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Complexity and Second Moment of the Mathematical Theory of Communication
[article]

2021
*
arXiv
*
pre-print

*The*performance

*of*an error correcting code is evaluated by its error probability, rate,

*and*en/decoding

*complexity*. ...

*The*framework that generates codes

*and*

*the*machinery that evaluates codes can be extended to many other scenarios in network information

*theory*. ... Shannon founded

*the*

*theory*

*of*information with an article titled A

*Mathematical*

*Theory*

*of*

*Communication*, which was later republished under

*the*name

*The*

*Mathematical*

*Theory*

*of*

*Communication*to reflect its ...

##
###
Page 1143 of Mathematical Reviews Vol. 12, Issue 11
[page]

1951
*
Mathematical Reviews
*

*The*reader who has mastered

*the*book will comprehend

*the*use

*of*

*complex*analysis in physics

*and*related fields; he will also be well equipped for further study

*of*

*complex*function

*theory*. ... . $7.00 A combined text

*and*reference work, this book presents basic statistical

*theory*, including

*the*elementary princi- ples

*of*probability, population

*and*sampling

*theory*with

*moment*-generating functions ...

##
###
Page 564 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 85, Issue 2
[page]

1957
*
American Mathematical Society. Transactions of the American Mathematical Society
*

Chern, Department

*of**Mathematics*, University*of*Chicago, Chicago 37, Ill. All other*communications*to*the*editors should be ad to*the*Managing Editor, W. S. ... REID On singularities*of*solutions*of*certain differential equations in three variables. By STEFAN BERGMAN*The*differential equations*of*birth-*and*-death processes,*and**the*Stieltjes*moment*problem. ...##
###
Preface to the Special Issue Mathematical modelling for complex systems: multi-agents methods

2018
*
Communications in Applied and Industrial Mathematics
*

New ideas

doi:10.2478/caim-2018-0019
fatcat:hjvtenue6fb4pdhpc5tx7yyiva
*and*new*mathematical*methods are needed to understand*the*main features*of**the*behaviour*of*such living,*and*hence,*complex*systems: as a consequence,*the*interest*of*mathematicians in new structures ...*The*modeling approach is based on*the*tools*of**the*so called kinetic*theory**of*active particles. ... Acknowledgements I would like to point out here*the*continuous support*and**the*very helpful assistance that I*and*all*the*Authors have received from Giorgio Fotia*and**the*whole CAIM editorial board. ...##
###
Special issues on moment methods in kinetic gas theory

2009
*
Continuum Mechanics and Thermodynamics
*

*The*first

*moments*are

*the*conservative variables

*of*gas dynamics,

*the*density,

*the*momentum density

*and*total energy density. Obviously,

*the*motivation is that

*Communicated*by M. Torrilhon M. ... This two-volume special issue

*of*'Continuum Mechanics

*and*Thermodynamics' is

*the*result

*of*an international meeting on

*moment*methods in kinetic gas

*theory*that took place in November 2008 at ETH Zurich ... They also demonstrate a close link between

*moment*equations

*and*

*the*constitutive

*theory*

*of*thermodynamics based on

*the*exploitation

*of*

*the*entropy law. ...

##
###
Page 1231 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

(A) (Hermite’s parameter)

*and**the*shaping gain y,(A) (or equivalently*the*normalized*second**moment*G(A)) are geometrical invariants*of*a lattice A that are figures*of*merit for coding*and*quantizing, respectively ... “These quantities appear in low-order terms*of**the*series ex- 94A .*Communication*, information 95b:94008 pansions*of**the*normalized (relevant) theta series*of*A*and**the*normalized*moment*-generating function ...##
###
Semiotics in Theory and Practice in Mathematics Education
[chapter]

2016
*
ICME-13 Topical Surveys
*

(González Rey 2011b, p. 259)

doi:10.1007/978-3-319-31370-2_2
fatcat:c4i3c66r5zb5hgzy3chsfbakmm
*The**second**moment*goes roughly from 1927 to 1931. It is in*the**second**moment*that we find Vygotsky elaborating his concept*of*sign. ... We can turn now to*the**second*semiotic dimension in*the**theory**of*objectification. ...##
###
Page 260 of Mathematical Reviews Vol. 9, Issue 5
[page]

1948
*
Mathematical Reviews
*

These

*second*order equations involve terms describing*the*magnetic*moment**of**the*meson. ... In addition to*the*proceedings*of**the*Congress, this volume contains forty-one lectures, which have been re- viewed separately in*Mathematical*Reviews.*Communications*on Applied*Mathematics*. ...##
###
Page 3116 of Mathematical Reviews Vol. 58, Issue 4
[page]

1979
*
Mathematical Reviews
*

Yao, K. 58 #20778

*Moment*space error bounds in digital*communication*systems.*Communication*systems*and*random process*theory*(Proc. 2nd NATO Advanced Study Inst., Darlington, 1977), pp. 605-618. ... We consider # bounding technique based on an isomorphism theorem from*the*}*theory**of**moment*spaces to evaluate upper*and*lower bounds W0*the*error probability. ...##
###
Page 610 of Mathematical Reviews Vol. 26, Issue 3
[page]

1963
*
Mathematical Reviews
*

In both papers

*the*statistical*theory**of**the*dis- tribution*of**the**complex*random vector £’ =(Z, ---, Zp) is developed. ... In*the**second*paper*the*distribution*of**the*determinant*of*z, is derived. ...##
###
Analyzing the Impact of Video Representation Complexity on Preservice Teacher Noticing of Children's Thinking

2018
*
Eurasia Journal of Mathematics, Science and Technology Education
*

Drawing from cognitive load

doi:10.29333/ejmste/99501
fatcat:akhkn2nh3vfcfkxl4givp6ymza
*theory*, we developed a rubric to code*the**complexity**of**the*salient teaching*and*learning events captured in video,*and*analyzed*the*relationship between video*complexity**and*... Despite*the*growing research base on preservice teacher noticing*of*children's*mathematical*thinking in video, few, if any studies consider*the**complex*nature*of**the*video representations themselves. ...*The**mathematical*content includes place value, whole*and*rational number operations, proportional reasoning,*and*certain aspects*of*number*theory*. ...##
###
Proof, Proving, and Teacher-Student Interaction: Theories and Contexts
[chapter]

2011
*
New ICMI Studies Series
*

Balacheff goes on to consider

doi:10.1007/978-94-007-2129-6_11
fatcat:o6mqtijp65hsbmcat5jmtxqnne
*the*didactical*complexity**of*learning*and*teaching*mathematical*proof by analyzing*the*gap between knowing*mathematics**and*proving in*mathematics*. ... As such,*mathematics*classroom*communities*involve students in*communicating*their reasoning*and*in building norms*and*representations that provide*the*necessary structures for*mathematical*proof to have ... Thus,*the**second*key hypothesis is that*the*work*of**the*teacher includes managing activities*and*objects within two different timescales:*the*work done*moment*-to-*moment*(at*the*scale*of**the*utterance) ...##
###
Ronald R. Kline, The Cybernetics Moment: or Why We Call Our Age the Information Age

2017
*
Canadian Journal of Academic Librarianship
*

,

doi:10.33137/cjal-rcbu.v2.27267
fatcat:lesoygazs5cphplrat6hzydycu
*and**the*highly*mathematical*targeting computer as a singular cohesive entity. ... This new way*of*thinking*and*looking at*the*world enabled a new conceptualization*of*organisms*and*machines (or technology) as information-feedback systems, each with varying methods*of**communication**and*... Kline uses clear wording*and*provides simple models to explain many*of**the**complex**mathematical*formulas*and**theories*that form*the*basis*of*cybernetics (Wiener's Cybernetics is described by Kline as " ...##
###
The Construction and Globalization of the Knowlege Base in Interhuman Communication Systems

2003
*
Canadian Journal of Communication
*

Abstract:

doi:10.22230/cjc.2003v28n3a1372
fatcat:2wfny3illra4fmmw45u5wczym4
*The*relationship between*the*knowledge base*and**the*globalization*of**communication*systems is discussed from*the*perspective*of**communication**theory*. ... At*the*first level information is exchanged*and*provided with meaning,*and*at*the**second*level meaning can reflexively be*communicated*. ... Shannon (1948) defined*the*uncertainty*of*information as equal to*the*probabilistic entropy*of**the**communication*system. ...##
###
Page 301 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 6, Issue
[page]

1900
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

*The*chapter considers in turn projec- tions,

*moments*, systems

*of*segments, couples,

*the*

*theory*

*of*

*the*right line,

*and*concludes with a beautiful application

*of*

*the*

*theory*

*of*

*complexes*to systems

*of*segments ...

*theory*

*of*linear

*complexes*

*and*that

*of*

*the*displacement

*of*a solid, determination

*of*a continuous motion when

*the*rotations are known,

*and*inverse move- ment. ...

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