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 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.

Especially important is the development of The OWLS Sports Club ( Opportunities Without Limits ), which will coordinate the development of a range of different sporting opportunities for persons with physical and / or learning eisabilities, and in many cases their siblings.

Without loss of generality this can be expressed in a simplified form after translation of the vertex A to the origin of the Cartesian coordinate systems, i. e., when.

Without a system of values there can be no society.

Without a writing system, the Ainu were masters of narration, with the Yukar and other forms of narration such as the Uepeker ( Uwepeker ) tales, being committed to memory and related at gatherings, often lasting many hours or even days.

Without this double feedback, the system would still be bistable, but would not be able to tolerate such a wide range of concentrations.

Without the price system to match consumer utility to incentives for production, or even indicate those utilities " without providing incentives ", state planners are much less likely to invest in new ideas to satisfy consumers ' desires.

Without soil as a buffer, any failure to the hydroponic system leads to rapid plant death.

Without a king, the entire colonial system lost its legitimacy, and the colonists revolted.

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 some specification of the self-reproducing steps, a genome-only system is probably better characterized as something like a crystal.

Without drugs in his system, THX falters during critical and hazardous phases of his job.

Without a robust whistleblower system, directors / trustees of the organization may fail in their oversight responsibilities.

Without such instrumentation one might have to have someone crouched over Windows Task Manager at the server to see how much CPU load the performance tests are generating ( assuming a Windows system is under test ).

"(...) Without taking the argument that far, it is evident that in a market system with uneven distribution of empowering work, such as Economic Democracy ( the model of market socialism David Schweickart has developed and refers to as " economic democracy "), some workers will be more able than others to capture the benefits of economic gain.

Without an extra Global navigation satellite system, receiver tracking is difficult, but not impossible, as the position of a mobile unit can be determined using a Doppler shift calculation from the satellite.

Without a sturdy and organized supply system and with overextended supply lines, Russian soldiers found it difficult to maintain combat readiness and good health.

# Without there would be an empty space between and in the Greek sound system (), and a voiced affricate would not have a voiceless correspondent.

Without him, the two empires go to war, and the Borg are able to enter the solar system.

Without a new tax bill and budgetary cuts, the nation would face even higher inflation " and the possible collapse of the monetary system ".

Without a crew or CSM, there was no need for a launch escape system.

Without effective water treatment, a cooling water system can suffer from scale formation, corrosion and fouling and may become a breeding ground for harmful bacteria such as those that cause Legionnaires ' Disease.

Without clarification from Sharp, it would seem their intention is to abandon the Linux powered devices, as their newest units are the WS003SH and WS004SH which, whilst adding wireless and cellular phone and data features, run the Windows Mobile 5. 0 operating system / application suite.

Without courts or law officers in the mining communities to enforce claims and justice, miners developed their own ad hoc legal system, based on the " mining codes " used in other mining communities abroad.

Without its founders active involvement, the system languished.