Example sentences of "we may write " in BNC.
Next page| No | Sentence |
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| 1 | You would probably say : " Assuming x is odd , we may write x = 2n + 1 for some suitable n ε Z. Then unc which is clearly odd " . |
| 2 | Proof We suppose unc so that we may write x = m/n where m , n ε Z. Clearly we may assume m , n have no common divisor |
| 3 | Clearly not , since we may write , for example , not only |
| 4 | Otherwise suppose b is a root of f in J. Then by 1.11.3 we may write f = ( x-b ) m where by exercise 1.9.9 deg m = k exactly . |
| 5 | Symbolically , we may write the operation as |
| 6 | In the simplest ( trivial ) case we may write A = AI = IA where I is the conformable unit matrix . |
| 7 | However , if D = Diag(1,2,3) we have that unc so that e = g = h = k = 0 leaving unc which we may write as Block Diag unc where unc Finally , we note that if unc for all i , then |
| 8 | We may write this equation as unc Equation ( 5 ) is known as a parametric solution : since we have only n — s independent relations we can determine only n — s unknowns ( y ) in terms of the remaining s quantities ( z ) , which may be regarded as arbitrary parameters in the problem . |
| 9 | First , suppose as above that the eigenvalues are all distinct ; then in view of ( 1.16.9 ) we may write the polynomial unc ( A ) as unc Now the diagonal matrix unc has for diagonal elements unc all of which vanish ; i.e. unc is null . |
| 10 | In terms of the isolating vector ei this may be written unc and if P(A) is expanded in this way , the first term , which is typical will be unc The square matrices on the right of these equations are all of unit rank ; we may write the last as unc where x1 is the first column of X , and unc the first row of |
| 11 | Hence we may write ( 8 ) as unc so that , in this case ( two equal roots and double degeneracy of the characteristic matrix ) , the form of ( 8 ) is unaltered . |
| 12 | With unc general , we may write the eigenvectors corresponding |
| 13 | Then we may write unc and D has the same degeneracy as C. The matrix unc will in general be fully populated ; if it is appropriately partitioned , we may write ( 18 ) as unc To be conformable with the first and last matrices in the triple product , unc must have — p rows and n — q columns . |
| 14 | Then we may write unc and D has the same degeneracy as C. The matrix unc will in general be fully populated ; if it is appropriately partitioned , we may write ( 18 ) as unc To be conformable with the first and last matrices in the triple product , unc must have — p rows and n — q columns . |
| 15 | For example , we may write it as unc and use the regression formula unc so that , for example , if Ro = 0 , we should obtain unc and so on . |
| 16 | In view of ( 3 ) we may write unc If ( 8 ) is used as postmultiplier of A , it is clear that A is deflated by the sweeping matrix in ( 8 ) to unc ( note that A1 here differs from the deflated form A1 of 2.7.2 ) . |
| 17 | For each root i there will be at least one linear relation between the columns of the pencil , so that we may write unc and unc is an eigenvector of the pencil . |
| 18 | The pencil is described as simple if there are n independent vectors unc so that we may write the set compendiously as unc where unc is of simple diagonal form , even through it may include multiple roots . |
| 19 | Assuming binding constraints , and taking the case where there is only one product y with price p ( or independent demands ) , means we may write the Lagrangean function from ( 4.2 ) with multipliers μ and λ as : Then , the first order conditions give ; unc being |
| 20 | So we may write eqn ( 2.30 ) in the form |
| 21 | Introducing subscripts 1 and 2 for denoting our quantities in the two dielectrics , we may write |
| 22 | Noting further that J.S = I and that I must be constant along the wire we may write eqn ( 3.15 ) in the modified form |
| 23 | For two line currents flowing in the opposite directions ( Fig. 3.5(b) ) , we may write Ampère 's law twice and add the magnetic fields or add the vector potentials . |
| 24 | We may write The first term on the right-hand side is symmetric in i and j , the second is anti-symmetric . |
| 25 | Denoting the intrinsic energy change by — U we have the equation and for the whole body Now the rate at which work is done by the external forces is The second integral converts by Gauss 's theorem to Now is we assume infinitesimal strains we may write and the second term vanishes in the summations . |
| 26 | This must be equal to the integral over the surface were v is the velocity and — the density ; n is the outward normal to the surface S which enclosed V. By Gauss 's theorem we may write and hence Since this must be true for any volume element we have the equation of continuity The conservation of momentum in continuum mechanics relates the rate of change of the momentum integrated over a volume V to the resultant of the forces on that volume . |
| 27 | Thus we may write , where t is a random , serially independent variable designed to pick up the random movements in the risk premium . |
| 28 | In the simplest possible photoionization event the whole of the photon energy is transferred to the electron , so we may write where hν is the energy of the incident photon , BE is the binding energy of the ejected electron and KE is its kinetic energy . |
| 29 | The returns from the two investment decisions are equal ; hence we may write , this reduces to , hence , . |