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In particular, it can be defined as a Dirichlet series, it has an Euler product expansion, it satisfies a functional equation, it has an analytic continuation to a meromorphic function on the complex plane C with only a simple pole at s = 1, and its values encode arithmetic data of K. The extended Riemann hypothesis states that if ΞΆ < sub > K </ sub >( s ) = 0 and 0 < Re ( s ) < 1, then Re ( s ) = 1 / 2.
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particular and can
Second, we can make assistance for particular projects conditional on the consistency of such projects with the program.
A group of native trees or plants which are outstanding in a particular county can be featured at the site.
It supplies local data which are useful in administration and which can be used as a basis for intensive studies in particular situations.
The practical operational problem of lexicostatistics is the establishment of a basic list of items of meaning against which the particular forms or terms of languages can be matched as the medium of comparison.
If he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??
What we can attempt with some hope of dependable conclusions is to point out the manner in which Christianity entered into particular aspects of the life of the nation.
Tylor in particular laid the groundwork for theories of cultural diffusionism, stating that there are three ways that different groups can have similar cultural forms or technologies: " independent invention, inheritance from ancestors in a distant region, transmission from one race to another.
The specific procedures for appealing, including even whether there is a right of appeal from a particular type of decision, can vary greatly from country to country.
Some appellate courts, particularly supreme courts, have the power of discretionary review, meaning that they can decide whether they will hear an appeal brought in a particular case.
Notably, these alerts can be customized to the particular person's risks.
Speakers from the different states of Austria can easily be distinguished from each other by their particular accents ( probably more so than Bavarians ), those of Carinthia, Styria, Vienna, Upper Austria, and the Tyrol being very characteristic.
In many cases such a selection can be made without invoking the axiom of choice ; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin.
Expanding upon Foucault's position, Alexander Nehamas writes that Foucault suggests " an author [...] is whoever can be understood to have produced a particular text as we interpret it ", not necessarily who penned the text.
While a character with Pattern, Logrus or Conjuration can acquire virtually any object, players can choose to spend character points to obtain objects with particular virtues-unbreakability, or a mind of their own.
In astronomy, a given point on the celestial sphere ( that is, the apparent position of an astronomical object ) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system.
The term may also refer to the physical region where the electron can be calculated to be, as defined by the particular mathematical form of the orbital.
Zwitterions have minimum solubility at their isolectric point and some amino acids ( in particular, with non-polar side-chains ) can be isolated by precipitation from water by adjusting the pH to the required isoelectric point.
With some simplifications, in particular constant density, they can be given as follows:
The < tt > MixColumns </ tt > step can also be viewed as a multiplication by a particular MDS matrix in a finite field.
A case can be made that discriminatory lines came to be drawn more sharply under Athenian democracy than before or elsewhere, in particular in relation to woman and slaves, as well as in the line between citizens and non-citizens.
Exact ( not asymptotic ) measures of efficiency can sometimes be computed but they usually require certain assumptions concerning the particular implementation of the algorithm, called model of computation.
The back and sides of a particular guitar are typically made of the same wood ; Brazilian or East Indian rosewood and Honduras mahogany are traditional choices, however, maple has been prized for the figuring that can be seen when it is cut in a certain way ( such as " flame " and " quilt " patterns ).
For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours ( 95 %) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour.
To express even smaller angles, standard SI prefixes can be employed ; in particular, the milliarcsecond, abbreviated mas, is used in astronomy.
particular and be
Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.
For Rachel, conceded to be the prettiest of the Szold girls -- and she did make a pretty picture sitting in the grape-arbor strumming her guitar and singing in her silvery tones -- there was no particular March counterpart ; ;
Moreover, because of the particular blot on your family escutcheon through what may only have been one unbridled moment on your grandmother's part, and because you had the lean-to kitchen and trundle bed of your childhood to outgrow, what you obviously most desired with both your conscious and unconscious person, what you bent your whole will, sensibility, and intelligence upon, was to be a lady.
In any inquiry into the way in which great literature affects the emotions, particularly with respect to the sense of harmony, or relief of tension, or sense of `` a transformed inner nature '' which may occur, a most careful exploration of the particular feature of the experience which produces the effect would be required.
It would seem, then, that movable property and equipment is not taxed as a whole but that certain types are taxed in towns where this is bound to be expedient for that particular kind of personal property.
It is not clear, however, whether they are thinking of all movable property or only of boats, trailers, aircraft or certain other types of personal property whose assessment would be advantageous to their particular towns.
In preparing the state guide plan, particular attention will be given means of strengthening the economy of the state through the development of industry and recreation.
The Armed Forces Epidemiological Board agreed to submit each month a report for one of its 12 commissions, so that each commission will report once a year on some phase of its work calculated to be of particular interest and value to medical officers of the Armed Forces.
If the resulting difference for the particular State is less or more than these extremes, the State's allotment percentage must be raised or lowered to the appropriate extreme.
If the resulting difference for the particular State is less or more than these extremes, the State's Federal share must be raised or lowered to the appropriate extreme.
While there should be no general age limit or restriction to one sex, there will be particular projects requiring special maturity and some open only to men or to women.
The extent of such interference -- which may be so slight as to be undetectable at any point where either of the stations renders a usable signal, or may be so great as to virtually destroy the service areas of both stations -- depends on many factors, among the principal ones being the distance between the stations, their respective radiated power, and, of particular significance here, the time of day.
However, in this case as elsewhere it was necessary to arrive at a single standard to be applied to all situations, representing an averaging of conditions, and thus to fix particular points in time which would be considered the dividing points between daytime and nighttime conditions.
Often, in working out-of-doors under all conditions of light and atmosphere, a particular passage that looked favorable in relation to the subject will be too bright, too dull, or too light, or too dark when viewed indoors in a mat.
Institutionalization Though undoubtedly all six processes are operative within the whole social system and its subsystems, two processes that are of crucial importance to this study will be singled out for particular emphasis.
For no particular reason, other than that the writer felt it might -- just might -- encourage both mates to be in attendance.
This approach requires that: ( 1 ) each text word be separated into smaller elements to establish a correspondence between the occurrence and dictionary entries, and ( 2 ) the information retrieved from several entries in the dictionary be synthesized into a description of the particular word.
Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.
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