Since both the normal and the Cauchy distribution are stable distributions, they are closed under convolution and it follows that the Voigt distribution will also be closed under convolution.

Since T is uniformly continuous on its domain, Tf < sub > j </ sub > is Cauchy in B < sub > 2 </ sub >.

Since the parameter is usually time, Cauchy conditions can also be called initial value conditions or initial value data or simply Cauchy data.

Since a black hole Cauchy horizon only forms in a region where the geodesics are outgoing, in radial coordinates, in a region where the central singularity is repulsive, it is hard to imagine exactly how it forms.

Since the Phage Φ-X174 was sequenced in 1977, the DNA sequences of thousands of organisms have been decoded and stored in databases.

Since they showed pictorial sequences of men and corpses covered with shrouds, those paintings are sometimes regarded as cultural precursors of the new genre.

Since 1993, the circumscriptions of these two subfamilies have been changed in light of phylogenetic studies of DNA sequences.

Since the chain termination method of DNA sequencing can only be used for fairly short strands ( 100 to 1000 basepairs ), longer sequences must be subdivided into smaller fragments, and subsequently re-assembled to give the overall sequence.

Since it sequences its laws by subject matter instead of by biblical context, the Mishnah discusses individual subjects more thoroughly than the Midrash, and it includes a much broader selection of halakhic subjects than the Midrash.

Since 1998, dancers have been required to include certain elements in their free dances, including step sequences, lifts, dance spins, and multi-rotation turns called twizzles.

Since the supremum and infimum of an unbounded set of real numbers may not exist ( the reals are not a complete lattice ), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the complete totally ordered set, which is a complete lattice.

Since the flag sequence could appear in user data, such sequences must be modified during transmission to keep the receiver from detecting a false frame delimiter.

Since Close Encounters was filmed anamorphically, the visual effects sequences were shot in 70 mm film to better conform with the 35 mm film used for the rest of the movie.

Since the 1815 eruption, the lowermost portion contains deposits of interlayered sequences of lava and pyroclastic materials.

Since it is possible to find sequences of 16 consecutive integers such that each inner member shares a factor with either the first or the last member, 16 is an Erdős – Woods number.

Since the development of methods of high-throughput production of gene and protein sequences, the rate of addition of new sequences to the databases increased exponentially.

Since the very first sequences of the insulin protein was characterised by Fred Sanger in 1951 biologists have been trying to use this knowledge to understand the function of molecules.

Since presently-available DNA sequencing technologies are ill-suited for reading long sequences, large pieces of DNA ( such as genomes ) are often sequenced by ( 1 ) cutting the DNA into small pieces, ( 2 ) reading the small fragments, and ( 3 ) reconstituting the original DNA by merging the information on various fragment.

Since S is non-empty, there is a rational number L such that L < s for some s in S. Now define sequences of rationals ( u < sub > n </ sub >) and ( l < sub > n </ sub >) as follows:

Since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member, 78 is an Erdős – Woods number.

Since it is possible to find sequences of 70 consecutive integers such that each inner member shares a factor with either the first or the last member, 70 is an Erdős – Woods number.

Since some original sequences did not fit in the ports for those systems, they were re-released only in a virtual sequel called Escape from Singe's Castle.

Since it is possible to find sequences of 22 consecutive integers such that each inner member shares a factor with either the first or the last member, 22 is an Erdős – Woods number.

Since it is possible to find sequences of 88 consecutive integers such that each inner member member shares a factor with either the first or the last member, 88 is an Erdős – Woods number.

Since it is possible to find sequences of 76 consecutive integers such that each inner member shares a factor with either the first or the last member, 76 is an Erdős – Woods number.

Beginning in 1992, data were published that reported sequences of genes belonging to the Crenarchaea in marine environments .< sup >,</ sup > Since then analysis of the abundant lipids from the membranes of Crenarchaea taken from the open ocean have been used to determine the concentration of these “ low temperature Crenarchaea ” ( See TEX-86 ).

Since it is possible to find sequences of 86 consecutive integers such that each inner member member shares a factor with either the first or the last member, 86 is an Erdős – Woods number.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since we can neither undo nor redo the past, we are limited to the events of today and tomorrow.

Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.

Since he can neither accept nor reject them all, he must be governed by the time and energy available for his prime professional obligations.

Since a Skeletal Age rating can be made at any age during growth, from Elbow, Shoulder, Knee, or Foot as well as Hand, it seems to be the method of choice when one wishes to study most aspects of skeletal developmental progress during childhood.

A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

Since morale is closely related to pattern maintenance and integration, the higher the morale and solidarity, the better the system can solve the problems of the system.

Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.

Since effective area coverage appears fairly remote, the requirement can be borne in mind while considering the elements: air, surface, sub-surface, fixed installations, mines, and intelligence.

Since the load L, under actual cutting conditions is caused by Af, it can be seen that Af

Since we are considering here relatively small diameter ( 1 - 1.5 inches ) fiber plates, their average thickness can be kept below 1/4 inch and their internal losses may be assumed as 15 percent ( per plate ).

Since the change to better nutrition, he feels he can report on improvements in health, though he considers the following statements observations and not scientific proof.

Since rococo music tends to be pretty and elegant above all, it can seem rather vacuous to twentieth-century ears that have grown accustomed to the stress and dissonances of composers from Beethoven to Boulez.

`` Since we're having coffee with them this afternoon '', he said, `` I think I'll ask the daughter if we can pay her to come in every day to clean for us ''.

Since altruism takes away resources from the altruist it can be a " honest signal " of resource availability and the abilities needed to gather resources.

Since the minting of coins was a prerogative accorded in Islamic practice only to a sovereign, it can be considered that Osmanli became independent of the Mongol Khans.

Since in oral languages the elements of sound are for the most part produced linearly in time ( that is, in a word like cat the a sound comes after the c sound, and the t sound comes after that ), they can generally be easily written in a linear ( one-dimensional ) writing system such as an alphabet.

Since Java's bytecode is platform-independent, Java applets can be executed by browsers running under many platforms, including Windows, Unix, Mac OS, and Linux.

Since the fluctuations are assumed to be small, products of the fluctuation terms can be neglected ( to first order ) and we have

Since all anchors that embed themselves in the bottom require the strain to be along the seabed, anchors can be broken out of the bottom by shortening the rode until the vessel is directly above the anchor ( at this point the anchor chain is " up and down " in naval parlance ).

Since 4 % can be expressed as. 04, gives the amount of alcohol in terms of ml — which, when divided by, shows the number of units.

Since algorithms are platform-independent ( i. e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system ), there are significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.

Since the target audience of pop music can vary greatly, so can the celebrated subject of the anthem.