This website uses cookies to ensure you get the best experience. Learn more

cz

In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.

00-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

00Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

00If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.

00The complete covariant and contravariant system includes no fewer than 34 forms; from its complexity it is desirable to consider the cubic in a simple canonical form; that chosen by Cayley was ax 3 +by 3 + cz 3 + 6dxyz (Amer.

00C or cz is pronounced as English ts; cs as English ch; ds as English j; zs as French j; gy as dy.

00BOULEUTERIOry CZ: By permission from plans by F.de Billi.

00These often agree with CZ against M, and the readings of CZZ are generally superior.

00of connection cuts off from any two lines drawn from a given CZ A1

00UK or CZ for example) which tells you which ' input locale ' is selected.

00We then have we then have w H Cz = u T Rx where C = R.

00In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.

00-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

00Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

00If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.

00The complete covariant and contravariant system includes no fewer than 34 forms; from its complexity it is desirable to consider the cubic in a simple canonical form; that chosen by Cayley was ax 3 +by 3 + cz 3 + 6dxyz (Amer.

00C or cz is pronounced as English ts; cs as English ch; ds as English j; zs as French j; gy as dy.

00BOULEUTERIOry CZ: By permission from plans by F.de Billi.

00These often agree with CZ against M, and the readings of CZZ are generally superior.

00of connection cuts off from any two lines drawn from a given CZ A1

00We then have w H Cz = u T Rx where C = R.

00Labels such as Biscotti, Baby CZ, D&G and Chloe manufacture adorable, high quality designs, none of which are particularly over-the-top when it comes to fashion, but include just enough pink and ruffles to make an adorable ensemble.

00Stones: Diamonds are popular on palm trees, but more affordable jewelry may use cubic zirconia (CZ) or other simulated gemstones.

00Emitations features Skyla's Pearl and CZ Cluster Earrings.

00Cubic zirconia (often abbreviated CZ) is a lab-created crystalline cubic form of zirconium oxide stabilized with small quantities of other minerals, typically yttrium or calcium.

00The first natural CZ was discovered in 1937 by German mineralogists.

00Diamonds can be found in many different colors, and so can CZ, depending on what different mineral oxides have been added to the zirconium oxide during crystal stabilization and cooling.

00The manmade gem is significantly heavier than diamond (65-75%), so weighing two stones of the same carat size would help determine which is CZ and which is diamond.

00Furthermore, because CZ is grown in a laboratory under tightly controlled conditions, it is typically flawless and lacks the diamond flaws and inclusions that mar natural stones.

00When choosing CZ rings, it is important to be familiar with different engagement ring designs, ring settings, metal choices, and other style options.

00If your heart is set on a true diamond, don't discount CZ entirely.

00Pave setting engagement rings, in particular, often use CZ or other simulated stones to create the illusion of a myriad of diamonds for far less expense.

00As with any piece of jewelry, CZ rings should be meticulously cleaned and cared for to be kept looking their best.

00Ultrasonic cleaners are also safe for CZ engagement rings.

00For more details about cubic zirconia and this leading company for cz jewelry, visit the official website www.ziamond.com or call 1-866-942-6663.

00The combination of cubic zirconia (CZ) and silver can make an interesting option for an engagement ring and can be found in exciting and unusual designs as well as being low cost.

00Fred Leighton Inspired Sterling Silver Princess-Cut Blue Sapphire CZ Pave Three-Sided Band Ring-This is perfect for those who love the look of sapphires and diamonds.

00Inspired by Designer Sterling Silver Diamond CZ Journey Bridal Wedding Band Ring-This isn't the traditional wedding band style.

00Inspired by Tiffany 14K Gold Vermeil Channel Set Diamond CZ Bridal Wedding Band Ring-Most cubic zirconia wedding pieces feature a white metal, such as silver.

00CZ Jewels: CZ Jewels specializes in cubic zirconia jewelry and has a nice selection of fake diamond rings.

00Reproductions of the Twilight engagement ring are generally designed with multiple brilliant cut stones (usually CZ stones or diamonds) in a cluster-style or open gallery setting with narrow yellow gold bands.

00The CZ, sterling silver and marcasite is one of the many variations of the Twilight engagement ring.

00Bella's engagement ring made from CZ and marcasite stones set in a sterling silver band is a lovely version that presents as well as CZ and white gold rings.

00CZ stones have a clarity and color that comes close to the beauty of diamonds.

00Combining CZ and marcasite creates a beautiful antique elegance.

00The brilliant cut shows the CZ stones off to advantage.

00However, there are many versions of the Twilight ring in CZ and sterling silver.

00Bangles of Hope: Bangles of Hope offers a version of the Twilight engagement ring in CZ, sterling silver and marcasite.

00Twilight Distinction: The Twilight Distinction Etsy Shop has a CZ and sterling silver version of Bella's engagement ring that follows a more traditional Victorian design than many other interpretations.

00A CZ, marcasite and sterling silver version of Bella's ring may be in the right price range for young couples who want a promise ring or a pre-engagement ring.

00Fantasy Jewelry Box: This site has a version of Kim's ring in CZ and silver for $59.95.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.