View allAll Photos Tagged polynomials
SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 5444 / length of data axis 1
NAXIS2 = 3803 / 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 = '2025-10-06T11:56:28' / UTC date that FITS file was created
DATE-OBS= '2025-10-06T10:09:06.886626' / YYYY-MM-DDThh🇲🇲ss observation start,
ROWORDER= 'TOP-DOWN' / Order of the rows in image array
EXPTIME = 836.25 / [s] Exposure time duration
OBSERVER= 'DaveMartin' / Observer name
FILTER = 'Dual ' / Active filter name
FOCALLEN= 956.82 / [mm] Focal length
CENTALT = 43.875 / [deg] Altitude of telescope
CENTAZ = 197.023888888889 / [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 = 19865 / [step] Focuser position
FOCTEMP = 8.30000019073486 / [degC] Focuser temperature
OBJECT = 'NGC1976 (M42, Great Orion Nebula, Orion Nebula)' / Name of the object
AIRMASS = 1.44068164488539 / Airmass at frame center (Gueymard 1993)
SITELAT = 39.3488888888889 / [deg] Observation site latitude
SITELONG= -78.8116666666667 / [deg] Observation site longitude
OBJCTRA = '05 35 15.799' / [H M S] Image center Right Ascension
OBJCTDEC= '-05 22 47.677' / [D M S] Image center Declination
RA = 83.8158281898562 / [deg] Image center Right Ascension
DEC = -5.37991021764815 / [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 = 2693.5 / Axis1 reference pixel
CRPIX2 = 1938.5 / Axis2 reference pixel
CRVAL1 = 83.8212837066781 / [deg] Axis1 reference value
CRVAL2 = -5.38889204929805 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000225139323345704 / [deg] X pixel size
CDELT2 = 0.000225169400022428 / [deg] Y pixel size
PC1_1 = -0.348038991134063 / Linear transformation matrix (1, 1)
PC1_2 = -0.937480058801457 / Linear transformation matrix (1, 2)
PC2_1 = 0.937494027453252 / Linear transformation matrix (2, 1)
PC2_2 = -0.348001362769574 / 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 = -1.64277020685452E-07
A_1_1 = 9.87549346279314E-09
A_0_2 = -8.69160424952199E-08
A_3_0 = -3.02073434291275E-10
A_2_1 = 5.06449749491843E-12
A_1_2 = -3.06521889392484E-10
A_0_3 = -7.11631122483371E-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 = -1.28288782073535E-08
B_1_1 = -5.68511798589425E-08
B_0_2 = -5.88039813473346E-08
B_3_0 = 2.51466443610045E-12
B_2_1 = -3.03411808507867E-10
B_1_2 = 1.88074302834745E-11
B_0_3 = -3.02158975629337E-10
AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = -0.00282500133597869
AP_1_0 = -1.43205078008135E-05
AP_0_1 = 6.69821284630872E-07
AP_2_0 = 1.66963688254827E-07
AP_1_1 = -1.00792430236529E-08
AP_0_2 = 8.76805314355769E-08
AP_3_0 = 3.06432679354613E-10
AP_2_1 = -5.24743960913225E-12
AP_1_2 = 3.1135956544913E-10
AP_0_3 = 6.95417774079078E-12
BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = -0.000587530962498615
BP_1_0 = 6.73660948648711E-07
BP_0_1 = -1.0370590796116E-05
BP_2_0 = 1.30208895607198E-08
BP_1_1 = 5.76814378001768E-08
BP_0_2 = 5.93230277432801E-08
BP_3_0 = -2.60709033909064E-12
BP_2_1 = 3.07758434362221E-10
BP_1_2 = -1.92588333919524E-11
BP_0_3 = 3.05579270177439E-10
PLTSOLVD= T / Siril internal solver
HISTORY Plate Solve
HISTORY Crop (x=431, y=223, w=5444, h=3803)
HISTORY Background extraction (Correction: Subtraction)
HISTORY StatStretch: m=0.20 l=True n=True c=True b=0.00
HISTORY GraXpert AI BGE: subtraction
HISTORY GraXpert AI denoise: strength 0.50
HISTORY GraXpert AI deconvolve: strength 0.50
HISTORY GraXpert AI deconvolve: strength 0.50
HISTORY GHS LINEAR BP: 0.08
HISTORY GHS pivot: 0.138, amount: 1.25, local: 0.00 [0.00 1.00]
HISTORY GHS LINEAR BP: 0.06
HISTORY GHS INV pivot: 0.116, amount: 0.82, local: 0.00 [0.00 1.00]
HISTORY Apply Signature
HISTORY GHS pivot: 0.179, amount: 2.38, local: 0.00 [0.00 1.00]
HISTORY GHS LINEAR BP: 0.03
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= '2025-10-06T10:24:13.1694766' / System Clock:Est. Frame Mid Point
DATE-END= '2025-10-06T10:39:19.4523264' / System Clock:Est. Frame End
EGAINSAV= 0.26355 / Electrons per ADU at saved bit depth
JD_UTC = 2460954.933485758 / Julian Date at mid exposure
PIERSIDE= 'EAST' /
RDNOISE = 1.77 / Read noise in electrons
RELGAIN = 2.964 / Multiplicative gain relative to minumum
SUBEXP = 3.75 /
END
Taylor polynomials on a nice sunny day with fun little shadows and all of that fun stuff.
I was just sitting there doing my math homework when I thought "hmm, this might make a good shot."
The Question was raised in page 121 of the book:
The History of Combinatorial Group Theory: A Case Study in the History of Ideas, by Chandler and Magus.
The moral of the story is that if a family of groups is very much like free group, as in the case of Parafree groups, then to discriminate members of such a family of groups you might try investigating topological properties of their representation varieties over an algebraic group where free groups embed, even if you don't know if the corresponding representation varieties are non-singular as is the case for the representation variety of a fg free group in SL(2,C). Using Andre Weil's deep observation we can just count points over a finite field of P elements, for a suitably chosen prime integer P, after reducing mod P the defining polynomials of the corresponding representation varieties of the two groups we are attempting to discriminate. This was a fruitful approach and quite amenable to computations using packages such a Singular, Gap, or the Computational Algebra System Magma... Etc.
SL gives a talk here on the representation varieties of Parafree Groups : youtu.be/rLL9IKoh0ms
Some basic facts on Parafree groups here:
SIMPLE = T / file does conform to FITS standard
BITPIX = -32 / number of bits per data pixel
NAXIS = 3 / number of data axes
NAXIS1 = 6596 / length of data axis 1
NAXIS2 = 3906 / 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
FILENAME= 'Img893.nef'
DATE = '2025-09-28T05:57:34' / UTC date that FITS file was created
DATE-OBS= '2025-09-28T01:59:12' / YYYY-MM-DDThh🇲🇲ss observation start, UT
ROWORDER= 'BOTTOM-UP' / Order of the rows in image array
EXPTIME = 120. / [s] Exposure time duration
ISOSPEED= 2000. / ISO camera setting
FOCALLEN= 349.015 / [mm] Focal length
XBINNING= 1 / Camera binning mode
YBINNING= 1 / Camera binning mode
XPIXSZ = 4.35 / [um] Pixel X axis size
YPIXSZ = 4.35 / [um] Pixel Y axis size
INSTRUME= 'Nikon Z 8' / Instrument name
STACKCNT= 90 / Stack frames
LIVETIME= 10800. / [s] Exposure time after deadtime correction
EXPSTART= 2460946.57153935 / [JD] Exposure start time (standard Julian date)
EXPEND = 2460946.69800926 / [JD] Exposure end time (standard Julian date)
OBJCTRA = '20 57 33.493' / [H M S] Image center Right Ascension
OBJCTDEC= '+44 20 8.204' / [D M S] Image center Declination
RA = 314.389552679012 / [deg] Image center Right Ascension
DEC = 44.3356122095578 / [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 = 3374.5 / Axis1 reference pixel
CRPIX2 = 2133.5 / Axis2 reference pixel
CRVAL1 = 314.316417410616 / [deg] Axis1 reference value
CRVAL2 = 44.4649849372378 / [deg] Axis2 reference value
LONPOLE = 180. / Native longitude of celestial pole
CDELT1 = -0.000714102839018755 / [deg] X pixel size
CDELT2 = 0.000714125578266618 / [deg] Y pixel size
PC1_1 = 0.999884345462982 / Linear transformation matrix (1, 1)
PC1_2 = -0.0152084087946279 / Linear transformation matrix (1, 2)
PC2_1 = 0.0151518083294775 / Linear transformation matrix (2, 1)
PC2_2 = 0.9998852047632 / 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 = 7.37232916860729E-08
A_1_1 = -3.19387560892366E-08
A_0_2 = -9.11536837244955E-09
A_3_0 = -6.02638794702981E-11
A_2_1 = 2.87763649378023E-12
A_1_2 = -5.97289421291022E-11
A_0_3 = -3.75472308572456E-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 = -7.06109054247092E-09
B_1_1 = 9.05949080901921E-08
B_0_2 = -2.46269058473928E-08
B_3_0 = -1.77256505830348E-13
B_2_1 = -5.7171644546712E-11
B_1_2 = 5.51659247284017E-12
B_0_3 = -6.1812439766824E-11
AP_ORDER= 3 / SIP polynomial degree, axis 1, sky-to-pixel
AP_0_0 = 0.000840734049471275
AP_1_0 = -1.6683227365144E-06
AP_0_1 = -1.56918762883889E-08
AP_2_0 = -7.41504606776651E-08
AP_1_1 = 3.2132301950985E-08
AP_0_2 = 9.06349284005886E-09
AP_3_0 = 6.05686493375772E-11
AP_2_1 = -2.90015438078615E-12
AP_1_2 = 6.00431324326385E-11
AP_0_3 = 3.76150735791593E-12
BP_ORDER= 3 / SIP polynomial degree, axis 2, sky-to-pixel
BP_0_0 = -0.000258888933924185
BP_1_0 = -2.89780433782433E-09
BP_0_1 = -9.7241646490609E-07
BP_2_0 = 7.11044840985938E-09
BP_1_1 = -9.09584691825188E-08
BP_0_2 = 2.4743373951236E-08
BP_3_0 = 1.75437908062712E-13
BP_2_1 = 5.7448756100725E-11
BP_1_2 = -5.54120846081177E-12
BP_0_3 = 6.20157977821203E-11
PLTSOLVD= T / Siril internal solver
HISTORY Background extraction (Correction: Subtraction)
HISTORY Asinh Transformation: (stretch= 486.8, bp=0.00400)
HISTORY SCNR (type=average neutral, amount=1.00, preserve=true)
HISTORY Plate Solve
HISTORY Photometric CC (algorithm: PCC)
HISTORY Crop (x=766, y=987, w=6596, h=3906)
HISTORY Deconvolution
END
Binomials 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.
Professor Manindra Agarwal, the principal author of the famous 2004 paper ``PRIMES is in P''. The paper described a polynomial time algorithm for testing the primality of a number.
It is a paper I enjoyed very much --- although I did not have occasion to tell him that in person. And of course it was a revolutionary paper.
Help to choose the right person to pay for math homework
Do you at any point ask yourself "Who would I be able to trust pay for math homework of mine?" or "Who will even do my mathematical tasks?" If you think that way, well don’t worry you are not alone. There are a huge number of students in schools across the world that battle with math courses and urgently attempt to discover dependable numerical schoolwork help. Let's be honest: Math is hard! Other than the entirety of the ideas, hypotheses and placing in a lot of basic reasoning, the steadily expanding issue of class sizes prompts educators being not able to give one-on-one help to students. Thus, more understudies these days are probably going to battle with the subject than the individuals who went to classes just 10 years prior. And keeping in mind that improving the instructive framework is out of our hands, we can positively assist with math schoolwork in manners that other homework help organizations can't.
We enlist just numerical experts to give you the numerical schoolwork help you need to refocus and acquire a spot at the head of the class. Our specialists have been reading upper-level math for quite a long time and can give you the most precise answers for little and enormous issue sets, composed reactions thus significantly more.
I'd like to pay for my math homework if necessary
Our obliging client assistance group is accessible to react to your inquiries every minute of every day. So in the event that you need assistance with math sometime later, AssignmentGeek.com will have somebody to help you. For since a long time ago composed pieces –, for example, math articles or research papers – you will get a rundown of qualified number related authors from which you can pick the master you need to employ. This is instrumental in building a positive learning experience since the essayist you pick will impart ideas in your paper that you should learn in anticipation of term-end or year-end tests. Investigate - here are some mathematical subjects our composing administration can assist you with:
•Algebra
•Geometry
•Trigonometry
•Pre-polynomial math
•And many more
Thus, on the off chance that you've been pondering "What site can assist me with pay for math homework?" the appropriate response is -. To be sure, we are among the best numerical homework benefits around in light of the fact that we treat each student separately and cater our administrations for each case. Just call us or send us an email with the title perusing "Do my mathematical task," and we'll get this show on the road. We'll finish your tasks rapidly and effectively, giving every one of the vital clarifications with the goal that you can either duplicate the work by hand to submit as your own or audit its substance or utilize an examination guide for tackling the numerical statements all alone.
We expect to complete things properly the first run through. We're so sure about our aptitude that we offer free updates on any venture you're not totally happy with. Simply check us out and we're certain you will not look for another schoolwork help administration. Try not to stand by till the year's end when you are overpowered with tests and different tasks. Stretch out beyond the bend by submitting your request today and discover firsthand why many understudies enroll our assistance every day. With regards to superior grade, moderate schoolwork help, there could be no greater choice!
Help With Math Homework from Top Experts
We don’t just offer top caliber and solid mathematical assistance administrations, yet additionally a quick help for those students who are in a rush. It doesn't make any difference on the off chance that you need to tackle polynomial math or calculation issues, or on the off chance that you need to compose a paper with respect to a number related point, in the event that you reach us, regardless of great importance, hope.
Now you have your gold key for marks and have answer to “pay for math homework concern”. Be unstoppable and fetch the marks you always wanted!