Least time

The least time eonsuming route here is to evaluate eaeh of the needed integrals first. 

Fundamental to the understanding of optics is the Principle of Least Time, developed by Fermat ( 1650), which says that light will take the path that... 

The principle of least time can also be used to examine reflection. If we perform a similar experiment to that above except that we make one medium reflective at the boundary we will discover that the only paths for which the flight time of the photon is a minimum are those for which the angle of incidence equals the angle of reflection. 

Use Lagrange s method of multipliers to derive the law of refraction of light from Fermat s principle of least time between two fixed points. 

To develop a system of mechanics from here without the introduction of any other concepts, apart from energy, some general principle that predicts the course of a mechanical change is required. This could be like the Maupertuis principle of least action or Fermat s principle of least time. It means that the actual path of the change will have an extreme value e.g. minimum) of either action or time, compared to all other possible paths. Based on considerations like these Hamilton formulated the principle that the action integral... 

Although all the methods mentioned above can generate reproducibly sized tumor spheroids, the one that we recommend is the method that uses round-bottom ultralow attachment 96-well plates (11). This method is the least time consuming (e.g., plates do not require any coating), reproducible (one centrally located spheroid/well is formed), and suitable for automated imaging. Thus it satisfies important requirements of cell-based HT assays. 

The least time consuming route here is to evaluate each of the needed integrals first. These are evaluated analogous to exercise 1, letting denote each of the individual Slater Type Orbitals. 

The aim of sample preparation is that the components of interest should be extracted from complex matrices with the least time and energy consumption but with highest efficiency and reproducibility. Conditions should be mild enough to avoid oxidation, thermal degradation, and other chemical and biochemical changes. Some procedures — CE, for example — necessitate more rigorous sample pretreatment than others. On the other hand, TLC requires an absolute minimum of sample preparation. 

Hold at Intermediate Hold Temperature for at least Time 1... 

No matter what kind of constraint is imposed, organizations must allow adequate time for validation. At the very least, time must be allotted for some degree of planning, for the requisite number of events planned to occur, and for the gathering of the results. If the validating department has been given a drop dead date for validation and if this date will not support the items mentioned above, there is likely no need to begin validation. 

The law of geometrical optics anticipated by Hero of Alexandria was formulated by Fermat (1601-1655) as a principle of least time, consistent with Snell s law of refraction (1621). The time for phase transmission from point P to point Q along a path x(r) is given by... 

Since the Forster cycle provides the simplest and least time-consuming route to p.K, it is not surprising that most values have been determined in this way, nor that there are many more pi Sx) entries than p-K(Tj). In all cases p.K-values are quoted as they appear in the original papers, although determinations of this kind cannot be reliable to better than 0-2 p/ units (corresponding to an error of... 

The above discussion implicitly obeys Huygens 97 principle, that each point on a spherical wavefront can be regarded as the source of a secondary wavelet (another spherical wave), as well as Fermat s98 principle of least time. 

A comparison of the batch and the SMB modes proved to greatly favor SMB The productivity and the eluent consumption was improved by three at least times using SMB. 

Not only mechanics but all of physics can be derived from the principle of least action. There are appropriate Lagrangian functions for electrodynamics, quantum mechanics, hydrodynamics, etc., which all allow us to derive the basic equations of the respective discipline from the principle of least action. In this sense, the principle of least action is the most powerful economy principle known in physics since it is sufficient to know the principle of least action, and the rest can be derived. Nature as a whole seems to be organized according to this principle. The principle of least action can be found under various names in nearly every branch of science. For instance the principle of least cost in economy or Fermat s principle of least time in optics. 

Classical methods of final measurement will long continue to be important. In the first place, they are inherently simple. For an occasional determination or standardization the use of a titration or gravimetric determination often will require the least time and effort and will involve no investment in expensive equipment. Second, classical methods are accurate. Many instrumental methods are designed for speed or sensitivity rather than accuracy, and often must be calibrated by classical methods. 

Chiral selector Immobilized great number of commercially available CSPs a combination of chiral selectors is difficult or at least time-consuming. Commonly mobile, commercially available chiral selectors are inexpensive, chiral selectors can be mixed in any desired ratio (only limited by the solubility). 

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