Hence the power, P, required by the pump:

* Starr, Martin P. ( 2004 ) A Hundred Years Hence: Visions of a Thelemic Future ( Conference Paper presented at the Thelema Beyond Crowley )

Hence, P equipped with the form η < sub > m </ sub > defines a ( first order ) H-structure on M. The form η < sub > h </ sub > defines a connection on the H-structure.

If ω and ω ' are principal connections on a principal bundle P, then the difference ω ' - ω is a-valued 1-form on P which is not only G-equivariant, but horizontal in the sense that it vanishes on any section of the vertical bundle V of P. Hence it is basic and so is determined by a 1-form on M with values in the adjoint bundle

Under the assumption that P ≠ NP, there exist many natural problems that require superpolynomial running time when complexity is measured in terms of the input size only, but that are computable in a time that is polynomial in the input size and exponential or worse in a parameter k. Hence, if k is fixed at a small value and the growth of the function over k is relatively small then such problems can still be considered " tractable " despite their traditional classification as " intractable ".

Hence, O leases the vehicle to P, and upon execution of the contract simultaneously sells ownership of the car to F and assigns the lease contract to F. It is standard for the contractual terms to prohibit P from parting with possession or control of the car to another ( if P does part with possession, this can be a theft of the car from F ).

Hence, British guidelines append the letter " P " to the stage of chronic kidney disease if there is significant protein loss.

Such name roots back to the " Zoroastrianism " era of Persia ( Iran ); However after the Arab invasion of Persia ( Iran ) many Persian words lost their original form as in Arabic there are no letter for pronouncing " G / P / ZH / CH "; Hence " Azar Paigān " came to be known as Azarbaijan.

# Hence P is a positive operator.

Hence P is a spectral projection for the Perron-Frobenius eigenvalue r, and is called the Perron projection.

Hence, given the radius, r, center, P < sub > c </ sub >, a point on the circle, P < sub > 0 </ sub > and a unit normal of the plane containing the circle,, one parametric equation of the circle starting from the point P < sub > 0 </ sub > and proceeding in a positively oriented ( i. e., right-handed ) sense about is the following:

Hence, the two lines joining P and S, and Q and T intersect at the radical center of the three circles, which lies on the radical axis of the given circles.

Hence the final budget for 1996-97 was presented by P. Chidambaram, who then belonged to Tamil Maanila Congress.

Hence, during the Alipore trial, Jatin took over the leadership of the secret society to be known as the Jugantar Party, and revitalises the links between the central organisation in Calcutta and its several branches spread all over Bengal, Bihar, Orissa and several places in U. P ..

Hence the prime issue, as I see it, is whether a democratic or free society can master technology for the benefit of mankind, or whether technology will rule and develop its own society compatible with its own needs as a force of nature.

Hence government must establish greater controls upon corporations so that their activities promote what is deemed essential to the national interest.

Hence, the only defensible procedure is to repress any and every notion, unless it gives evidence that it is perfectly safe.

Hence the natural setting of tragedy is the palace gate, the public square, or the court chamber.

Hence, the condition of freedom is a necessary condition for choice.

Hence it is difficult to conceive of a packing of the atoms in this material in which the oxygen atoms are far from geometrical equivalence.

Hence the minimal polynomial for Af is Af.

Hence the totality of singular lines is the T order complex of lines which meet Aj.

Hence, thought of as a line in a particular plane **yp, any tangent to Q has a unique image and moreover this image is the same for all planes through L.

Hence C' is a Af curve on Q.

Hence, when the address Af is computed from Af, the cell Af and all Y-cells in its chain must be inspected to determine whether Af is already in the form list or whether it should be added to the form list and the chain.

Hence, the Af factor for the output fiber coupler is Af.

Hence, if what is in question is whether in a given theology myth is or is not completely rejected, it is unimportant whether only a little bit of myth or a considerable quantity is accepted ; ;

Hence he was in his lifetime, as is the memory of him afterwards, a canker within the liberal sensitivity.

Hence, such an appellate court will not consider an appellant's argument if it is based on a theory that is raised for the first time in the appeal.

Hence, the Rb / Sr ratio in residual magma may increase over time, resulting in rocks with increasing Rb / Sr ratios with increasing differentiation.

Hence positive punishment is sometimes a confusing term, as it denotes the " addition " of a stimulus or increase in the intensity of a stimulus that is aversive ( such as spanking or an electric shock ).

Hence, the losses increase faster in the rotor than in the stator.

Hence in liquid helium, its ground state energy can decrease by a naturally-occurring increase in its average interatomic distance.

Hence, government provision of UI has the potential to increase efficiency.

Hence, an increase in angle dθ by implies traces an arc of magnitude dθ, and as is orthogonal to, we have:

Hence, demand may expand or contract and increase or decrease.

Hence, there are more particles losing energy to the wave than gaining from the wave, which leads to a resultant increase in the wave energy.

Hence Somerville's insistence on a refit to increase her speed.

Hence, improving technology would tend to increase, rather than reduce, the rate at which England's coal deposits were being depleted.

Hence, it is necessary to increase the collision probability of the particles at the interaction point for each bunch crossing.

Hence to increase the reaction rate, high temperatures ( 450 ° C ), medium pressures ( 1-2 atm ), and vanadium ( V ) oxide ( V < sub > 2 </ sub > O < sub > 5 </ sub >) are used to ensure a 96 % conversion.

Hence, the Rb / Sr ratio in residual magma may increase over time, resulting in rocks with increasing Rb / Sr ratios with increasing differentiation.