Since one degree is defined as one three hundred and sixtieth () of a rotation, one minute of arc is of a rotation.

This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of K < sup > sep </ sup >, of degree > 1.

Since its commercial release, Ethernet has retained a good degree of compatibility.

Since the Emperor was seen as a divine figure and linked to the deities, pollution of such extreme degree committed by the highest source was seen as extremely ruinous.

Since the reign of Edward VII a clerk in holy orders in the Church of England has not normally received the accolade on being appointed to a degree of knighthood.

Since the amount of physical capital affects MRP, and since financial capital flows can affect the amount of physical capital available, MRP and thus wages can be affected by financial capital flows within and between countries, and the degree of capital mobility within and between countries.

Since, the degree of a variable without a written exponent is one.

Since most of the symptoms depend on self report and are not concrete and observable, there is a degree of subjectivity in making the diagnosis.

Since there is no smaller degree dependency, the minimal polynomial of is:.

Since the generator polynomial is of degree 4, this code has 11 data bits and 4 checksum bits.

Since the generator polynomial is of degree 8, this code has 7 data bits and 8 checksum bits.

Since California considers “ all persons concerned in the commission of a crime, whether they directly commit the act constituting the offense … principals in any crime so committed ,” San Marin County Superior Judge Peter Allen Smith charged Davis with “ aggravated kidnapping and first degree murder in the death of Judge Harold Haley ” and issued a warrant for her arrest.

Since the Mind concerned chooses its own name this may sometimes even indicate a degree of self-hatred over its purpose for existence.

Since many insects exhibit a degree of endemism ( occurring only in certain places ), or have a well-defined phenology ( active only at a certain season, or time of day ), their presence in association with other evidence can demonstrate potential links to times and locations where other events may have occurred.

Since September 1965, Louisiana Tech has offered on-base degree programs through its satellite campus at Barksdale Air Force Base in Bossier City, Louisiana.

Since its founding, the college expanded its degree program to include chemical engineering, civil engineering, electrical engineering, industrial engineering, and mechanical engineering.

Since programmes are all within the social sciences, they closely resemble each other, and undergraduate students usually take at least one course module in a subject outside of their degree for their first and second years of study, promoting a broader education in the social sciences.

Since its inception, Stirling has offered modular degree programmes allowing greater flexibility and choice.

Since a bachelor's degree usually takes three years to complete, either Part I or Part II is two years, and the other one year.

Since he knew that he was designing the show for television, he purposely limited the design to a certain degree ( designing the nose and mouth, for instance, in a Hanna-Barbera style to animate easily ).

Since the planes are fixed, each rotation has only one degree of freedom, its angle.

Since these graduates do not have a separate Bachelor ’ s degree ( which is in fact – in retrospect – incorporated into the program ), the Master ’ s degree is their first academic degree.

Since practical rectifiers have non-zero voltage drop, accuracy and sensitivity is poor at low values.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

Since only finitely many coefficients a < sub > i </ sub > and b < sub > j </ sub > are non-zero, all sums in effect have only finitely many terms, and hence represent Laurent polynomials.

Since neither x nor y can equal zero ( if k is non-zero ), the graph will never cross either axis.

Since v is non-zero, this means that the matrix I − A is singular ( non-invertible ), which in turn means that its determinant is 0.

Since the residue classes ( mod p ) are a field, every non-zero a has a unique multiplicative inverse, a < sup >− 1 </ sup >.

Since the Lorentz group has no non-trivial unitary representation of finite dimension, it naively seems that one cannot construct a state with finite, non-zero spin and positive, Lorentz-invariant norm.

Since only finitely many coefficients a < sub > i </ sub > and b < sub > j </ sub > are non-zero, all sums in effect have only finitely many terms, and hence represent polynomials from K.

Since there are an infinite number of modes this implies infinite heat capacity ( infinite energy at any non-zero temperature ), as well as an unphysical spectrum of emitted radiation that grows without bound with increasing frequency, a problem known as the ultraviolet catastrophe.

Since each memory location within the zero page of a 16-bit address bus computer may be addressed by a single byte, it was faster, in 8-bit data bus machines, to access such a location rather than a non-zero page location.

Since the Walsh – Hadamard code is a linear code, the distance is equal to the minimum Hamming weight among all of its non-zero codewords.

Since no ideal sources of either variety exist ( all real-world examples have finite and non-zero source impedance ), any current source can be considered as a voltage source with the same source impedance and vice versa.

Let X be a finite subset of U, minimal with respect to the property that it generates U. Since U is non-zero, this set X is nonempty.

Since condensates are scalar, it seems like a good first approximation that the vacuum contains some non-zero but homogeneous field which gives rise to these condensates.

Since the one-dimensional representations of B correspond to the representations of the diagonal matrices, with non-zero complex entries z and z < sup >− 1 </ sup >, and thus have the form

Since the left-hand side of the Lorentz reciprocity theorem vanishes for integration over all space with any non-zero losses, it must also vanish in the limit as the losses go to zero.

Since a point cannot support rotation or angular momentum in classical physics ( general relativity being a classical theory ), the minimal shape of the singularity that can support these properties is instead a ring with zero thickness but non-zero radius, and this is referred to as a ring singularity or Kerr singularity.

Since all problems in NP can be reduced to this problem it follows that for all problems in NP we can construct a non-deterministic Turing machine that decides the complement of the problem in polynomial time, i. e., NP is a subset of co-NP.

Since the polynomials with integer coefficients are countable, and since each such polynomial has a finite number of zeroes, the algebraic numbers must also be countable.

* Omission of the high-order bit of the divisor polynomial: Since the high-order bit is always 1, and since an n-bit CRC must be defined by an ( n + 1 )- bit divisor which overflows an n-bit register, some writers assume that it is unnecessary to mention the divisor's high-order bit.

* Omission of the low-order bit of the divisor polynomial: Since the low-order bit is always 1, authors such as Philip Koopman represent polynomials with their high-order bit intact, but without the low-order bit ( the or 1 term ).

* Since NP-complete problems transform to each other by polynomial-time many-one reduction ( also called polynomial transformation ), all NP-complete problems can be solved in polynomial time by a reduction to H, thus all problems in NP reduce to H ; note, however, that this involves combining two different transformations: from NP-complete decision problems to NP-complete problem L by polynomial transformation, and from L to H by polynomial Turing reduction ;

Since an arbitrary rearrangement of the roots of the product form still produces the same polynomial, e. g.:

Since the eigenvalues of this matrix coincide with the roots of the polynomial, one can use any eigenvalue algorithm to find the roots of the polynomial.

Since an nth degree polynomial equation can only have n distinct roots, this implies that the powers of a primitive root z, z < sup > 2 </ sup >, ... z < sup > n − 1 </ sup >, z < sup > n </ sup >

Since the entries of the matrix are ( linear or constant ) polynomials in λ, the determinant is also a polynomial in λ.

Since the complex roots of a real polynomial are in conjugate pairs, the irreducible polynomials over the field of real numbers are the linear polynomials and the quadratic polynomials with no real roots.

Since the error term is proportional to the fourth derivative of f at, this shows that Simpson's rule provides exact results for any polynomial f of degree three or less, since the fourth derivative of such a polynomial is zero at all points.

Since f is a polynomial, this definition is purely algebraic and makes no assumption about the nature of the field F, which in particular need not be the real or complex numbers.

Since a quartic function is a polynomial of even degree, it has the same limit when the argument goes to positive or negative infinity.

Since the formal derivative of a positive degree polynomial can be zero only if the field has prime characteristic, for an irreducible polynomial to not have distinct roots its coefficients must lie in a field of prime characteristic.