Without this capacity, which is often the case in practice, to produce a representation with lower resolution or lower fidelity than a given one, one needs to start with the original source signal and encode, or start with a compressed representation and then decompress and re-encode it ( transcoding ), though the latter tends to cause digital generation loss.

Without dubbing capability, an audio or video edit could not be done in-place on master cassette, and requires the editing output be captured to another tape, incurring generational loss.

Without loss of generality we assume

Without hormone replacement therapy ( HRT ), typical symptoms ( similar to those experienced by menopausal women ) include hot flashes, gradual bone-density loss resulting in osteopenia or osteoporosis, and potential weight gain or redistribution of body fat to the hips / chest.

Without loss of generality, we will define the optical axis so that it coincides with the z-axis of a fixed coordinate system.

Without loss of generality we can assume at least 3 of these edges, connecting to vertices r, s and t, are blue.

Without loss of generality, we will take λ to be non-negative.

# REDIRECT Without loss of generality

Without loss of generality ( abbreviated to WLOG ; less commonly stated as without any loss of generality or with no loss of generality ) is a frequently used expression in mathematics.

Without loss of generality, the coordinate system can be shifted, such that the reference point is set to be the origin.

Without this drug, Jem ' Hadar go into severe withdrawal, resulting in loss of cognitive and motor functions.

Without loss of generality, assume that the first columns of are linearly independent.

Without loss of generality, let's assume that.

* Without loss of generality, a common expression in mathematical proofs

* Without loss of generality –

Without loss of generality, we can take this action to be effective.

Without loss of generality, it can be assumed that D is connected.

Without these subsidies, global deep-sea fisheries would operate at a loss of $ 50 million a year.

Without it dispersion causes the loss of integrity of the original waveshape and is seen as smearing of what were originally sharp edges in the picture.

Without the ATU, SWR from a mismatched antenna could cause reflections of power back into the transmitter, which will cause heating in the transmitter and significant power loss.

Without loss of generality, let there exist a function such that

Without loss of generality, we may eliminate the normal rotational symmetry by choosing the Cartesian coordinates such that the z-axis is aligned with the angular momentum vector L and the momentum hodographs are aligned as they are in Figure 7, with the centers of the circles on the y-axis.

This bonus is multiplied according to the contract ; if the contract is Guard Without, the gain or loss for a single hand score is adjusted by 40 points one way or the other.

* Without affecting the generality of the main objects, the Society shall have the following ancillary objects:

Without loss of generality, we can demand also that j ( M ) contains all its sequences of length λ.

Without loss of generality, we can consider only centered profiles which peak at zero.

Without loss of generality, consider firm 1's problem:

Without loss of generality, we can take the projection line to be the x-axis.

Without loss of generality, we can take that plane to be the yz-plane so that

Without loss of generality, choose a coordinate system so that the axis of revolution is the z axis.

Without loss of generality, this edge is usually chosen to be the closest one on a face, so that in parallel view this edge corresponds to the same one in a perspective view.

Without saying or seeming to say that in portraying the Sartoris and the Compson families Faulkner's chief concern is social criticism, we can say nevertheless that through those families he dramatizes his comment on the planter dynasties as they have existed since the decades before the Civil War.

Without the good magazines, without their book reviews, their hospitality to European writers, without above all their awareness of literary standards, we might very well have had a generation of Krim's heroes -- Wolfes, Farrells, Dreisers, and I might add, Sandburgs and Frosts and MacLeishes in verse -- and then where would we be??

Without this power we lay open any American industry which the Europeans may find it economically profitable to destroy to the will of others.

Without such uncertainty we are left with a set of dogmas and myths.

Without agreeing with every phrase in this statement, we must certainly assert the great difference between Christian love and any form of resistance, and then go on beyond the Mennonite position and affirm that Christian love-in-action must first justify and then determine the moral principles limiting resistance.

Without such a declaration, Paine concluded, “ he custom of all courts is against us, and will be so, until, by an independence, we take rank with other nations .”

: " Without mercy, without sparing, we will kill our enemies in scores of hundreds.

If only layer C changes, we should find a way to avoid re-blending all of the layers when computing F. Without any special considerations, four full-image blends would need to occur.

Without ambiguity, for all in, we denote by the unique inverse of.

Without it, we will turn back the sexual revolution and return to an earlier, puritanical time.

Without limits on rage against our enemies, we are worse than animals.

The Philadelphia Press drama critic said, " Without having brother Edwin's culture and grace, Mr. Booth has far more action, more life, and, we are inclined to think, more natural genius.

" Without the help of Doña Marina ," he writes, " we would not have understood the language of New Spain and Mexico.

Without altering the system, we can take multiple samples, which will have a range of values of k, but the system will always be characterized by the same λ.

Without at least one of these two pieces of information, we are not obviously justified in seeing design in such cases … he problem for the fine-tuning argument is that we lack both of the pieces that are needed to justify an inference of design.

Without assuming this spatial and temporal invariance, we have no basis for extrapolating from the known to the unknown and, therefore, no way of reaching general conclusions from a finite number of observations.

Without compromising our principles, we must convince and win back former Republicans, and we must reinforce our ranks with Constitution-loving Democrats.

: Without hoping to know whether each separate hypothesis is true or false, we may search for rules to govern our behaviour with regard to them, in following which we insure that, in the long run of experience, we shall not be too often wrong.

Without, in any way, referring to the merits of the Cause in which we have been engaged, your courage and determination, as exhibited on many hard-fought fields, has elicited the respect and admiration of friend and foe.