If the player loses all of their lives or runs out of time, they have the option to continue at the cost of a considerable sum of their overall points.

She runs away from Alfitaria during the game because she is scared of her duties, but is eventually inspired by the caravan and decides to return home giving a large sum of money to the caravan.

A Gaussian period P is a sum of the primitive n-th roots of unity, where runs through all of the elements in a fixed coset of H in G.

where the sum runs over all pairs p, q with p + q = k and where

Then the sum S < sub > t </ sub > of the Q < sub > a, t </ sub >, where a runs over all the roots of P, can be taken as a particular Q < sub > t </ sub >.

Each competitor has two runs on the course, and the final result is based either on the faster run ( in smaller races or lower division races ) or the sum of the two runs ( in national and international competitions ).

Extra base hits are often not listed separately in tables of baseball statistics, but are easily determined by calculating the sum total of a batter's doubles, triples, and home runs.

These generators are paid a sum based on their peak net supply over three proving runs over the course of the year.

The number of a team's plate appearances is to equal the sum of that team's runs, that team's LOB, and the opposing team's putouts.

( Here, the graph Γ ( T ) is a linear subspace of the direct sum, defined as the set of all pairs, where x runs over the domain of T ).

We can replace N by its complex group algebra C, and again form a product in a similar way ; this algebra is a sum of subspaces gC as g runs through the elements of G, and is the group algebra of.

She had quarreled with Lucien, she had resisted his demands for money -- and if she died, by the provisions of her marriage contract, Lucien would inherit legally not only the immediate sum of gold under the floorboards in the office, but later, when the war was over, her father's entire estate.

where the first sum is over positive energy states and the second over those of negative energy.

He soon transferred his services to Teos's cousin and rival Nectanebo II, who, in return for his help, gave him a sum of over 200 talents.

For private suits the minimum jury size was 201 ( increased to 401 if a sum of over 1000 drachmas was at issue ), for public suits 501.

and mean that the sum or product is over all prime numbers:

Similarly, and mean that the sum or product is over all prime powers with strictly positive exponent ( so 1 is not counted ):

and mean that the sum or product is over all positive divisors of n, including 1 and n.

The notations can be combined: and mean that the sum or product is over all prime divisors of n.

and similarly and mean that the sum or product is over all prime powers dividing n.

If more than one wavelength is present ( as is usually the case ), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.

Corporatism refers to a form of collectivism that views the whole as being greater than the sum of its individual parts, and gives priority to group rights over individual rights.

The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories.

In sum, given an equivalence relation ~ over A, there exists a transformation group G over A whose orbits are the equivalence classes of A under ~.

Some ecological principles, however, do exhibit collective properties where the sum of the components explain the properties of the whole, such as birth rates of a population being equal to the sum of individual births over a designated time frame.

If we allow to incorporate the algebraic sign, this becomes a sum and implies that there is a function of state which is conserved over a complete cycle.

In such case the total decay rate is the sum over all rates:

The amplitude for scattering is the sum of each possible interaction history over all possible intermediate particle states.

The Dyson series can be alternately rewritten as a sum over Feynman diagrams, where at each interaction vertex both the energy and momentum are conserved, but where the length of the energy momentum four vector is not equal to the mass.

:, where is the sum over any n-sequence of length N.

: where is the sum over any k-sequence of length N.

In her prime, she made over $ 50, 000 a year, then a vast sum, far more than her husband's $ 20, 000 per year.

where the sum is taken over all particles and their corresponding potentials ; the result is that the Hamiltonian of the system is the sum of the separate Hamiltonians for each particle.

Determine the sum of the products obtained in item 8 above, for all the States.

Determine the ratio that the amount being allotted is to the sum of the products for all the States.

I discern no limits to a faith vested in God and Christ, who is the sum of all wisdom and knowledge, and daring to trust Him even though called to stand alone before the world.

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

and the latter is the total sum of all the numbers in the square, by which all the other numbers are overshadowed and in which they may be said to be absorbed.

it is also their mathematical mean, since it is equal to half the sum of every opposing pair, all of which equal 10.

Anarcho-capitalists argue for a society based on the voluntary trade of private property and services ( in sum, all relationships not caused by threats or violence, including exchanges of money, consumer goods, land, and capital goods ) in order to minimize conflict while maximizing individual liberty and prosperity.

The Trust was funded by a gift of $ 10 million ( a then unprecedented sum: at the time, total government assistance to all four Scottish universities was about £ 50, 000 a year ) and its aim was to improve and extend the opportunities for scientific research in the Scottish universities and to enable the deserving and qualified youth of Scotland to attend a university.

As the title implies, any active device received the sum of all transmitted messages in universal space-time, in a single pulse, so that demultiplexing yielded information about the past, present, and future.

In February 1705, Queen Anne, who had made Marlborough a Duke in 1702, granted him the Park of Woodstock and promised a sum of £ 240, 000 to build a suitable house as a gift from a grateful crown in recognition of his victory – a victory which British historian Sir Edward Shepherd Creasy considered one of the pivotal battles in history, writing – " Had it not been for Blenheim, all Europe might at this day suffer under the effect of French conquests resembling those of Alexander in extent and those of the Romans in durability.

The slope of the surface adjusts to make all three forces sum to zero.

To quote Anthony and Brackett: Moreover, because the element of water does not move, the sum of all three forces must be zero.

* Arithmetic mean – the sum of all measurements divided by the number of observations in the data set

The total contact force on the particular internal surface is then expressed as the sum ( surface integral ) of the contact forces on all differential surfaces:

Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by

In On War, Clausewitz sees all wars as the sum of decisions, actions, and reactions in an uncertain and dangerous context, and also as a socio-political phenomenon.

The censors had the general superintendence of all the public buildings and works ( opera publica ), and to meet the expenses connected with this part of their duties, the senate voted them a certain sum of money or certain revenues, to which they were restricted, but which they might at the same time employ according to their discretion.

The reflected light being the sum of the incoming light ( L < sub > i </ sub >) from all directions, multiplied by the surface reflection and incoming angle.

He theorized that all humans are born free of any knowledge and are the sum of their experiences.