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| author | Juan Marín Noguera <juan@mnpi.eu> | 2025-05-16 22:18:44 +0200 |
|---|---|---|
| committer | Juan Marín Noguera <juan@mnpi.eu> | 2025-05-16 22:18:44 +0200 |
| commit | 4f670b750af5c11e1eac16d9cd8556455f89f46a (patch) | |
| tree | e0f8d7b33df2727d89150f799ee8628821fda80a /3.2.1.3.lyx | |
| parent | 16ccda6c459c0fd7ca2081e9d541124c28b0c556 (diff) | |
Changed layout for more manageable volumes
Diffstat (limited to '3.2.1.3.lyx')
| -rw-r--r-- | 3.2.1.3.lyx | 273 |
1 files changed, 0 insertions, 273 deletions
diff --git a/3.2.1.3.lyx b/3.2.1.3.lyx deleted file mode 100644 index e94ce2c..0000000 --- a/3.2.1.3.lyx +++ /dev/null @@ -1,273 +0,0 @@ -#LyX 2.4 created this file. For more info see https://www.lyx.org/ -\lyxformat 620 -\begin_document -\begin_header -\save_transient_properties true -\origin unavailable -\textclass book -\begin_preamble -\input defs -\end_preamble -\use_default_options true -\maintain_unincluded_children no -\language english -\language_package default -\inputencoding utf8 -\fontencoding auto -\font_roman "default" "default" -\font_sans "default" "default" -\font_typewriter "default" "default" -\font_math "auto" "auto" -\font_default_family default -\use_non_tex_fonts false -\font_sc false -\font_roman_osf false -\font_sans_osf false -\font_typewriter_osf false -\font_sf_scale 100 100 -\font_tt_scale 100 100 -\use_microtype false -\use_dash_ligatures true -\graphics default -\default_output_format default -\output_sync 0 -\bibtex_command default -\index_command default -\float_placement class -\float_alignment class -\paperfontsize default -\spacing single -\use_hyperref false -\papersize default -\use_geometry false -\use_package amsmath 1 -\use_package amssymb 1 -\use_package cancel 1 -\use_package esint 1 -\use_package mathdots 1 -\use_package mathtools 1 -\use_package mhchem 1 -\use_package stackrel 1 -\use_package stmaryrd 1 -\use_package undertilde 1 -\cite_engine basic -\cite_engine_type default -\biblio_style plain -\use_bibtopic false -\use_indices false -\paperorientation portrait -\suppress_date false -\justification true -\use_refstyle 1 -\use_formatted_ref 0 -\use_minted 0 -\use_lineno 0 -\index Index -\shortcut idx -\color #008000 -\end_index -\secnumdepth 3 -\tocdepth 3 -\paragraph_separation indent -\paragraph_indentation default -\is_math_indent 0 -\math_numbering_side default -\quotes_style english -\dynamic_quotes 0 -\papercolumns 1 -\papersides 1 -\paperpagestyle default -\tablestyle default -\tracking_changes false -\output_changes false -\change_bars false -\postpone_fragile_content false -\html_math_output 0 -\html_css_as_file 0 -\html_be_strict false -\docbook_table_output 0 -\docbook_mathml_prefix 1 -\end_header - -\begin_body - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -exerc1[M10] -\end_layout - -\end_inset - -Show that, - no matter what the byte size -\begin_inset Formula $B$ -\end_inset - - of -\family typewriter -MIX -\family default - happens to be, - the code (3) yields a random number generator of maximum period. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -answer -\end_layout - -\end_inset - -This generator has -\begin_inset Formula $a=B^{2}+1$ -\end_inset - -, - -\begin_inset Formula $c=1$ -\end_inset - -, - and -\begin_inset Formula $m=B^{5}$ -\end_inset - -. - Since the prime divisors of -\begin_inset Formula $B^{5}$ -\end_inset - - and -\begin_inset Formula $B^{2}$ -\end_inset - - are the same, - the conditions of Theorem 3.2.1.2A are satisfied. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -exerc2[10] -\end_layout - -\end_inset - -What is the potency of the generator represented by the -\family typewriter -MIX -\family default - code (3)? -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -answer -\end_layout - -\end_inset - -3. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -rexerc6[20] -\end_layout - -\end_inset - -Which of the values of -\begin_inset Formula $m=w\pm1$ -\end_inset - - in Table 3.2.1–1 can be used in a linear congruential sequence of maximum period whose potency is 4 or more? - (Use the result of exercise 5.) -\end_layout - -\begin_layout Standard -\begin_inset ERT -status open - -\begin_layout Plain Layout - - -\backslash -answer -\end_layout - -\end_inset - -By exercise 5, - for a modulus -\begin_inset Formula $m=p_{1}^{e_{1}}\cdots p_{t}^{e_{t}}$ -\end_inset - - with -\begin_inset Formula $e_{1}\geq\dots\geq e_{t}$ -\end_inset - -, - -\begin_inset Formula $a=p_{1}+1$ -\end_inset - - has the maximum potency, - which is -\begin_inset Formula $e_{1}$ -\end_inset - -, - except that if -\begin_inset Formula $m=p_{1}$ -\end_inset - -, - then the maximum potency is 0, - corresponding to -\begin_inset Formula $a=1$ -\end_inset - -. - Thus the values from the table that can be used are -\begin_inset Formula $10^{9}-1=3^{4}\cdot37\cdot333667$ -\end_inset - - and -\begin_inset Formula $2^{27}+1=3^{4}\cdot19\cdot87211$ -\end_inset - -. -\end_layout - -\end_body -\end_document |
