '1], [987, 369, 1], [1059, 399, 1], [21, 471, 1], [108, 456, 1], &'

CONTINUE '[195, 471, 1], [267, 471, 1], [339, 471, 1], [381, 471, 1], &'

CONTINUE '[636.9381107491859, 480.5211726384365, 1.0], [579.6091205211728, &'

CONTINUE '464.88599348534206, 1.0], [627, 441, 1], [699, 471, 1], [771, 471, &'

CONTINUE '1], [813, 441, 1], [915, 471, 1], [987, 441, 1], [1029, 471, 1], &'

CONTINUE '[21, 543, 1], [93, 543, 1], [195, 543, 1], [237, 543, 1], [339, &'

CONTINUE '543, 1], [381, 543, 1], [437.85016286644964, 548.2736156351791, &'

CONTINUE '1.0], [814.1368078175897, 354.3973941368078, 1.0], [627, 543, 1], &'

CONTINUE '[699, 543, 1], [741, 543, 1], [843, 513, 1], [915, 513, 1], [957, &'

CONTINUE '543, 1], [1059, 543, 1], [51, 615, 1], [123, 615, 1], [165, 585, &'

CONTINUE '1], [237, 585, 1], [324, 600, 1], [381, 615, 1], &'

CONTINUE '[667.1661237785017, 576.4169381107491, 1.0], [794.3322475570033, &'

CONTINUE '522.2149837133551, 1.0], [699, 615, 1], [771, 615, 1], [843, 615, &'

CONTINUE '1], [915, 585, 1], [987, 615, 1], [1059, 615, 1], [51, 687, 1], &'

CONTINUE '[93, 687, 1], [195, 687, 1], [267, 687, 1], [309, 657, 1], [396, &'

CONTINUE '672, 1], [454.52768729641707, 675.4397394136807, 1.0], &'

CONTINUE '[916.2866449511403, 651.4657980456026, 1.0], [699, 687, 1], [771, &'

CONTINUE '657, 1], [843, 687, 1], [779.7394136807818, 704.6254071661238, &'

CONTINUE '1.0], [987, 657, 1], [1029, 687, 1], [21, 729, 1], [123, 759, 1], &'

CONTINUE '[180, 744, 1], [267, 759, 1], [324, 744, 1], [396, 744, 1], [453, &'

CONTINUE '729, 1], [478.501628664495, 760.9120521172639, 1.0], [627, 729, &'

CONTINUE '1], [699, 729, 1], [771, 759, 1], [843, 729, 1], &'

CONTINUE '[855.830618892508, 766.1237785016286, 1.0], [972, 744, 1], [1029, &'

CONTINUE '759, 1], [51, 831, 1], [123, 831, 1], [165, 831, 1], [267, 831, &'

CONTINUE '1], [309, 801, 1], [396, 816, 1], [453, 801, 1], &'

CONTINUE '[462.86644951140056, 779.6742671009772, 1.0], [627, 801, 1], [684, &'

CONTINUE '816, 1], [741, 801, 1], [813, 831, 1], [915, 801, 1], [987, 831, &'

CONTINUE '1], [1059, 801, 1], [51, 873, 1], [123, 873, 1], [195, 873, 1], &'

CONTINUE '[267, 873, 1], [309, 873, 1], [381, 873, 1], [320.0651465798046, &'

CONTINUE '696.28664495114, 1.0], [902.7361563517916, 696.28664495114, 1.0], &'

CONTINUE '[699, 903, 1], [771, 903, 1], [813, 903, 1], [915, 873, 1], [972, &'

CONTINUE '888, 1], [1059, 903, 1], [51, 945, 1], [123, 945, 1], [165, 945, &'

CONTINUE '1], [252, 960, 1], [309, 945, 1], [213.74592833876227, &'

CONTINUE '1382.1498371335506, 1.0], [443.0618892508144, 1079.8697068403908, &'

CONTINUE '1.0], [707.8175895765471, 977.7198697068404, 1.0], [771, 945, 1], &'

CONTINUE '[843, 975, 1], [885, 975, 1], [972, 960, 1], [1059, 975, 1], [51, &'

CONTINUE '1047, 1], [123, 1017, 1], [165, 1017, 1], [237, 1047, 1], [309, &'

CONTINUE '1017, 1], [381, 1047, 1], [65.73289902280135, 1291.4657980456027, &'

CONTINUE '1.0], [627, 1047, 1], [699, 1017, 1], [771, 1047, 1], [813, 1017, &'

CONTINUE '1], [885, 1017, 1], [972, 1032, 1], [1029, 1017, 1], [51, 1119, &'

CONTINUE '1], [123, 1089, 1], [165, 1119, 1], [252, 1104, 1], [309, 1089, &'

CONTINUE '1], [396, 1104, 1], [453, 1119, 1], [457.6547231270358, &'

CONTINUE '1111.14006514658, 1.0], [627, 1119, 1], [699, 1119, 1], [741, &'

CONTINUE '1089, 1], [843, 1089, 1], [885, 1089, 1], [957, 1119, 1], [1029, &'

CONTINUE '1119, 1], [51, 1161, 1], [123, 1191, 1], [165, 1191, 1], [267, &'

CONTINUE '1191, 1], [309, 1161, 1], [381, 1191, 1], [453, 1161, 1], &'

CONTINUE '[472.24755700325727, 1158.0456026058632, 1.0], [627, 1191, 1], &'

CONTINUE '[699, 1161, 1], [741, 1161, 1], [813, 1161, 1], [885, 1161, 1], &'

CONTINUE '[972, 1176, 1], [1029, 1191, 1], [51, 1233, 1], [108, 1248, 1], &'

CONTINUE '[195, 1233, 1], [267, 1233, 1], [339, 1233, 1], [396, 1248, 1], &'

CONTINUE '[453, 1233, 1], [451.4006514657981, 1287.2964169381107, 1.0], &'

CONTINUE '[627, 1233, 1], [699, 1233, 1], [771, 1263, 1], [813, 1233, 1], &'

CONTINUE '[915, 1233, 1], [957, 1233, 1], [1029, 1263, 1], [51, 1335, 1], &'

CONTINUE '[108, 1320, 1], [195, 1305, 1], [237, 1305, 1], [324, 1320, 1], &'

CONTINUE '[381, 1335, 1], [483, 1335, 1], [534.7882736156353, &'

CONTINUE '1338.371335504886, 1.0], [627, 1305, 1], [699, 1305, 1], [771, &'

CONTINUE '1335, 1], [813, 1335, 1], [915, 1335, 1], [957, 1335, 1], [1059, &'

CONTINUE '1335, 1], [36, 1392, 1], [93, 1377, 1], [165, 1377, 1], [267, &'

CONTINUE '1377, 1], [309, 1377, 1], [381, 1407, 1], [483, 1407, 1], [555, &'

CONTINUE '1407, 1], [720.3257328990228, 1431.14006514658, 1.0], [699, 1377, &'

CONTINUE '1], [741, 1407, 1], [813, 1407, 1], [885, 1407, 1], [987, 1407, &'

CONTINUE '1], [1029, 1407, 1], [51, 1449, 1], [93, 1449, 1], [267, 1449, 1], &'

CONTINUE '[309, 1449, 1], [411, 1479, 1], [483, 1449, 1], [555, 1479, 1], &'

CONTINUE '[699, 1479, 1], [771, 1479, 1], [843, 1479, 1], [915, 1479, 1], &'

CONTINUE '[987, 1479, 1], [1059, 1449, 1], [36, 1536, 1], [93, 1521, 1], &'

CONTINUE '[165, 1551, 1], [237, 1551, 1], [339, 1521, 1], [381, 1551, 1], &'

CONTINUE '[483, 1521, 1], [555, 1521, 1], [485.7980456026057, &'

CONTINUE '1740.7166123778502, 1.0], [684, 1536, 1], [771, 1551, 1], [843, &'

CONTINUE '1551, 1], [885, 1521, 1], [987, 1551, 1], [1029, 1521, 1], [51, &'

CONTINUE '1623, 1], [93, 1593, 1], [195, 1593, 1], [237, 1623, 1], [309, &'

CONTINUE '1623, 1], [411, 1623, 1], [453, 1623, 1], [525, 1623, 1], &'

CONTINUE '[590.0325732899023, 1612.5081433224755, 1.0], [699, 1623, 1], &'

CONTINUE '[771, 1623, 1], [843, 1593, 1], [915, 1623, 1], [987, 1623, 1], &'

CONTINUE '[1029, 1593, 1], [51, 1695, 1], [123, 1665, 1], [195, 1665, 1], &'

CONTINUE '[267, 1665, 1], [339, 1695, 1], [411, 1695, 1], &'

CONTINUE '[483.71335504885997, 1707.3615635179153, 1.0], [532.7035830618893, &'

CONTINUE '1688.599348534202, 1.0], [654.657980456026, 1709.4462540716613, &'

CONTINUE '1.0], [699, 1665, 1], [771, 1695, 1], [843, 1695, 1], [915, 1695, &'

CONTINUE '1], [987, 1695, 1], [1029, 1695, 1], [21, 1767, 1], [108, 1752, &'

CONTINUE '1], [165, 1767, 1], [267, 1767, 1], [309, 1767, 1], [396, 1752, &'

CONTINUE '1], [483, 1737, 1], [555, 1767, 1], [627, 1767, 1], [699, 1767, &'

CONTINUE '1], [771, 1767, 1], [843, 1767, 1], [915, 1767, 1], [987, 1767, &'

CONTINUE '1], [1029, 1767, 1], [21, 1839, 1], [93, 1839, 1], [165, 1839, 1], &'

CONTINUE '[252, 1824, 1], [339, 1809, 1], [411, 1839, 1], [483, 1839, 1], &'

CONTINUE '[555, 1839, 1], [627, 1809, 1], [699, 1809, 1], [771, 1839, 1], &'

CONTINUE '[843, 1809, 1], [915, 1839, 1], [987, 1839, 1], [1059, 1839, 1], &'

CONTINUE '[21, 1911, 1], [93, 1881, 1], [165, 1911, 1], [267, 1881, 1], &'

CONTINUE '[309, 1881, 1], [411, 1881, 1], [483, 1881, 1], [555, 1881, 1], &'

CONTINUE '[627, 1881, 1], [699, 1911, 1], [771, 1911, 1], [843, 1911, 1], &'

CONTINUE '[915, 1911, 1], [987, 1911, 1], [1059, 1911, 1], [32, 322, 1], &'

CONTINUE '[51, 339, 1], [123, 309, 1], [36, 396, 1], [123, 411, 1], [123, &'

CONTINUE '267, 1], [53, 93, 1], [93, 51, 1], [180, 36, 1], [51, 93, 1], &'

CONTINUE '[108, 108, 1], [195, 123, 1], [21, 165, 1], [123, 165, 1], [74, &'

CONTINUE '290, 1], [51, 267, 1], [214, 202, 1], [267, 195, 1], [321, 48, 1], &'

CONTINUE '[309, 51, 1], [411, 51, 1], [483, 51, 1], [267, 93, 1], [917, 48, &'

CONTINUE '1], [885, 51, 1], [987, 21, 1], [1044, 36, 1], [1029, 123, 1], &'

CONTINUE '[926, 106, 1], [927, 213, 1], [741, 339, 1], [456, 1570, 1], [339, &'

CONTINUE '1563, 1], [195, 1491, 1], [237, 1491, 1], [495, 1570, 1]]'

END

 

Symmetrically-reflected complex polynomial iteration with crafted seeds combining reflections of complex polynomial cross-products with just a hint of plasma cloud.

More of the same. I'm exhausted. I was at work from 10am-6:15pm, walked into the Exec Team meeting late, stayed on campus until 10:45 doing homework. Didn't get it finished, need to be back at class in 8 hours. So glad I figured out how to make Matlab factor 5th order polynomials for me.

Tomorrow I start being a slave to Array Attachment again. At least all my homework for the week is over with.

Factoring Polynomials Calculator Polynomial Factoring is a phenomenon which is just an opposite process of Polynomial Multiplications. Whenever we factor a numeric value, we go for prime factors and their product gives original number. Factoring Polynomials Calculator is an Online tool to factor the given polynomial. Trying out this calculator and it makes your calculations easy and fast.

 

Chebyshev Polynomial Approximation for Distributed Signal Processing

Polynomial Functions Function f (y) is called as polynomial function if it is expressed in following wayf (y) = b m y m + b (m – 1) y (m – 1) +…+ b 2 y 2+ b 1 y + b 0Here 'm' is non negative Integer and b 0, b 1… b (m – 1), b m are constant coefficients. Polynomial Functions can be with one or more than one terms.

Naomi Corti, Zachary Gonder, Olivia Bell, and KJ Takahashi perform Gianna Riesen's "Dancer Polynomials" in NOW: Premieres at the 2025 Vail Dance Festival. Photo by Christopher Duggan.

A New York City J Users Group logo with letter "J" cut from image of randomly-generated polynomial applied to the complex plane, and a boid.

The m&m's show an example of a polynomial

Note to family: Original size is for a 5x7 inch print.

 

View On Black

"Zeros of real random polynomials spanned by OPUC"

What is a Binomial Polynomials (many terms) are algebraic expressions formed by adding or subtracting monomials (single terms with positive exponents or constants). A Binomial is a polynomial containing two terms, bi meaning two.In terms of nomenclature, “bi” means 2 hence binomial means two terms. So in general, a binomial is a polynomial containing two terms. The general form can be written as axn ± bym.A different and simpler way of defining a binomial is that it is an algebraic expression containing two terms connected by a sum of a difference sign. Example: 3x+5y,a+3x, x2-3x…etc.

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 = '2025-06-20T16:19:09' / UTC date that FITS file was created

DATE-OBS= '2025-06-20T08:27:21.106301' / 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= 249. / [mm] Focal length

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= 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= 136 / Stack frames

LIVETIME= 24480. / [s] Exposure time after deadtime correction

EXPSTART= 2460843.8380686 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460846.85441095 / [JD] Exposure end time (standard Julian date)

OBJECT = 'NGC7000 ' / Name of the object of interest

SITELAT = 34.1986 / [deg] Observation site latitude

SITELONG= -118.919 / [deg] Observation site longitude

OBJCTRA = '20 57 2.307' / [H M S] Image center Right Ascension

OBJCTDEC= '+43 57 31.662' / [D M S] Image center Declination

RA = 314.259613433003 / [deg] Image center Right Ascension

DEC = 43.9587950570444 / [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 = 9.87654321E+107 / Equatorial equinox

CRPIX1 = 2956.13273112 / Axis1 reference pixel

CRPIX2 = 2315.55782064 / Axis2 reference pixel

CRVAL1 = 314.024832448 / [deg] Axis1 reference value

CRVAL2 = 44.1358299954 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.00086542917605275 / [deg] X pixel size

CDELT2 = 0.000865158789727985 / [deg] Y pixel size

PC1_1 = 0.169311961724374 / Linear transformation matrix (1, 1)

PC1_2 = 0.985562509238782 / Linear transformation matrix (1, 2)

PC2_1 = -0.985596324825061 / Linear transformation matrix (2, 1)

PC2_2 = 0.169115003743997 / Linear transformation matrix (2, 2)

A_ORDER = 2 / SIP polynomial degree, axis 1, pixel-to-sky

A_0_0 = 0.

A_1_0 = 0.

A_0_1 = 0.

A_2_0 = 1.39326404121E-07

A_1_1 = -1.26645692543E-07

A_0_2 = -4.07583389495E-08

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

B_0_0 = 0.

B_1_0 = 0.

B_0_1 = 0.

B_2_0 = -3.54669938264E-08

B_1_1 = 9.4514157273E-08

B_0_2 = -1.7368879975E-07

AP_ORDER= 2 / SIP polynomial degree, axis 1, sky-to-pixel

AP_0_0 = -8.67703989764E-05

AP_1_0 = 2.90751445713E-07

AP_0_1 = -1.61428422671E-07

AP_2_0 = -1.39290503247E-07

AP_1_1 = 1.26616236203E-07

AP_0_2 = 4.07484240312E-08

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

BP_0_0 = 9.77642188248E-05

BP_1_0 = -1.65834928503E-07

BP_0_1 = 2.94150812971E-07

BP_2_0 = 3.54504873416E-08

BP_1_1 = -9.44731207578E-08

BP_0_2 = 1.73640545059E-07

HISTORY GraXpert AI BGE: subtraction

HISTORY Photometric CC (algorithm: PCC)

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

HISTORY Histogram Transf. (mid=0.000, lo=0.000, 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

 

The board explains how finite difference method is used to calculate polynomials.

Continuity And Differentiability If the addition of function ‘f’ is Limx⇢p+ f (x) = f (p) and Limx⇢q- f (x) = f (q) then the given function ‘f’ is continuous in the close interval [p, q]. If the function is polynomial then these polynomial function are continuous. Let us have a rational function f (p).

Naomi Corti, Zachary Gonder, Olivia Bell, and KJ Takahashi perform Gianna Riesen's "Dancer Polynomials" in NOW: Premieres at the 2025 Vail Dance Festival. Photo by Christopher Duggan.

Polynomial Diffusion Models for Life Insurance Liabilities. Biagini, Zhang arxiv.org/abs/1602.07910 #q-fin

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 945 / length of data axis 1

NAXIS2 = 1729 / 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 27_20.0s_LP_20250601-035817.fit'

DATE = '2025-06-03T04:46:47' / UTC date that FITS file was created

DATE-OBS= '2025-06-01T08:57:54.377825' / 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= 251.859 / [mm] Focal length

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.9 / [um] Pixel X axis size

YPIXSZ = 2.9 / [um] Pixel Y axis size

INSTRUME= 'Seestar S50' / Instrument name

CCD-TEMP= 15.3125 / [degC] CCD temperature

GAIN = 80 / Sensor gain

FOCPOS = 1620 / [step] Focuser position

STACKCNT= 133 / Stack frames

LIVETIME= 2660. / [s] Exposure time after deadtime correction

EXPSTART= 2460827.81081978 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460827.89166513 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M 27 ' / Name of the object of interest

SITELAT = 41.7559 / [deg] Observation site latitude

SITELONG= -88.1817 / [deg] Observation site longitude

OBJCTRA = '19 59 41.273' / [H M S] Image center Right Ascension

OBJCTDEC= '+22 44 22.461' / [D M S] Image center Declination

RA = 299.921969223822 / [deg] Image center Right Ascension

DEC = 22.7395724348345 / [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 = 485.5 / Axis1 reference pixel

CRPIX2 = 847.5 / Axis2 reference pixel

CRVAL1 = 299.913820271712 / [deg] Axis1 reference value

CRVAL2 = 22.7275394907915 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000659747133158036 / [deg] X pixel size

CDELT2 = 0.00065970321238653 / [deg] Y pixel size

PC1_1 = 0.998078149581276 / Linear transformation matrix (1, 1)

PC1_2 = 0.0619677926701853 / Linear transformation matrix (1, 2)

PC2_1 = -0.0619206937298492 / Linear transformation matrix (2, 1)

PC2_2 = 0.998081072703022 / 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 = -3.53747170344176E-07

A_1_1 = -2.5157063787241E-07

A_0_2 = -4.80319305990762E-09

A_3_0 = -1.04696407013158E-10

A_2_1 = -3.68762474410932E-10

A_1_2 = -1.82332944083092E-10

A_0_3 = -1.28205142943169E-10

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 = -1.99185435081301E-07

B_1_1 = 1.15641901235075E-07

B_0_2 = -3.99721223861734E-07

B_3_0 = 4.59013551317123E-10

B_2_1 = 1.57789955694643E-10

B_1_2 = -1.80813630847316E-12

B_0_3 = 5.08181097060919E-11

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

AP_0_0 = -3.76027099853418E-05

AP_1_0 = -6.14272077648081E-09

AP_0_1 = -8.55321174296654E-09

AP_2_0 = 3.53956116634201E-07

AP_1_1 = 2.51828088827321E-07

AP_0_2 = 5.03793892017271E-09

AP_3_0 = 1.04951160000075E-10

AP_2_1 = 3.6907193905666E-10

AP_1_2 = 1.8261200658298E-10

AP_0_3 = 1.28228656618685E-10

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

BP_0_0 = 2.39517809413289E-05

BP_1_0 = 1.4484987329225E-08

BP_0_1 = 1.1243771469438E-08

BP_2_0 = 1.98984005629928E-07

BP_1_1 = -1.15718086979604E-07

BP_0_2 = 3.99585300582188E-07

BP_3_0 = -4.58982127773712E-10

BP_2_1 = -1.57806193006496E-10

BP_1_2 = 1.56669462539423E-12

BP_0_3 = -5.05046275658598E-11

HISTORY Saturation enhancement (amount=-0.14)

HISTORY Curves Transformation with 10 points

HISTORY Curves Transformation with 2 points

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

BG-EXTR = 'GraXpert'

CBG-1 = 0.0032965415

CBG-2 = 0.0032965415

CBG-3 = 0.0032965415

INTP-OPT= 'RBF '

HIERARCH SMOOTHING = 0.9

HIERARCH CORR-TYPE = 'Subtraction'

HIERARCH SAMPLE-SIZE = 15

HIERARCH RBF-KERNEL = 'thin_plate'

HIERARCH SPLINE-ORDER = 3

BG-PTS = '[[555, 9, 1], [627, 9, 1], [699, 9, 1], [741, 9, 1], [813, 9, 1], &'

CONTINUE '[411, 111, 1], [555, 111, 1], [627, 111, 1], [699, 111, 1], [771, &'

CONTINUE '111, 1], [813, 111, 1], [885, 111, 1], [339, 183, 1], [381, 183, &'

CONTINUE '1], [453, 183, 1], [525, 183, 1], [597, 183, 1], [699, 183, 1], &'

CONTINUE '[771, 183, 1], [843, 153, 1], [885, 183, 1], [987, 183, 1], [1029, &'

CONTINUE '183, 1], [267, 255, 1], [339, 255, 1], [396, 240, 1], [453, 255, &'

CONTINUE '1], [525, 255, 1], [597, 255, 1], [699, 255, 1], [771, 225, 1], &'

CONTINUE '[828, 240, 1], [885, 255, 1], [987, 255, 1], [1044, 240, 1], [195, &'

CONTINUE '297, 1], [267, 327, 1], [324, 312, 1], [396, 312, 1], [453, 327, &'

CONTINUE '1], [540, 312, 1], [597, 297, 1], [699, 327, 1], [771, 297, 1], &'

CONTINUE '[843, 297, 1], [915, 327, 1], [972, 312, 1], [1029, 327, 1], [195, &'

CONTINUE '399, 1], [237, 399, 1], [309, 369, 1], [381, 399, 1], [453, 399, &'

CONTINUE '1], [555, 369, 1], [597, 399, 1], [699, 369, 1], [756, 384, 1], &'

CONTINUE '[843, 399, 1], [915, 399, 1], [987, 369, 1], [1059, 399, 1], [21, &'

CONTINUE '471, 1], [108, 456, 1], [195, 471, 1], [267, 471, 1], [339, 471, &'

CONTINUE '1], [381, 471, 1], [483, 441, 1], [525, 471, 1], [627, 441, 1], &'

CONTINUE '[699, 471, 1], [771, 471, 1], [813, 441, 1], [915, 471, 1], [987, &'

CONTINUE '441, 1], [1029, 471, 1], [21, 543, 1], [93, 543, 1], [195, 543, &'

CONTINUE '1], [237, 543, 1], [339, 543, 1], [381, 543, 1], [453, 543, 1], &'

CONTINUE '[555, 543, 1], [627, 543, 1], [699, 543, 1], [741, 543, 1], [843, &'

CONTINUE '513, 1], [915, 513, 1], [957, 543, 1], [1059, 543, 1], [51, 615, &'

CONTINUE '1], [123, 615, 1], [165, 585, 1], [237, 585, 1], [324, 600, 1], &'

CONTINUE '[381, 615, 1], [453, 615, 1], [555, 615, 1], [597, 615, 1], [699, &'

CONTINUE '615, 1], [771, 615, 1], [843, 615, 1], [915, 585, 1], [987, 615, &'

CONTINUE '1], [1059, 615, 1], [51, 687, 1], [93, 687, 1], [195, 687, 1], &'

CONTINUE '[267, 687, 1], [309, 657, 1], [396, 672, 1], [453, 657, 1], [525, &'

CONTINUE '687, 1], [597, 657, 1], [699, 687, 1], [771, 657, 1], [843, 687, &'

CONTINUE '1], [779.7394136807818, 704.6254071661238, 1.0], [987, 657, 1], &'

CONTINUE '[1029, 687, 1], [21, 729, 1], [123, 759, 1], [180, 744, 1], [267, &'

CONTINUE '759, 1], [324, 744, 1], [396, 744, 1], [453, 729, 1], [525, 759, &'

CONTINUE '1], [627, 729, 1], [699, 729, 1], [771, 759, 1], [843, 729, 1], &'

CONTINUE '[855.830618892508, 766.1237785016286, 1.0], [972, 744, 1], [1029, &'

CONTINUE '759, 1], [51, 831, 1], [123, 831, 1], [165, 831, 1], [267, 831, &'

CONTINUE '1], [309, 801, 1], [396, 816, 1], [453, 801, 1], [555, 801, 1], &'

CONTINUE '[627, 801, 1], [684, 816, 1], [741, 801, 1], [813, 831, 1], [915, &'

CONTINUE '801, 1], [987, 831, 1], [1059, 801, 1], [51, 873, 1], [123, 873, &'

CONTINUE '1], [195, 873, 1], [267, 873, 1], [309, 873, 1], [381, 873, 1], &'

CONTINUE '[497.2638436482084, 832.8338762214984, 1.0], [580.6514657980456, &'

CONTINUE '849.5114006514658, 1.0], [623.3876221498372, 848.4690553745928, &'

CONTINUE '1.0], [699, 903, 1], [771, 903, 1], [813, 903, 1], [915, 873, 1], &'

CONTINUE '[972, 888, 1], [1059, 903, 1], [51, 945, 1], [123, 945, 1], [165, &'

CONTINUE '945, 1], [252, 960, 1], [309, 945, 1], [381, 945, 1], [453, 945, &'

CONTINUE '1], [699, 975, 1], [771, 945, 1], [843, 975, 1], [885, 975, 1], &'

CONTINUE '[972, 960, 1], [1059, 975, 1], [51, 1047, 1], [123, 1017, 1], &'

CONTINUE '[165, 1017, 1], [237, 1047, 1], [309, 1017, 1], [381, 1047, 1], &'

CONTINUE '[483, 1047, 1], [627, 1047, 1], [699, 1017, 1], [771, 1047, 1], &'

CONTINUE '[813, 1017, 1], [885, 1017, 1], [972, 1032, 1], [1029, 1017, 1], &'

CONTINUE '[51, 1119, 1], [123, 1089, 1], [165, 1119, 1], [252, 1104, 1], &'

CONTINUE '[309, 1089, 1], [396, 1104, 1], [453, 1119, 1], [525, 1089, 1], &'

CONTINUE '[627, 1119, 1], [699, 1119, 1], [741, 1089, 1], [843, 1089, 1], &'

CONTINUE '[885, 1089, 1], [957, 1119, 1], [1029, 1119, 1], [51, 1161, 1], &'

CONTINUE '[123, 1191, 1], [165, 1191, 1], [267, 1191, 1], [309, 1161, 1], &'

CONTINUE '[381, 1191, 1], [453, 1161, 1], [525, 1161, 1], [627, 1191, 1], &'

CONTINUE '[699, 1161, 1], [741, 1161, 1], [813, 1161, 1], [885, 1161, 1], &'

CONTINUE '[972, 1176, 1], [1029, 1191, 1], [51, 1233, 1], [108, 1248, 1], &'

CONTINUE '[195, 1233, 1], [267, 1233, 1], [339, 1233, 1], [396, 1248, 1], &'

CONTINUE '[453, 1233, 1], [525, 1233, 1], [627, 1233, 1], [699, 1233, 1], &'

CONTINUE '[771, 1263, 1], [813, 1233, 1], [915, 1233, 1], [957, 1233, 1], &'

CONTINUE '[1029, 1263, 1], [51, 1335, 1], [108, 1320, 1], [195, 1305, 1], &'

CONTINUE '[237, 1305, 1], [324, 1320, 1], [381, 1335, 1], [483, 1335, 1], &'

CONTINUE '[540, 1320, 1], [627, 1305, 1], [699, 1305, 1], [771, 1335, 1], &'

CONTINUE '[813, 1335, 1], [915, 1335, 1], [957, 1335, 1], [1059, 1335, 1], &'

CONTINUE '[36, 1392, 1], [93, 1377, 1], [165, 1377, 1], [267, 1377, 1], &'

CONTINUE '[309, 1377, 1], [381, 1407, 1], [483, 1407, 1], [555, 1407, 1], &'

CONTINUE '[627, 1407, 1], [699, 1377, 1], [741, 1407, 1], [813, 1407, 1], &'

CONTINUE '[885, 1407, 1], [987, 1407, 1], [1029, 1407, 1], [51, 1449, 1], &'

CONTINUE '[93, 1449, 1], [267, 1449, 1], [309, 1449, 1], [411, 1479, 1], &'

CONTINUE '[483, 1449, 1], [555, 1479, 1], [627, 1479, 1], [699, 1479, 1], &'

CONTINUE '[771, 1479, 1], [843, 1479, 1], [915, 1479, 1], [987, 1479, 1], &'

CONTINUE '[1059, 1449, 1], [36, 1536, 1], [93, 1521, 1], [165, 1551, 1], &'

CONTINUE '[237, 1551, 1], [339, 1521, 1], [381, 1551, 1], [483, 1521, 1], &'

CONTINUE '[555, 1521, 1], [627, 1521, 1], [681.758957654723, &'

CONTINUE '1564.5602605863191, 1.0], [771, 1551, 1], [843, 1551, 1], [885, &'

CONTINUE '1521, 1], [987, 1551, 1], [1029, 1521, 1], [51, 1623, 1], [93, &'

CONTINUE '1593, 1], [195, 1593, 1], [237, 1623, 1], [309, 1623, 1], [411, &'

CONTINUE '1623, 1], [453, 1623, 1], [525, 1623, 1], [627, 1623, 1], [699, &'

CONTINUE '1623, 1], [771, 1623, 1], [843, 1593, 1], [915, 1623, 1], [987, &'

CONTINUE '1623, 1], [1029, 1593, 1], [51, 1695, 1], [123, 1665, 1], [195, &'

CONTINUE '1665, 1], [267, 1665, 1], [339, 1695, 1], [411, 1695, 1], [483, &'

CONTINUE '1695, 1], [555, 1695, 1], [627, 1695, 1], [699, 1665, 1], [771, &'

CONTINUE '1695, 1], [843, 1695, 1], [915, 1695, 1], [987, 1695, 1], [1029, &'

CONTINUE '1695, 1], [21, 1767, 1], [108, 1752, 1], [165, 1767, 1], [267, &'

CONTINUE '1767, 1], [309, 1767, 1], [396, 1752, 1], [483, 1737, 1], [555, &'

CONTINUE '1767, 1], [627, 1767, 1], [699, 1767, 1], [771, 1767, 1], [843, &'

CONTINUE '1767, 1], [915, 1767, 1], [987, 1767, 1], [1029, 1767, 1], [21, &'

CONTINUE '1839, 1], [93, 1839, 1], [165, 1839, 1], [252, 1824, 1], [339, &'

CONTINUE '1809, 1], [411, 1839, 1], [483, 1839, 1], [555, 1839, 1], [627, &'

CONTINUE '1809, 1], [699, 1809, 1], [771, 1839, 1], [843, 1809, 1], [915, &'

CONTINUE '1839, 1], [987, 1839, 1], [1059, 1839, 1], [21, 1911, 1], [93, &'

CONTINUE '1881, 1], [165, 1911, 1], [267, 1881, 1], [309, 1881, 1], [411, &'

CONTINUE '1881, 1], [483, 1881, 1], [555, 1881, 1], [627, 1881, 1], [699, &'

CONTINUE '1911, 1], [771, 1911, 1], [843, 1911, 1], [915, 1911, 1], [987, &'

CONTINUE '1911, 1], [1059, 1911, 1], [32, 322, 1], [51, 339, 1], [123, 309, &'

CONTINUE '1], [36, 396, 1], [123, 411, 1], [123, 267, 1], [53, 93, 1], [93, &'

CONTINUE '51, 1], [180, 36, 1], [51, 93, 1], [108, 108, 1], [195, 123, 1], &'

CONTINUE '[21, 165, 1], [123, 165, 1], [74, 290, 1], [51, 267, 1], [214, &'

CONTINUE '202, 1], [267, 195, 1], [321, 48, 1], [309, 51, 1], [411, 51, 1], &'

CONTINUE '[483, 51, 1], [267, 93, 1], [917, 48, 1], [885, 51, 1], [987, 21, &'

CONTINUE '1], [1044, 36, 1], [1029, 123, 1], [926, 106, 1], [927, 213, 1], &'

CONTINUE '[741, 339, 1], [456, 1570, 1], [339, 1563, 1], [195, 1491, 1], &'

CONTINUE '[237, 1491, 1], [495, 1570, 1], [568, 1559, 1], [635, 208, 1], &'

CONTINUE '[339, 411, 1], [525, 411, 1], [627, 483, 1], [195, 627, 1], [267, &'

CONTINUE '627, 1], [62, 757, 1], [627, 339, 1], [451, 464, 1]]'

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 2727 / length of data axis 1

NAXIS2 = 2914 / 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

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

DATE = '2025-09-07T15:54:45' / UTC date that FITS file was created

DATE-OBS= '2025-09-06T21:50:05.809000' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light Frame' / Type of image

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

EXPTIME = 180. / [s] Exposure time duration

TELESCOP= 'Slywatcher Evolux 62 ED 400@F\6.5' / Telescope used to acquire this i

FOCALLEN= 362.507 / [mm] Focal length

CENTALT = 39.89957 / [deg] Altitude of telescope

CENTAZ = 32.74331 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 4.8 / [um] Pixel X axis size

YPIXSZ = 4.8 / [um] Pixel Y axis size

INSTRUME= 'QHY CCD QHY168C-f3c2994' / Instrument name

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

GAIN = 10 / Sensor gain

OFFSET = 50 / Sensor gain offset

STACKCNT= 91 / Stack frames

LIVETIME= 16380. / [s] Exposure time after deadtime correction

EXPSTART= 2460925.38793968 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460925.63782278 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M 31 ' / Name of the object of interest

AIRMASS = 1.557501 / Airmass at frame center (Gueymard 1993)

SITELAT = 47.91667 / [deg] Observation site latitude

SITELONG= 1.933056 / [deg] Observation site longitude

OBJCTRA = '00 42 30.672' / [H M S] Image center Right Ascension

OBJCTDEC= '+41 12 22.659' / [D M S] Image center Declination

RA = 10.6277982528625 / [deg] Image center Right Ascension

DEC = 41.2062942758214 / [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 = 1364. / Axis1 reference pixel

CRPIX2 = 1457.5 / Axis2 reference pixel

CRVAL1 = 10.6277982528625 / [deg] Axis1 reference value

CRVAL2 = 41.2062942758214 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000758721053819356 / [deg] X pixel size

CDELT2 = 0.000758599487695311 / [deg] Y pixel size

PC1_1 = -0.336820836673126 / Linear transformation matrix (1, 1)

PC1_2 = -0.941568756906693 / Linear transformation matrix (1, 2)

PC2_1 = 0.941480486837379 / Linear transformation matrix (2, 1)

PC2_2 = -0.337067490132841 / 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 = 3.97578917841809E-07

A_1_1 = -2.44774798826953E-08

A_0_2 = 9.22941238005915E-08

A_3_0 = -1.12035964590002E-09

A_2_1 = 5.12191944642339E-12

A_1_2 = -1.1009892822829E-09

A_0_3 = 3.73598524888844E-13

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 = 1.19579208308998E-07

B_1_1 = 2.91051781005884E-07

B_0_2 = 1.02802639174333E-07

B_3_0 = -1.3611124041332E-11

B_2_1 = -1.07757308897139E-09

B_1_2 = 1.73284258110139E-12

B_0_3 = -1.1172753794729E-09

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

AP_0_0 = 0.000988225551640077

AP_1_0 = -1.24879495848607E-05

AP_0_1 = 1.15890752822243E-07

AP_2_0 = -4.025349097176E-07

AP_1_1 = 2.41075310703775E-08

AP_0_2 = -9.34493958401128E-08

AP_3_0 = 1.13489542756861E-09

AP_2_1 = -5.25179707652799E-12

AP_1_2 = 1.11750286044444E-09

AP_0_3 = -4.17413704041954E-13

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

BP_0_0 = 0.000952212066372248

BP_1_0 = 3.76735565828782E-07

BP_0_1 = -1.33797912759137E-05

BP_2_0 = -1.21044688351177E-07

BP_1_1 = -2.9451504048561E-07

BP_0_2 = -1.04667173896164E-07

BP_3_0 = 1.36872185686008E-11

BP_2_1 = 1.09420708095768E-09

BP_1_2 = -1.93156721119263E-12

BP_0_3 = 1.13223326583511E-09

PLTSOLVD= T / Siril internal solver

HISTORY Rotation (-90.0deg, recadrage=TRUE, clamp =TRUE)

HISTORY Rotation (180.0deg, recadrage=TRUE, clamp =TRUE)

HISTORY GraXpert AI BGE: subtraction

HISTORY Extraction du gradient (Correction : Subtraction)

HISTORY R solution astrom trique

HISTORY Photom trie CC (algorithme : PCC)

HISTORY Transformation asinh : (stretch= 4.0, bp=0.00000)

HISTORY Transf. histogramme (mid=0.004, lo=0.018, hi=1.000)

HISTORY D bruitage NL-Bayes (mod=0.800, SOS activ (iters=3, rho=0.200), CC

HISTORY Filtre m dian (filtre=3x3 px)

HISTORY Rehaussement de la saturation (quantit =0.30)

HISTORY Rehaussement de la saturation (quantit =0.30)

FRAME = 'Light ' / Frame Type

APTDIA = 6.200E+01 / Telescope diameter (mm)

SCALE = 2.750667E+00 / arcsecs per pixel

PIERSIDE= 'WEST ' / West, looking East

RADECSYS= 'FK5 ' / RADECSYS

SECPIX1 = 2.7506667760E+00 / SECPIX1

SECPIX2 = 2.7506667760E+00 / SECPIX2

COMMENT Generated by INDI

END

 

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 3840 / length of data axis 1

NAXIS2 = 2160 / 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

FILENAME= 'M33_Light_007.fits'

DATE = '2025-10-07T14:22:12' / UTC date that FITS file was created

DATE-OBS= '2025-09-26T03:18:33.122000' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light Frame' / Type of image

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

EXPTIME = 120. / [s] Exposure time duration

TELESCOP= 'ALTAIR 60ED 285@F\4.8' / Telescope used to acquire this image

FOCALLEN= 282.427 / [mm] Focal length

CENTALT = 59.27759 / [deg] Altitude of telescope

CENTAZ = 256.0784 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 2.9 / [um] Pixel X axis size

YPIXSZ = 2.9 / [um] Pixel Y axis size

INSTRUME= 'ZWO CCD ASI585MC Pro' / Instrument name

CCD-TEMP= -4. / [degC] CCD temperature

GAIN = 252 / Sensor gain

OFFSET = 10 / Sensor gain offset

FOCPOS = 4374 / [step] Focuser position

FOCTEMP = 12.39 / [degC] Focuser temperature

STACKCNT= 24 / Stack frames

LIVETIME= 2880. / [s] Exposure time after deadtime correction

EXPSTART= 2460944.63047238 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460944.66653491 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M33 ' / Name of the object of interest

AIRMASS = 1.162987 / Airmass at frame center (Gueymard 1993)

SITELAT = 44.21667 / [deg] Observation site latitude

SITELONG= 3.733333 / [deg] Observation site longitude

OBJCTRA = '01 33 51.346' / [H M S] Image center Right Ascension

OBJCTDEC= '+30 43 54.340' / [D M S] Image center Declination

RA = 23.4639414522693 / [deg] Image center Right Ascension

DEC = 30.7317611951257 / [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 = 1920.5 / Axis1 reference pixel

CRPIX2 = 1080.5 / Axis2 reference pixel

CRVAL1 = 23.4639414522693 / [deg] Axis1 reference value

CRVAL2 = 30.7317611951257 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000588343541611957 / [deg] X pixel size

CDELT2 = 0.000588298038962793 / [deg] Y pixel size

PC1_1 = -0.99980948754387 / Linear transformation matrix (1, 1)

PC1_2 = 0.0195189297161632 / Linear transformation matrix (1, 2)

PC2_1 = -0.0192970232107256 / Linear transformation matrix (2, 1)

PC2_2 = -0.999813795111472 / 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 = 1.07633023399987E-07

A_1_1 = -1.03472319180805E-07

A_0_2 = 1.32930877148794E-08

A_3_0 = -6.57151224594346E-10

A_2_1 = 2.19309594585955E-12

A_1_2 = -6.159783259075E-10

A_0_3 = 7.93413632800894E-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 = -2.15550446034261E-08

B_1_1 = 9.83105344833731E-08

B_0_2 = -1.28414967164704E-07

B_3_0 = 6.34817643575336E-12

B_2_1 = -6.34857530992924E-10

B_1_2 = 1.09957798042837E-11

B_0_3 = -7.13488957249123E-10

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

AP_0_0 = 0.0010251321176434

AP_1_0 = -8.76095863777682E-06

AP_0_1 = -2.24111701317955E-07

AP_2_0 = -1.09126412217438E-07

AP_1_1 = 1.04476756931874E-07

AP_0_2 = -1.44075117066647E-08

AP_3_0 = 6.64463016878538E-10

AP_2_1 = -2.27804775793203E-12

AP_1_2 = 6.24575281634439E-10

AP_0_3 = -7.94670122482519E-11

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

BP_0_0 = -8.86207801563109E-05

BP_1_0 = -2.42201345358436E-07

BP_0_1 = -5.93827281658577E-06

BP_2_0 = 2.17884611100473E-08

BP_1_1 = -9.93412857448403E-08

BP_0_2 = 1.28982123758204E-07

BP_3_0 = -6.37600494261096E-12

BP_2_1 = 6.41773348315693E-10

BP_1_2 = -1.05777688734352E-11

BP_0_3 = 7.19818562269301E-10

PLTSOLVD= T / Siril internal solver

HISTORY Background extraction (Correction: Subtraction)

HISTORY Plate Solve

HISTORY Photometric CC (algorithm: PCC)

HISTORY Photometric CC (algorithm: PCC)

HISTORY Saturation enhancement (amount=0.45)

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

HISTORY GHS pivot: 0.000, amount: 1.54, local: 0.00 [0.00 1.00]

HISTORY GHS pivot: 0.000, amount: 2.88, local: 0.00 [0.00 1.00]

HISTORY GHS pivot: 0.000, amount: 1.76, local: 3.26 [0.00 1.00]

HISTORY GHS LINEAR BP: 0.04

HISTORY GHS pivot: 0.195, amount: 1.82, local: 0.00 [0.00 1.00]

HISTORY GHS LINEAR BP: 0.01

HISTORY GHS pivot: 0.000, amount: 1.65, local: 0.00 [0.00 0.73]

HISTORY GHS LINEAR BP: 0.01

HISTORY GHS SAT pivot: 0.233, amount: 3.70, local: 0.00 [0.00 1.00]

HISTORY GHS LINEAR BP: 0.01

HISTORY Background neutralization

FRAME = 'Light ' / Frame Type

APTDIA = 6.000E+01 / Telescope diameter (mm)

SCALE = 2.099193E+00 / arcsecs per pixel

RADECSYS= 'FK5 ' / RADECSYS

SECPIX1 = 2.0991930515E+00 / SECPIX1

SECPIX2 = 2.0991930515E+00 / SECPIX2

COMMENT Generated by INDI

WB_R = 5.500E+01 / White Balance - Red

WB_B = 7.500E+01 / White Balance - Blue

END

"Limits of Optimal Polynomial Approximants"

SIMPLE = T / file does conform to FITS standard

BITPIX = -32 / number of bits per data pixel

NAXIS = 3 / number of data axes

NAXIS1 = 2727 / length of data axis 1

NAXIS2 = 2914 / 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 = 382 / Upper visualization cutoff

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

DATE = '2025-09-07T16:04:32' / UTC date that FITS file was created

DATE-OBS= '2025-09-06T21:50:05.809000' / YYYY-MM-DDThh🇲🇲ss observation start,

IMAGETYP= 'Light Frame' / Type of image

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

EXPTIME = 180. / [s] Exposure time duration

TELESCOP= 'Slywatcher Evolux 62 ED 400@F\6.5' / Telescope used to acquire this i

FILTER = 'mixed ' / Active filter name

FOCALLEN= 362.507 / [mm] Focal length

CENTALT = 39.89957 / [deg] Altitude of telescope

CENTAZ = 32.74331 / [deg] Azimuth of telescope

XBINNING= 1 / Camera binning mode

YBINNING= 1 / Camera binning mode

XPIXSZ = 4.8 / [um] Pixel X axis size

YPIXSZ = 4.8 / [um] Pixel Y axis size

INSTRUME= 'QHY CCD QHY168C-f3c2994' / Instrument name

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

GAIN = 10 / Sensor gain

OFFSET = 50 / Sensor gain offset

STACKCNT= 182 / Stack frames

LIVETIME= 32760. / [s] Exposure time after deadtime correction

EXPSTART= 2460925.38793968 / [JD] Exposure start time (standard Julian date)

EXPEND = 2460925.63782278 / [JD] Exposure end time (standard Julian date)

OBJECT = 'M 31 ' / Name of the object of interest

AIRMASS = 1.557501 / Airmass at frame center (Gueymard 1993)

SITELAT = 47.91667 / [deg] Observation site latitude

SITELONG= 1.933056 / [deg] Observation site longitude

OBJCTRA = '00 42 30.672' / [H M S] Image center Right Ascension

OBJCTDEC= '+41 12 22.659' / [D M S] Image center Declination

RA = 10.6277982528625 / [deg] Image center Right Ascension

DEC = 41.2062942758214 / [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 = 1364. / Axis1 reference pixel

CRPIX2 = 1457.5 / Axis2 reference pixel

CRVAL1 = 10.6277982528625 / [deg] Axis1 reference value

CRVAL2 = 41.2062942758214 / [deg] Axis2 reference value

LONPOLE = 180. / Native longitude of celestial pole

CDELT1 = -0.000758721053819356 / [deg] X pixel size

CDELT2 = 0.000758599487695311 / [deg] Y pixel size

PC1_1 = -0.336820836673126 / Linear transformation matrix (1, 1)

PC1_2 = -0.941568756906693 / Linear transformation matrix (1, 2)

PC2_1 = 0.941480486837379 / Linear transformation matrix (2, 1)

PC2_2 = -0.337067490132841 / 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 = 3.97578917841809E-07

A_1_1 = -2.44774798826953E-08

A_0_2 = 9.22941238005915E-08

A_3_0 = -1.12035964590002E-09

A_2_1 = 5.12191944642339E-12

A_1_2 = -1.1009892822829E-09

A_0_3 = 3.73598524888844E-13

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 = 1.19579208308998E-07

B_1_1 = 2.91051781005884E-07

B_0_2 = 1.02802639174333E-07

B_3_0 = -1.3611124041332E-11

B_2_1 = -1.07757308897139E-09

B_1_2 = 1.73284258110139E-12

B_0_3 = -1.1172753794729E-09

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

AP_0_0 = 0.000988225551640077

AP_1_0 = -1.24879495848607E-05

AP_0_1 = 1.15890752822243E-07

AP_2_0 = -4.025349097176E-07

AP_1_1 = 2.41075310703775E-08

AP_0_2 = -9.34493958401128E-08

AP_3_0 = 1.13489542756861E-09

AP_2_1 = -5.25179707652799E-12

AP_1_2 = 1.11750286044444E-09

AP_0_3 = -4.17413704041954E-13

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

BP_0_0 = 0.000952212066372248

BP_1_0 = 3.76735565828782E-07

BP_0_1 = -1.33797912759137E-05

BP_2_0 = -1.21044688351177E-07

BP_1_1 = -2.9451504048561E-07

BP_0_2 = -1.04667173896164E-07

BP_3_0 = 1.36872185686008E-11

BP_2_1 = 1.09420708095768E-09

BP_1_2 = -1.93156721119263E-12

BP_0_3 = 1.13223326583511E-09

FRAME = 'Light ' / Frame Type

APTDIA = 6.200E+01 / Telescope diameter (mm)

SCALE = 2.750667E+00 / arcsecs per pixel

PIERSIDE= 'WEST ' / West, looking East

RADECSYS= 'FK5 ' / RADECSYS

SECPIX1 = 2.7506667760E+00 / SECPIX1

SECPIX2 = 2.7506667760E+00 / SECPIX2

COMMENT Generated by INDI

END

 

B1. GPU in Zernike Polynomical Adaptive Optics Atmospheric Aberration Correction and Epidemiology

 

*Minzhao Liu, Narendra K. Jaggi - Illinois Wesleyan University - 5 - Student Research

 

Graphic processing unit (GPU) acceleration is now widely available to researchers and students, enabling unprecedented speed of progress in science and technologies. Two fields in which GPU acceleration is implemented in Illinois Wesleyan is Optics and Epidemiology. Real time atmospheric aberration correction for free space laser communication is challenging due to the high rate of aberration change. Deep neural networks were proposed to speed up aberration correction using Zernike polynomials, commonly used to represent optical aberration. We attempt a physical implementation of this scheme using a spatial light modulator, with GPU accelerating the generation of aberration correction profile from the polynomial coefficients. On the other end, epidemic simulations using networks mimicking real-life social networks are studied to understand the effects of network degree distribution and clustering on the spread of diseases. We propose a GPU accelerated program to enable parallel execution of hundreds of simulations with different epidemiological parameters to help researchers quickly characterize response surfaces of these parameters.

Binomial Probability Formula is deals with the polynomial that has two terms is known as a binomial e.g.5x + 3y, 2x2 – 5xy.Probability is the arithmetical quantify of the possibility of an event to occur. If in an examine there are n feasible ways completely and mutually exclusive and out of them in m ways in the event A occur, it is given by (m / n) if in a random sequence of n trails of an events, M are favor to the event, then ratio is (M / n).by studying in both combined as binomial probability as P(A) = m / n.The possibility of an event can be conveyed as a binomial probability if its conclusions can be wrecked down into two probability of p and q, where p and q are balancing (i.e. p + q = 1).

"Zeros of real random polynomials spanned by OPUC"

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