sec results from the CPAN

The default namespace is C<DPPP_>.

=back

The good thing is that most of the above can be checked by running
F<ppport.h> on your source code. See the next section for
details.

=head1 EXAMPLES

To verify whether F<ppport.h> is needed for your module, whether you

 * 1. #define MY_CXT_KEY to a unique string, e.g. "DynaLoader_guts"
 * 2. Declare a typedef named my_cxt_t that is a structure that contains
 *    all the data that needs to be interpreter-local.
 * 3. Use the START_MY_CXT macro after the declaration of my_cxt_t.
 * 4. Use the MY_CXT_INIT macro such that it is called exactly once
 *    (typically put in the BOOT: section).
 * 5. Use the members of the my_cxt_t structure everywhere as
 *    MY_CXT.member.
 * 6. Use the dMY_CXT macro (a declaration) in all the functions that
 *    access MY_CXT.
 */

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Algorithm-Step

1 match

lib/Algorithm/Step.pm view on Meta::CPAN

=over 4

=item B<algorithm>

Begins an algorithm. It takes two arguments. The first one is the name of this
algorithm, the second one is the short description.

=item B<end_algorithm>

Ends an algorithm.

view all matches for this distribution

Algorithm-StringHash-FromCSharp35-XS

1 match

The default namespace is C<DPPP_>.

=back

The good thing is that most of the above can be checked by running
F<ppport.h> on your source code. See the next section for
details.

=head1 EXAMPLES

To verify whether F<ppport.h> is needed for your module, whether you

 * 1. #define MY_CXT_KEY to a unique string, e.g. "DynaLoader_guts"
 * 2. Declare a typedef named my_cxt_t that is a structure that contains
 *    all the data that needs to be interpreter-local.
 * 3. Use the START_MY_CXT macro after the declaration of my_cxt_t.
 * 4. Use the MY_CXT_INIT macro such that it is called exactly once
 *    (typically put in the BOOT: section).
 * 5. Use the members of the my_cxt_t structure everywhere as
 *    MY_CXT.member.
 * 6. Use the dMY_CXT macro (a declaration) in all the functions that
 *    access MY_CXT.
 */

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Algorithm-TicketClusterer

3 results

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN


    #  Of the various constructor parameters shown above, the following two
    #  are critical to how information is extracted from an Excel
    #  spreadsheet: `clustering_fieldname' and `unique_id_fieldname'.  The
    #  first is the heading of the column that contains the textual content
    #  of the tickets.  The second is the heading of the column that
    #  contains a unique integer identifier for each ticket.

    #  The nine database related constructor parameters (these end in the
    #  suffix `_db') are there in order to avoid repeated parsing of the
    #  spreadsheet and preprocessing of the tickets every time you need to

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

and corrects would, in general, depend on the application domain of the
tickets.  (It is not uncommon for engineering services to use jargon words
and acronyms that look like spelling errors to those not familiar with the
services.)  The module expects to see a file that is supplied through the
constructor parameter C<misspelled_words_file> that contains misspelled
words in the first column and their corrected versions in the second
column.  An example of such a file is included in the C<examples>
directory.  You would need to create your own version of such a file for
your application domain. Since conjuring up the misspellings that your
ticket submitters are likely to throw at you is futile, you might consider
using the following approach which I prefer to actually reading the tickets

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

WordNet.

=item I<min_idf_threshold:>

First recall that IDF stands for Inverse Document Frequency.  It is calculated during
the second of the three-stage processing of the tickets as described in the section
B<THE THREE STAGES OF PROCESSING TICKETS>.  The IDF value of a word gives us a
measure of the discriminatory power of the word.  Let's say you have a word that
occurs in only one out of 1000 tickets.  Such a word is obviously highly
discriminatory and its IDF would be the logarithm (to base 10) of the ratio of 1000
to 1, which is 3.  On the other hand, for a word that occurs in every one of 1000

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

As to what extent you can improve ticket retrieval precision with the addition of
synonyms depends on the degree to which you can make corrections on the fly for the
spelling errors that occur frequently in tickets.  That fact makes the file you
supply through this constructor parameter very important.  For the current version of
the module, this file must contain exactly two columns, with the first entry in each
row the misspelled word and the second entry the correctly spelled word.  See this
file in the C<examples> directory for how to format it.

=item I<processed_tickets_db:>

As mentioned earlier in B<DESCRIPTION>, the tickets must be subject to various

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

faster to load the database back into the runtime environment than to process a large
spreadsheet.

=item I<stemmed_tickets_db:>

As mentioned in the section B<THE THREE STAGES OF PROCESSING>, one of the first
things you do in the second stage of processing is to stem the words in the tickets.
Stemming is important because it reduces the size of the vocabulary.  To illustrate,
stemming would reduce both the words `programming' and `programmed' to the common
root 'program'.  This module uses a very simple stemmer whose rules can be found in
the utility subroutine C<_simple_stemmer()>.  It would be trivial to expand on these
rules, or, for that matter, to use the Perl module C<Lingua::Stem::En> for a full

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

given word regardless of how many times the word appears in all of the tickets.

=item I<which_worksheet:>

This specifies the Excel worksheet that contains the tickets.  Its value should be 1
for the first sheet, 2 for the second, and so on.

=back

=begin html

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN


=item  B<display_inverted_index_for_given_query( $ticket_id )>

The above three methods are useful for troubleshooting the issues that are related to
the generation of the inverted index.  The first method shows the entire inverted
index, the second the inverted index for a single specified word, and the third for
all the words in a query ticket.

=item  B<display_tickets_vocab()>

    $clusterer->display_tickets_vocab()

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN


=item  B<get_ticket_vocabulary_and_construct_inverted_index()>

    $clusterer->get_ticket_vocabulary_and_construct_inverted_index()

As mentioned in B<THE THREE STAGES OF PROCESSING>, the second stage of processing ---
doc modeling of the tickets --- starts with the stemming of the words in the tickets,
constructing a vocabulary of all the stemmed words in all the tickets, and
constructing an inverted index for the vocabulary words.  All of these things are
accomplished by this method.

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

=item  B<store_stemmed_tickets_and_inverted_index_on_disk()>

    $clusterer->store_stemmed_tickets_and_inverted_index_on_disk()

This method stores in a database file the stemmed tickets and the inverted index that
are produced at the end of the second stage of processing.

=item B<show_stemmed_ticket_clustering_data_for_given_id()>

    $clusterer->show_stemmed_ticket_clustering_data_for_given_id( $ticket_num );

lib/Algorithm/TicketClusterer.pm view on Meta::CPAN

    WordNet::QueryData
    Storable
    SDBM_File

the first for extracting information from the old-style Excel sheets that are
commonly used for storing tickets, the second for extracting the same information
from the new-style Excel sheets, the third for interfacing with WordNet for
extracting the synonyms and antonyms, the fourth for creating the various disk-based
database files needed by the module, and the last for disk-based hashes used to lend
persistence to the extraction of the alphabet used by the tickets and the inverse
document frequencies of the words.

view all matches for this distribution

Algorithm-TimelinePacking

4 results

lib/Algorithm/TimelinePacking.pm view on Meta::CPAN

use POSIX qw(floor);
use List::Util qw(max shuffle);

our $VERSION = '0.01';

# minimum space (in units, i.e. most frequently pixels) between 2 consecutive
# items on a line
has space => (
    is      => 'rw',
    isa     => Int->where('$_ >= 0'),
    default => 0,

lib/Algorithm/TimelinePacking.pm view on Meta::CPAN

=head2 space

    my $packer = Algorithm::TimelinePacking->new(space => 10);

Minimum space (in the same units as your timestamps) required between
consecutive intervals on the same line. Default: 0.

=head2 width

    my $packer = Algorithm::TimelinePacking->new(width => 800);

lib/Algorithm/TimelinePacking.pm view on Meta::CPAN


=over 4

=item 1.

Sort intervals by start time (secondary sort by end time)

=item 2.

Normalize all timestamps to start at 0

view all matches for this distribution

Algorithm-TokenBucket

4 results

lib/Algorithm/TokenBucket.pm view on Meta::CPAN

=over 4

=item new($$;$$)

The constructor requires at least the C<rate of information> in items per
second and the C<burst size> in items as its input parameters. It can also
take the current token counter and last check time but this usage is mostly
intended for restoring a saved bucket. See L</state()>.

=cut

lib/Algorithm/TokenBucket.pm view on Meta::CPAN

    ($self->{_tokens} -= $size) < 0 and $self->{_tokens} = 0;
}

=item until($)

This method returns the number of seconds until I<N> tokens can be removed
from the bucket. It is especially useful in multitasking environments like
L<POE> where you cannot busy-wait. One can safely schedule the next
C<< conform($N) >> check in C<< until($N) >> seconds instead of checking
repeatedly.

Note that C<until()> does not take into account C<burst size>. This means
that a bucket will not conform to I<N> even after sleeping for C<< until($N) >>
seconds if I<N> is greater than C<burst size>.

=cut

sub until {
    my Algorithm::TokenBucket $self = shift;

lib/Algorithm/TokenBucket.pm view on Meta::CPAN


Documentation lacks the actual algorithm description. See links or read
the source (there are about 20 lines of sparse Perl in several subs).

C<until($N)> does not return infinity if C<$N> is greater than C<burst
size>. Sleeping for infinity seconds is both useless and hard to debug.

=head1 ACKNOWLEDGMENTS

Yuval Kogman contributed the L</until($)> method, proper L<Storable> support
and other things.

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Algorithm-Toy-HashSC

1 match

lib/Algorithm/Toy/HashSC.pm view on Meta::CPAN

#
# Toy deterministic separate chain hash implementation, based on code in
# "Algorithms (4th Edition)" by Robert Sedgewick and Kevin Wayne. This
# code is not for any sort of use where performance is critical, or
# where malicious input may cause "Algorithmic Complexity Attacks" (see
# perlsec(1)).
#
# run perldoc(1) on this file for additional documentation

package Algorithm::Toy::HashSC;

lib/Algorithm/Toy/HashSC.pm view on Meta::CPAN

be added by varying the modulus, or changing the B<hash> or
B<hashcode> methods.

This module is not for use where performance is a concern, or where
untrusted user input may be supplied for the key material.
L<perlsec/"Algorithmic Complexity Attacks"> discusses why Perl's hash
are no longer deterministic and thus not suitable for deterministic
music composition.

=head1 CONSTRUCTOR

lib/Algorithm/Toy/HashSC.pm view on Meta::CPAN

the hash key can be an object that provides a B<hashcode> method, in
which case this issue falls out of scope of this module.

=head1 SEE ALSO

L<perlsec/"Algorithmic Complexity Attacks"> - details on why Perl's hash
do not behave so simply as that of this module do.

"Algorithms" (4th Edition) by Robert Sedgewick and Kevin Wayne.

L<Hash::Util> - insight into Perl's hashes.

view all matches for this distribution

Algorithm-TravelingSalesman-BitonicTour

1 match

lib/Algorithm/TravelingSalesman/BitonicTour.pm view on Meta::CPAN

=over 4

=item

Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford
(2001). Introduction to Algorithms, second edition, MIT Press and McGraw-Hill.
ISBN 978-0-262-53196-2.

=item

Bentley, Jon L. (1990), "Experiments on traveling salesman heuristics", Proc.

view all matches for this distribution

Algorithm-Tree-NCA

2 results

NCA.pm view on Meta::CPAN


=head1 EXAMPLES

=head2 ALGORITHM

This section describes the algorithm used for preprocessing and for
nearest common ancestor retrieval. It does not provide any intuition
to I<why> the algorithm works, just a description how it works. For
the algorithm description, it is assumed that the nodes themself
contain all necessary information. The algorithm is described in a
Pascal-like fashion. For detailed information about the algorithm,

NCA.pm view on Meta::CPAN

      Done
      node.max := num;
      Return (num,node.run)
  End;

In the second phase, we compute the I<leader> for each run (which we
can since we know the run for each node) and the I<magic> number. The
leader I<has> to be stored so that we can access is through a node
number, so we store it in an array.
  
  VAR Leader : Array [1..NODE_COUNT] of NodePtr;

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Algorithm-TrunkClassifier

4 results

lib/Algorithm/TrunkClassifier/Util.pm view on Meta::CPAN

use strict;

our $VERSION = 'v1.0.1';

#Description: Sorts two arrays in accending order based on values in the first
#Parameters: (1) Numerical array reference, (2) second array reference
#Return value: None
sub dataSort($ $){
	my ($numArrayRef, $secondArrayRef) = @_;
	my $limiter = 1;
	for(my $outer = 0; $outer < scalar(@{$numArrayRef}); $outer++){
		for(my $inner = 0; $inner < scalar(@{$numArrayRef}) - $limiter; $inner++){
			if(${$numArrayRef}[$inner] > ${$numArrayRef}[$inner+1]){
				my $buffer = ${$numArrayRef}[$inner];
				${$numArrayRef}[$inner] = ${$numArrayRef}[$inner+1];
				${$numArrayRef}[$inner+1] = $buffer;
				$buffer = ${$secondArrayRef}[$inner];
				${$secondArrayRef}[$inner] = ${$secondArrayRef}[$inner+1];
				${$secondArrayRef}[$inner+1] = $buffer;
			}
		}
		$limiter++;
	}
}

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Algorithm-VSM

20 results

examples/calculate_precision_and_recall_from_file_based_relevancies_for_VSM.pl view on Meta::CPAN

#    the documents relevant to each of the queries:
#$vsm->display_doc_relevancies();

#    Use only one of the following statements.  If you wish to carry out
#    precision vs. recall analysis for LSA, comment out the first and
#    uncomment the second.
$vsm->precision_and_recall_calculator('vsm');

$vsm->display_precision_vs_recall_for_queries();

$vsm->display_average_precision_for_queries_and_map();

view all matches for this distribution

Algorithm-Voting

1 match

t/sortition/10-rfc3797.t view on Meta::CPAN


my $avs = 'Algorithm::Voting::Sortition';
use_ok($avs);

# verify that A::V::S generates the same keystring as in
# L<http://tools.ietf.org/html/rfc3797#section-6>
{
    my @source = (
        "9319",
        [ qw/ 2 5 12 8 10 / ],      # <= this one gets sorted
        [ qw/ 9 18 26 34 41 45 /],

t/sortition/10-rfc3797.t view on Meta::CPAN

    my $ks = q(9319./2.5.8.10.12./9.18.26.34.41.45./);
    is ($avs->make_keystring(@source), $ks);
}

# verify that A::V::S generates checksums identical to
# L<http://tools.ietf.org/html/rfc3797#section-6>
{
    my $ks = q(9319./2.5.8.10.12./9.18.26.34.41.45./);
    my $box = Algorithm::Voting::Sortition->new(candidates => [], n => 10, keystring => $ks);
    is($box->n, 10);
    is($box->keystring, $ks);

view all matches for this distribution

Algorithm-WordLevelStatistics

1 match

sufficiently obvious to ensure that differences of opinion are
scarcely likely to arise as to its applicability in practice.

*** A refinement and modification of these views does not become
necessary until we come to deal with the general theory of relativity,
treated in the second part of this book.



SPACE AND TIME IN CLASSICAL MECHANICS

see the stone descend in a straight line. A pedestrian who observes
the misdeed from the footpath notices that the stone falls to earth in
a parabolic curve. I now ask: Do the "positions" traversed by the
stone lie "in reality" on a straight line or on a parabola? Moreover,
what is meant here by motion "in space" ? From the considerations of
the previous section the answer is self-evident. In the first place we
entirely shun the vague word "space," of which, we must honestly
acknowledge, we cannot form the slightest conception, and we replace
it by "motion relative to a practically rigid body of reference." The
positions relative to the body of reference (railway carriage or
embankment) have already been defined in detail in the preceding
section. If instead of " body of reference " we insert " system of
co-ordinates," which is a useful idea for mathematical description, we
are in a position to say : The stone traverses a straight line
relative to a system of co-ordinates rigidly attached to the carriage,
but relative to a system of co-ordinates rigidly attached to the
ground (embankment) it describes a parabola. With the aid of this

the man at the railway-carriage window is holding one of them, and the
man on the footpath the other. Each of the observers determines the
position on his own reference-body occupied by the stone at each tick
of the clock he is holding in his hand. In this connection we have not
taken account of the inaccuracy involved by the finiteness of the
velocity of propagation of light. With this and with a second
difficulty prevailing here we shall have to deal in detail later.


  Notes

the motion of the raven would be one of different velocity and
direction, but that it would still be uniform and in a straight line.
Expressed in an abstract manner we may say : If a mass m is moving
uniformly in a straight line with respect to a co-ordinate system K,
then it will also be moving uniformly and in a straight line relative
to a second co-ordinate system K1 provided that the latter is
executing a uniform translatory motion with respect to K. In
accordance with the discussion contained in the preceding section, it
follows that:

If K is a Galileian co-ordinate system. then every other co-ordinate
system K' is a Galileian one, when, in relation to K, it is in a
condition of uniform motion of translation. Relative to K1 the

relativity must therefore apply with great accuracy in the domain of
mechanics. But that a principle of such broad generality should hold
with such exactness in one domain of phenomena, and yet should be
invalid for another, is a priori not very probable.

We now proceed to the second argument, to which, moreover, we shall
return later. If the principle of relativity (in the restricted sense)
does not hold, then the Galileian co-ordinate systems K, K1, K2, etc.,
which are moving uniformly relative to each other, will not be
equivalent for the description of natural phenomena. In this case we
should be constrained to believe that natural laws are capable of

would be different from that emitted if the axis of the pipe were
placed perpendicular to this direction.

Now in virtue of its motion in an orbit round the sun, our earth is
comparable with a railway carriage travelling with a velocity of about
30 kilometres per second. If the principle of relativity were not
valid we should therefore expect that the direction of motion of the
earth at any moment would enter into the laws of nature, and also that
physical systems in their behaviour would be dependent on the
orientation in space with respect to the earth. For owing to the
alteration in direction of the velocity of revolution of the earth in

along the rails with a constant velocity v, and that a man traverses
the length of the carriage in the direction of travel with a velocity
w. How quickly or, in other words, with what velocity W does the man
advance relative to the embankment during the process ? The only
possible answer seems to result from the following consideration: If
the man were to stand still for a second, he would advance relative to
the embankment through a distance v equal numerically to the velocity
of the carriage. As a consequence of his walking, however, he
traverses an additional distance w relative to the carriage, and hence
also relative to the embankment, in this second, the distance w being
numerically equal to the velocity with which he is walking. Thus in
total be covers the distance W=v+w relative to the embankment in the
second considered. We shall see later that this result, which
expresses the theorem of the addition of velocities employed in
classical mechanics, cannot be maintained ; in other words, the law
that we have just written down does not hold in reality. For the time
being, however, we shall assume its correctness.



There is hardly a simpler law in physics than that according to which
light is propagated in empty space. Every child at school knows, or
believes he knows, that this propagation takes place in straight lines
with a velocity c= 300,000 km./sec. At all events we know with great
exactness that this velocity is the same for all colours, because if
this were not the case, the minimum of emission would not be observed
simultaneously for different colours during the eclipse of a fixed
star by its dark neighbour. By means of similar considerations based
on observa- tions of double stars, the Dutch astronomer De Sitter was

embankment. Now let us suppose that our railway carriage is again
travelling along the railway lines with the velocity v, and that its
direction is the same as that of the ray of light, but its velocity of
course much less. Let us inquire about the velocity of propagation of
the ray of light relative to the carriage. It is obvious that we can
here apply the consideration of the previous section, since the ray of
light plays the part of the man walking along relatively to the
carriage. The velocity w of the man relative to the embankment is here
replaced by the velocity of light relative to the embankment. w is the
required velocity of light with respect to the carriage, and we have

simultaneity; if we discard this assumption, then the conflict between
the law of the propagation of light in vacuo and the principle of
relativity (developed in Section 7) disappears.

We were led to that conflict by the considerations of Section 6,
which are now no longer tenable. In that section we concluded that the
man in the carriage, who traverses the distance w per second relative
to the carriage, traverses the same distance also with respect to the
embankment in each second of time. But, according to the foregoing
considerations, the time required by a particular occurrence with
respect to the carriage must not be considered equal to the duration
of the same occurrence as judged from the embankment (as
reference-body). Hence it cannot be contended that the man in walking
travels the distance w relative to the railway line in a time which is
equal to one second as judged from the embankment.

Moreover, the considerations of Section 6 are based on yet a second
assumption, which, in the light of a strict consideration, appears to
be arbitrary, although it was always tacitly made even before the
introduction of the theory of relativity.


A priori it is by no means certain that this last measurement will
supply us with the same result as the first. Thus the length of the
train as measured from the embankment may be different from that
obtained by measuring in the train itself. This circumstance leads us
to a second objection which must be raised against the apparently
obvious consideration of Section 6. Namely, if the man in the
carriage covers the distance w in a unit of time -- measured from the
train, -- then this distance -- as measured from the embankment -- is
not necessarily also equal to w.



THE LORENTZ TRANSFORMATION


The results of the last three sections show that the apparent
incompatibility of the law of propagation of light with the principle
of relativity (Section 7) has been derived by means of a
consideration which borrowed two unjustifiable hypotheses from
classical mechanics; these are as follows:

vertical direction by means of a framework of rods, so that an event
which takes place anywhere can be localised with reference to this
framework. Fig. 2 Similarly, we can imagine the train travelling with
the velocity v to be continued across the whole of space, so that
every event, no matter how far off it may be, could also be localised
with respect to the second framework. Without committing any
fundamental error, we can disregard the fact that in reality these
frameworks would continually interfere with each other, owing to the
impenetrability of solid bodies. In every such framework we imagine
three surfaces perpendicular to each other marked out, and designated
as " co-ordinate planes " (" co-ordinate system "). A co-ordinate

nothing more nor less than the results of measurements obtainable by
means of measuring-rods and clocks. If we had based our considerations
on the Galileian transformation we should not have obtained a
contraction of the rod as a consequence of its motion.

Let us now consider a seconds-clock which is permanently situated at
the origin (x1=0) of K1. t1=0 and t1=I are two successive ticks of
this clock. The first and fourth equations of the Lorentz
transformation give for these two ticks :

                                t = 0


                        eq. 07: file eq07.gif

As judged from K, the clock is moving with the velocity v; as judged
from this reference-body, the time which elapses between two strokes
of the clock is not one second, but

                        eq. 08: file eq08.gif

seconds, i.e. a somewhat larger time. As a consequence of its motion
the clock goes more slowly than when at rest. Here also the velocity c
plays the part of an unattainable limiting velocity.

THE EXPERIMENT OF FIZEAU


Now in practice we can move clocks and measuring-rods only with
velocities that are small compared with the velocity of light; hence
we shall hardly be able to compare the results of the previous section
directly with the reality. But, on the other hand, these results must
strike you as being very singular, and for that reason I shall now
draw another conclusion from the theory, one which can easily be
derived from the foregoing considerations, and which has been most
elegantly confirmed by experiment.


                      Figure 03: file fig03.gif


man walking along the carriage, or of the moving point in the present
section. If we denote the velocity of the light relative to the tube
by W, then this is given by the equation (A) or (B), according as the
Galilei transformation or the Lorentz transformation corresponds to
the facts. Experiment * decides in favour of equation (B) derived
from the theory of relativity, and the agreement is, indeed, very
exact. According to recent and most excellent measurements by Zeeman,


                        eq. 17: file eq17.gif


When eq. 18 is small compared with unity, the third of these terms is
always small in comparison with the second,

which last is alone considered in classical mechanics. The first term
mc^2 does not contain the velocity, and requires no consideration if
we are only dealing with the question as to how the energy of a
point-mass; depends on the velocity. We shall speak of its essential

the behaviour of the electron. We arrived at a similar conclusion in
Section 13 in connection with the experiment of Fizeau, the result
of which is foretold by the theory of relativity without the necessity
of drawing on hypotheses as to the physical nature of the liquid.

The second class of facts to which we have alluded has reference to
the question whether or not the motion of the earth in space can be
made perceptible in terrestrial experiments. We have already remarked
in Section 5 that all attempts of this nature led to a negative
result. Before the theory of relativity was put forward, it was
difficult to become reconciled to this negative result, for reasons

It is true that this important law had hitherto been recorded in
mechanics, but it had not been interpreted. A satisfactory
interpretation can be obtained only if we recognise the following fact
: The same quality of a body manifests itself according to
circumstances as " inertia " or as " weight " (lit. " heaviness '). In
the following section we shall show to what extent this is actually
the case, and how this question is connected with the general
postulate of relativity.

acceleration of the body towards the floor of the chest is always of
the same magnitude, whatever kind of body he may happen to use for the
experiment.

Relying on his knowledge of the gravitational field (as it was
discussed in the preceding section), the man in the chest will thus
come to the conclusion that he and the chest are in a gravitational
field which is constant with regard to time. Of course he will be
puzzled for a moment as to why the chest does not fall in this
gravitational field. just then, however, he discovers the hook in the
middle of the lid of the chest and the rope which is attached to it,

In the first place, it can be compared with the reality. Although a
detailed examination of the question shows that the curvature of light
rays required by the general theory of relativity is only exceedingly
small for the gravitational fields at our disposal in practice, its
estimated magnitude for light rays passing the sun at grazing
incidence is nevertheless 1.7 seconds of arc. This ought to manifest
itself in the following way. As seen from the earth, certain fixed
stars appear to be in the neighbourhood of the sun, and are thus
capable of observation during a total eclipse of the sun. At such
times, these stars ought to appear to be displaced outwards from the
sun by an amount indicated above, as compared with their apparent
position in the sky when the sun is situated at another part of the
heavens. The examination of the correctness or otherwise of this
deduction is a problem of the greatest importance, the early solution
of which is to be expected of astronomers.[2]*

In the second place our result shows that, according to the general
theory of relativity, the law of the constancy of the velocity of
light in vacuo, which constitutes one of the two fundamental
assumptions in the special theory of relativity and to which we have
already frequently referred, cannot claim any unlimited validity. A
curvature of rays of light can only take place when the velocity of

used before. Let us consider a space time domain in which no
gravitational field exists relative to a reference-body K whose state
of motion has been suitably chosen. K is then a Galileian
reference-body as regards the domain considered, and the results of
the special theory of relativity hold relative to K. Let us supposse
the same domain referred to a second body of reference K1, which is
rotating uniformly with respect to K. In order to fix our ideas, we
shall imagine K1 to be in the form of a plane circular disc, which
rotates uniformly in its own plane about its centre. An observer who
is sitting eccentrically on the disc K1 is sensible of a force which
acts outwards in a radial direction, and which would be interpreted as

them by means of a number. The Curves u= 1, u= 2 and u= 3 are drawn in
the diagram. Between the curves u= 1 and u= 2 we must imagine an
infinitely large number to be drawn, all of which correspond to real
numbers lying between 1 and 2. fig. 04 We have then a system of
u-curves, and this "infinitely dense" system covers the whole surface
of the table. These u-curves must not intersect each other, and
through each point of the surface one and only one curve must pass.
Thus a perfectly definite value of u belongs to every point on the
surface of the marble slab. In like manner we imagine a system of
v-curves drawn on the surface. These satisfy the same conditions as
the u-curves, they are provided with numbers in a corresponding

continua. For example, this obviously holds in the case of the marble
slab of the table and local variation of temperature. The temperature
is practically constant for a small part of the slab, and thus the
geometrical behaviour of the rods is almost as it ought to be
according to the rules of Euclidean geometry. Hence the imperfections
of the construction of squares in the previous section do not show
themselves clearly until this construction is extended over a
considerable portion of the surface of the table.

We can sum this up as follows: Gauss invented a method for the
mathematical treatment of continua in general, in which "

Minkowski found that the Lorentz transformations satisfy the following
simple conditions. Let us consider two neighbouring events, the
relative position of which in the four-dimensional continuum is given
with respect to a Galileian reference-body K by the space co-ordinate
differences dx, dy, dz and the time-difference dt. With reference to a
second Galileian system we shall suppose that the corresponding
differences for these two events are dx1, dy1, dz1, dt1. Then these
magnitudes always fulfil the condition*

     dx2 + dy2 + dz2 - c^2dt2 = dx1 2 + dy1 2 + dz1 2 - c^2dt1 2.


Thus, if we choose as time-variable the imaginary variable sq. rt. -I
. ct instead of the real quantity t, we can regard the space-time
contintium -- accordance with the special theory of relativity -- as a
", Euclidean " four-dimensional continuum, a result which follows from
the considerations of the preceding section.


  Notes

*) Cf. Appendixes I and 2. The relations which are derived

been known that the ellipse corresponding to the orbit of Mercury,
after it has been corrected for the influences mentioned above, is not
stationary with respect to the fixed stars, but that it rotates
exceedingly slowly in the plane of the orbit and in the sense of the
orbital motion. The value obtained for this rotary movement of the
orbital ellipse was 43 seconds of arc per century, an amount ensured
to be correct to within a few seconds of arc. This effect can be
explained by means of classical mechanics only on the assumption of
hypotheses which have little probability, and which were devised
solely for this purponse.

On the basis of the general theory of relativity, it is found that the
ellipse of every planet round the sun must necessarily rotate in the
manner indicated above ; that for all the planets, with the exception
of Mercury, this rotation is too small to be detected with the
delicacy of observation possible at the present time ; but that in the
case of Mercury it must amount to 43 seconds of arc per century, a
result which is strictly in agreement with observation.

Apart from this one, it has hitherto been possible to make only two
deductions from the theory which admit of being tested by observation,
to wit, the curvature of light rays by the gravitational field of the



COSMOLOGICAL DIFFICULTIES OF NEWTON'S THEORY


Part from the difficulty discussed in Section 21, there is a second
fundamental difficulty attending classical celestial mechanics, which,
to the best of my knowledge, was first discussed in detail by the
astronomer Seeliger. If we ponder over the question as to how the
universe, considered as a whole, is to be regarded, the first answer
that suggests itself to us is surely this: As regards space (and time)

sense in the statement, because they mean that they can perform the
constructions of plane Euclidean geometry with their rods. In this
connection the individual rods always represent the same distance,
independently of their position.

Let us consider now a second two-dimensional existence, but this time
on a spherical surface instead of on a plane. The flat beings with
their measuring-rods and other objects fit exactly on this surface and
they are unable to leave it. Their whole universe of observation
extends exclusively over the surface of the sphere. Are these beings
able to regard the geometry of their universe as being plane geometry

its eccentricity, c the velocity of light, and T the period of
revolution of the planet. Our result may also be stated as follows :
According to the general theory of relativity, the major axis of the
ellipse rotates round the sun in the same sense as the orbital motion
of the planet. Theory requires that this rotation should amount to 43
seconds of arc per century for the planet Mercury, but for the other
Planets of our solar system its magnitude should be so small that it
would necessarily escape detection. *

In point of fact, astronomers have found that the theory of Newton
does not suffice to calculate the observed motion of Mercury with an
exactness corresponding to that of the delicacy of observation
attainable at the present time. After taking account of all the
disturbing influences exerted on Mercury by the remaining planets, it
was found (Leverrier: 1859; and Newcomb: 1895) that an unexplained
perihelial movement of the orbit of Mercury remained over, the amount
of which does not differ sensibly from the above mentioned +43 seconds
of arc per century. The uncertainty of the empirical result amounts to
a few seconds only.

 (b) Deflection of Light by a Gravitational Field

In Section 22 it has been already mentioned that according to the
general theory of relativity, a ray of light will experience a

D[2], i.e. at a somewhat greater distance from the centre of the sun
than corresponds to its real position.

In practice, the question is tested in the following way. The stars in
the neighbourhood of the sun are photographed during a solar eclipse.
In addition, a second photograph of the same stars is taken when the
sun is situated at another position in the sky, i.e. a few months
earlier or later. As compared whh the standard photograph, the
positions of the stars on the eclipse-photograph ought to appear
displaced radially outwards (away from the centre of the sun) by an
amount corresponding to the angle a.

was necessary in making the adjustments required for the taking of the
photographs, and in their subsequent measurement.

The results of the measurements confirmed the theory in a thoroughly
satisfactory manner. The rectangular components of the observed and of
the calculated deviations of the stars (in seconds of arc) are set
forth in the following table of results :

                      Table 01: file table01.gif

 (c) Displacement of Spectral Lines Towards the Red

view all matches for this distribution

Algorithm-X-DLX

5 results

examples/dlx.pl view on Meta::CPAN

my $opt_print_solutions = $opts{p} || $opts{v};
my $opt_sparse          = $opts{s};
my $opt_print_tree      = $opts{t};

chomp(my $line = <STDIN>);
my ($width, $secondary_columns) = split ' ', $line;

my @input_rows;
while (defined($line = <STDIN>)) {
  chomp($line);

examples/dlx.pl view on Meta::CPAN

    @row = split ' ', $line;
  }
  push @input_rows, \@row if @row;
}

my $problem = $opt_sparse ? Algorithm::X::ExactCoverProblem->new($width, \@input_rows, $secondary_columns)
                          : Algorithm::X::ExactCoverProblem->dense(\@input_rows, $secondary_columns);

my $dlx = Algorithm::X::DLX->new($problem);

my $result = $dlx->search();

examples/dlx.pl view on Meta::CPAN

 -v print solutions by outputting the rows themselves
 -t print nodes inspected for each recursion level
 -s input is a sparse matrix

The first line of input states the problem matrix width (all columns), optionally 
followed by a space and the number of secondary columns therein, at the right.
All following lines are the matrix rows (space separated).

HELP
;
  exit(1);

view all matches for this distribution

Alice

11 results

inc/Module/Install/Metadata.pm view on Meta::CPAN

	my $name     = shift;
	my $features = ( $self->{values}->{features} ||= [] );
	my $mods;

	if ( @_ == 1 and ref( $_[0] ) ) {
		# The user used ->feature like ->features by passing in the second
		# argument as a reference.  Accomodate for that.
		$mods = $_[0];
	} else {
		$mods = \@_;
	}

view all matches for this distribution

Alien-7zip

1 match

t/00-report-prereqs.t view on Meta::CPAN


my @full_reports;
my @dep_errors;
my $req_hash = $HAS_CPAN_META ? $full_prereqs->as_string_hash : $full_prereqs;

# Add static includes into a fake section
for my $mod (@include) {
    $req_hash->{other}{modules}{$mod} = 0;
}

for my $phase ( qw(configure build test runtime develop other) ) {

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Alien-ActiveMQ

4 results

inc/Module/Install/AutoInstall.pm view on Meta::CPAN


    $self->makemaker_args( Module::AutoInstall::_make_args() );

    my $class = ref($self);
    $self->postamble(
        "# --- $class section:\n" .
        Module::AutoInstall::postamble()
    );
}

sub installdeps_target {

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Alien-Adaptagrams

1 match

perlcritic.rc view on Meta::CPAN

theme = ( core + pbp + security + maintenance ) * bugs
include = CodeLayout::ProhibitSpaceIndentation CodeLayout::ProhibitTrailingWhitespace CodeLayout::RequireConsistentNewlines CodeLayout::TabIndentSpaceAlign

[-Subroutines::ProhibitSubroutinePrototypes]

[TestingAndDebugging::RequireUseStrict]

view all matches for this distribution

Alien-Autotools

1 match

and utility programs needed for reproducing the Combined Work from the
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  To "propagate" a work means to do anything with it that, without
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  You may convey verbatim copies of the Program's source code as you
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  You may charge any price or no price for each copy that you convey,
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  You may convey a work based on the Program, or the modifications to
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  7. Additional Terms.

  Notwithstanding any other provision of this License, for material you
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    a) Disclaiming warranty or limiting liability differently from the
    terms of sections 15 and 16 of this License; or

    b) Requiring preservation of specified reasonable legal notices or
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  All other non-permissive additional terms are considered "further
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your receipt of the notice.

  Termination of your rights under this section does not terminate the
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  You are not required to accept this License in order to receive or
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Alien-BCM2835

1 match

t/00-report-prereqs.t view on Meta::CPAN


my @full_reports;
my @dep_errors;
my $req_hash = $HAS_CPAN_META ? $full_prereqs->as_string_hash : $full_prereqs;

# Add static includes into a fake section
for my $mod (@include) {
    $req_hash->{other}{modules}{$mod} = 0;
}

for my $phase ( qw(configure build test runtime develop other) ) {

view all matches for this distribution

Alien-Base-Dino

10 results

lib/Alien/Base/Dino.pm view on Meta::CPAN

B<building> dynamic libraries for an L<Alien> B<share> install introduce 
a number of challenges, and honestly I don't see the point of using 
them, if you can avoid it.  So far I haven't actually seen a situation 
where it couldn't be avoided.  Just to be clear: dynamic libraries are 
fine for Alien, and in fact desirable when you are using the system 
provided libraries.  You get the patches and security fixes supplied by 
your operating system.

Okay, so why not build a dynamic library for a B<share> install?

For this discussion, say you have an alienized library C<Alien::libfoo>

lib/Alien/Base/Dino.pm view on Meta::CPAN


=item Your platform may not be supported

=back

Also, this module should start with the caveat section and then go from 
there.  Most modules I write are not like that.

These platforms seem to work: Linux, OS X, Windows, Cygwin, FreeBSD, 
NetBSD, OpenBSD, Debian kFreeBSD.

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Alien-Base-ModuleBuild

10 results

lib/Alien/Base/ModuleBuild.pm view on Meta::CPAN

or C<digest_and_encrypt>.  This is based on the C<ALIEN_DOWNLOAD_RULE>
environment variable.

=head1 GUIDE TO DOCUMENTATION

The documentation for C<Module::Build> is broken up into sections:

=over

=item General Usage (L<Module::Build>)

lib/Alien/Base/ModuleBuild.pm view on Meta::CPAN


Set to a true value to install to an arch-specific directory.

=item B<ALIEN_DOWNLOAD_RULE>

This controls security options for fetching alienized packages over the internet.
The legal values are:

=over 4

=item C<warn>

lib/Alien/Base/ModuleBuild.pm view on Meta::CPAN

the L<Alien>.  This will be the default in the near future.

=item C<digest_and_encrypt>

Fetch will only happen if the alienized package has a cryptographic signature digest,
and is fetched via a secure protocol (like C<https>).  Bundled packages are also
considered fetch via a secure protocol, but will still require a digest.

=back

=item B<ALIEN_FORCE>

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Alien-Base-Wrapper

2 results

lib/Alien/Base/Wrapper.pm view on Meta::CPAN

compiler and linker that Perl is configured to use.  It takes the normal compiler and
linker flags and adds the flags provided by the Aliens specified, and then executes the
command.  It will print the command to the console so that you can see exactly what is
happening.

In the second example (from Makefile.PL non-dynamic), this class is used to generate the
appropriate L<ExtUtils::MakeMaker> (EUMM) arguments needed to C<WriteMakefile>.

In the third example (from Makefile.PL dynamic), we do a quick check to see if the simple
linker flag C<-lfoo> will work, if so we use that.  If not, we use a wrapper around the
compiler and linker that will use the alien flags that are known at build time.  The

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Alien-Base

1 match

Changes view on Meta::CPAN


0.022_01  Fri Jul 31, 2015
  - Add support for ALIEN_INSTALL_TYPE environment variable

0.022  Mon Jul 20, 2015
  - Correction for the section "How do I specify a minumum or exact version
    requirement for packages that use pkg-config?" in the FAQ.

0.021_01  Wed Jul 15, 2015
  - Added a default %{pkg_config} helper
  - Fixed bug introduced in 0.016_01 where using --destdir or $ENV{DESTDIR}

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Alien-BatToExeConverter

2 results

inc/Module/Install/Metadata.pm view on Meta::CPAN

	my $name     = shift;
	my $features = ( $self->{values}{features} ||= [] );
	my $mods;

	if ( @_ == 1 and ref( $_[0] ) ) {
		# The user used ->feature like ->features by passing in the second
		# argument as a reference.  Accomodate for that.
		$mods = $_[0];
	} else {
		$mods = \@_;
	}

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Alien-Bazel

6 results

CONTRIBUTING view on Meta::CPAN


You hereby agree that if You have or acquire hereafter any patent or interface copyright or other intellectual property interest dominating the software or documentation contributed to by the Work (or use of that software or documentation), such domi...

You hereby represent and warrant that You are the sole copyright holder for the Work and that You have the right and power to enter into this legally-binding contractual agreement.  You hereby indemnify and hold harmless APTech, its heirs, assignees,...

3. Grant of Patent License.  Subject to the terms and conditions of this Agreement, You hereby grant to APTech and to recipients of software distributed by APTech a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as ...

4. You represent that you are legally entitled to assign the above copyright and grant the above patent license.  If your employer(s) or contractee(s) have rights to intellectual property that you create that includes your Contributions, then you rep...

5. You represent that each of Your Contributions is Your original creation and is not subject to any third-party license or other restriction (including, but not limited to, related patents and trademarks) of which you are personally aware and which ...

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Alien-Bit

3 results

lib/Alien/Bit.pm view on Meta::CPAN

This module provides a procedural Perl interface to the C library C<Bit>,
for creating and manipulating containers of bitsets (BitDB). It uses
C<FFI::Platypus> to wrap the C functions and C<Alien::Bit> to locate and link
to the C library. The main purpose of this library is to provide multithreaded
and hardware accelerated (e.g. GPU) versions of container operations e.g. forming
the population count of the intersection of two containers of bitsets.

=item L<Bit|https://github.com/chrisarg/Bit>

Bit is a high-performance, uncompressed bitset implementation in C, optimized 
for modern architectures. The library provides an efficient way to create, 
manipulate, and query bitsets with a focus on performance and memory alignment. 
The API and the interface is largely based on David Hanson's Bit_T library 
discussed in Chapter 13 of "C Interfaces and Implementations", 
Addison-Wesley ISBN 0-201-49841-3 extended to incorporate additional operations 
(such as counts on unions/differences/intersections of sets), 
fast population counts using the libpocnt library and GPU operations for packed 
containers of (collections) of Bit(sets).

=item L<libpopcnt|https://github.com/kimwalisch/libpopcnt>

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Alien-Box2D

1 match

and telling the user how to view a copy of this License. (Exception: if the
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your work based on the Program is not required to print an announcement.)

These requirements apply to the modified work as a whole. If identifiable
sections of that work are not derived from the Program, and can be reasonably
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and its terms, do not apply to those sections when you distribute them as
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which is a work based on the Program, the distribution of the whole must be on
the terms of this License, whose permissions for other licensees extend to the
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Thus, it is not the intent of this section to claim rights or contest your rights to
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the distribution of derivative or collective works based on the Program.

In addition, mere aggregation of another work not based on the Program with the
Program (or with a work based on the Program) on a volume of a storage or

customarily used for software interchange; or,

c) Accompany it with the information you received as to the offer to distribute
corresponding source code. (This alternative is allowed only for noncommercial
distribution and only if you received the program in object code or executable
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The source code for a work means the preferred form of the work for making
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source code for all modules it contains, plus any associated interface definition
files, plus the scripts used to control compilation and installation of the

not permit royalty-free redistribution of the Program by all those who receive
copies directly or indirectly through you, then the only way you could satisfy
both it and this License would be to refrain entirely from distribution of the
Program.

If any portion of this section is held invalid or unenforceable under any particular
circumstance, the balance of the section is intended to apply and the section as
a whole is intended to apply in other circumstances.

It is not the purpose of this section to induce you to infringe any patents or other
property right claims or to contest validity of any such claims; this section has
the sole purpose of protecting the integrity of the free software distribution
system, which is implemented by public license practices. Many people have
made generous contributions to the wide range of software distributed through
that system in reliance on consistent application of that system; it is up to the
author/donor to decide if he or she is willing to distribute software through any
other system and a licensee cannot impose that choice.

This section is intended to make thoroughly clear what is believed to be a
consequence of the rest of this License.

8. If the distribution and/or use of the Program is restricted in certain countries
either by patents or by copyrighted interfaces, the original copyright holder who
places the Program under this License may add an explicit geographical

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Alien-Brotli

2 results

alienfile view on Meta::CPAN

    pkg_name        => [qw/ libbrotlicommon libbrotlienc libbrotlidec /],
    minimum_version => MINIMUM_VERSION,
);
plugin 'Probe::CommandLine' => (
    command => 'brotli',
    secondary => 1,
);

share {
    requires 'Alien::bc::GNU' => '0';

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Alien-Build

30 results