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E-raamat: High Dimensional Space to Formulate Marriage and Birth Functions [Taylor & Francis e-raamat]

(Teikyo University, Department of Sociology, 359 Ootuka, Hachiouji, Tokyo 192-0395 Japan)
  • Formaat: 362 pages, 58 Tables, black and white; 202 Line drawings, black and white; 32 Halftones, black and white; 234 Illustrations, black and white
  • Ilmumisaeg: 07-Jul-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9780429060182
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  • Taylor & Francis e-raamat
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High Dimensional Space to Formulate Marriage and Birth FunctionsSuurem pilt
  • Formaat: 362 pages, 58 Tables, black and white; 202 Line drawings, black and white; 32 Halftones, black and white; 234 Illustrations, black and white
  • Ilmumisaeg: 07-Jul-2022
  • Kirjastus: CRC Press
  • ISBN-13: 9780429060182
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9780429060182
With the collapse of Demographic Transition Theory, new theories of population must not just be explanations, but should be falsifiable theories which can compute the number of occurrences of marriages and births. This book reviews computable marriage and birth function using dynamic properties. To do that, the functions are defined in high dimensional space. The reaction-diffusion equation of the number of children in a space is applied to these phenomena, providing solutions to many problems concerning a decline in fertility. The functions are developed as stochastic maps based on the present behaviors of successive behaviors in a geographical space. As we assume that there is an inter-dependence of human behaviors, we use the law of dynamics concerning the function of marriage and birth. The exact mathematical definition of interactions in a space naturally implies a causal relation. For the function concerning the number of children of parents, two geographical-dimensional spaces are required.

The decline in fertility in Belgium due to different languages is explained, and the longer fertility period in Brittany is explained by the Laplacian of the diffusion equation. Depending on the degree of symbolic control over behaviors, we need to add the degree of the dimension of the space. For the marriage function, we add age as a biological dimension to the geographical space. In this higher dimensional space, the mapping from neighboring present marriages to neighboring successive marriages is no less than that of the marriage function. These chain reactions caused the baby boom as an exothermal reaction-diffusion. Birth functions require one to add the marriage-age dimension to two geographical and age dimensions so that it is a five dimensional hypersurface. It can, thus, determine birth probabilities of a female who married at a certain age. The phenomenon of modern fertility decline may only be the result of these chain reactions. These processes are solely dependent upon time-space, and not on socioeconomic conditions. This is the very reason why we are able to predict it mathematically.

The book provides a new thinking in fertility decline for demographic research. Readers need to be aware that the fertility decline experienced throughout the modern era is a spatial pattern formation (as a reaction-diffusion). The author hopes new mathematical applications in human activities are developed through these new models.
Foreword iii
Preface iv
Section I History of Geometrical Diffusion Model
1 The Dawn of Reaction-Diffusion Dynamics
2(16)
1.1 Fisher's Advantageous Genes
3(3)
1.1.1 Fisher's Equation
3(1)
1.1.1.1 Mapping
3(1)
1.1.1.2 Autonomy---Background Independence
4(1)
1.1.2 Progressive Wave
4(1)
1.1.3 Do Genes Really Propagate?
5(1)
1.2 Skellam's Muskrats Diffusion Model
6(1)
1.2.1 Skellam's Instance
6(1)
1.3 Hagerstrand
7(7)
1.3.1 Concrete Record of the Diffusion Process
8(2)
1.3.2 Limitations of Hagerstrand's Work
10(1)
1.3.2.1 Absence of a Mathematical Formulation
10(1)
1.3.3 Entities that Spread in Space
11(3)
1.3.3.1 Information does not Diffuse
14(1)
1.4 Delay in Human Conscious Sensory Awareness
14(2)
1.4.0.1 Interpretation of Conscious Motivations is Tedious
15(1)
1.4.1 Geographical Dimensions
15(1)
1.5 A.M. Turing, Hodgkin, and Huxley---Autonomous Pattern Formation
16(2)
2 Decline of the Number of Children
18(50)
2.1 Fertility Decline---Demographic Transition?
18(7)
2.1.1 Early Diffusionists
18(1)
2.1.1.1 Diffusion of Lower Fertility
19(4)
2.1.2 Reaction-Diffusion System
23(1)
2.1.2.1 Variances in Fertility Decline are Proportional to Time During the Initial Stage
24(1)
2.1.2.2 Diffusion is not Imitation
24(1)
2.2 Search for a Singularity Origin of Fertility Decline in Europe
25(7)
2.2.1 Progressive Wave
25(1)
2.2.1.1 Velocity for One-Dimensional Space
25(3)
2.2.1.2 Velocity in Two-Dimensional Space
28(1)
2.2.2 The Year a Singularity Appeared
28(1)
2.2.2.1 Differences in Time from Isomorphism
29(1)
2.2.2.2 Where was the Singularity?
30(1)
2.2.2.3 Lot-et-Garonne
31(1)
2.3 Diffusion of Fertility Decline is Background Independent
32(2)
2.3.1 Why did the Singularity Occur at it Lot-et-Garonne?
33(1)
2.3.1.1 Probability of Disintegration of the Balance
33(1)
2.4 Visualized Fertility Decline Process in France
34(18)
2.4.1 Delay of Fertility Decline in Brittany
34(7)
2.4.1.1 Effect of Religion
41(1)
2.4.1.2 Linguistic Difference Assumption
42(1)
2.4.1.3 Inadequacy of Economic Factors
42(2)
2.4.1.4 System of Inheritance
44(1)
2.4.2 Differing Laplacian Ac
45(1)
2.4.2.1 Simulation of the Peninsula
46(2)
2.4.2.2 Other Demonstrations
48(2)
2.4.3 Speculations for Coefficients and Time-Space Scale
50(1)
2.4.3.1 Rounding Errors Cause a Delay in the Wave
51(1)
2.4.3.2 Lattice Space Errors
51(1)
2.4.3.3 Section Conclusions
51(1)
2.5 Decline of Number of Children in Japan
52(2)
2.5.1 Graphical Representation of the Decline of the Number of Children in the Kanto Area
52(2)
2.6 Diffusion as a Fire Leap
54(2)
2.7 Fertility Decline in Brazil
56(1)
2.7.1 Diffusion from Several Regions (Points)
56(1)
2.7.1.1 Map from 1991 and Ratio of the Total Area of Diffusion
56(2)
2.7.1.2 Periods between 1991--2000 and 2000--2010
58(1)
2.7.2 Traffic
58(3)
2.7.3 Conclusions Based on the Analysis of Brazil
61(1)
2.8 Numerical Consideration of the Geographical Obstacles in the Model
62(2)
2.8.1 Simulation Results
62(1)
2.8.1.1 Obstacle Size must Exceed a Quantity
62(2)
2.8.1.2 Laplacian is Extremely Small
64(1)
2.9
Chapter Conclusions
64(4)
Section II Marriage Function in High Dimensional Space
3 History of the Marriage Function
68(17)
3.1 Discovery of the Marriage Function
68(7)
3.1.1 Uniformity of Marriage Function
69(1)
3.1.1.1 Adjustment of Scale and Origin
69(2)
3.1.2 Flaws of Coale--McNeil Distribution
71(1)
3.1.2.1 Convolution Model
72(1)
3.1.2.2 Vital Gap---Never Asymptotic to 0
72(1)
3.1.2.3 Extreme Event
73(1)
3.1.2.4 Why Does the Marriage Function Differ Across Cultures?
74(1)
3.1.2.5 Why are They not Dynamic?
75(1)
3.2 Hernes Function
75(4)
3.2.1 Definition of the Hernes Function
76(1)
3.2.2 Advantages of the Hernes Function
76(1)
3.2.3 Flaws of the Hernes Function
77(1)
3.2.3.1 Asymptotic Comparison
78(1)
3.2.4 Conclusions on the Hernes Function
79(1)
3.3 Other Marriage Functions
79(4)
3.3.1 T Distribution
79(1)
3.3.2 Generalized logΓ Distribution
80(1)
3.3.3 Log-Logistic Model
80(2)
3.3.4 Sickle Model
82(1)
3.3.5 Problem with Existing Marriage Functions
82(1)
3.4 Do Marriages Occur as a Result of our Conscious Choices?
83(2)
3.4.1 Early or Late Marriages: Mere Individual Differences?
83(1)
3.4.1.1 Lifetime or Survival Functions are not Marriage Functions
83(1)
3.4.2 Explaining the Dynamics of the Marriage Function
84(1)
4 Marriage Function as an Integral Function
85(21)
4.1 Integral Function
85(7)
4.1.1 The More Marriages Evident within a Space, the Higher the Marriage Occurrences
86(1)
4.1.1.1 ∫t0 F(t)(dt) is not Social Pressure
86(2)
4.1.1.2 Monotonic Decreasing Element
88(1)
4.1.1.3 Monotonic Decrease in the Never-Married Segment
88(1)
4.1.2 Formulation of an Integral Equation
89(1)
4.1.2.1 Characteristics of SDSMF---Thicker Right Tail and Higher Kurtosis
89(1)
4.1.2.2 Background Independence of Marriage Occurrences
90(1)
4.1.3 Fit of SDSMF to the Data
91(1)
4.1.3.1 Inflection Point Method
91(1)
4.1.3.2 Estimation Results
91(1)
4.2 Decisive Evidence of SDSMF
92(4)
4.2.1 A Good Theory can Predict Some Theoretical Values
92(2)
4.2.1.1 Test Results
94(1)
4.2.2 Comparing SDSMF to the Coale--McNeil and Double Exponential Distributions
95(1)
4.2.2.1 Decisive Discriminant Test
95(1)
4.2.2.2 Proportion of Ever-Married Population for the 1960 Cohort
95(1)
4.3 Testing SDSMF in Other Countries
96(5)
4.3.1 Testing SDSMF using Cohorts within the Swiss Population
96(1)
4.3.1.1 Similarities to the Japanese Cases
96(2)
4.3.2 Marriage at Young Ages: The Second Decisive Discriminant Test
98(1)
4.3.2.1 How Often do Marriages at Young Ages Occur?
99(1)
4.3.3 Test using Algerian Data
100(1)
4.4 Marriage Function Tests Using Kurtosis
101(2)
4.4.1 Definition of Kurtosis
101(1)
4.4.1.1 For Discreet Distribution
101(1)
4.4.1.2 Kurtosis of Sample
102(1)
4.4.1.3 Calculation of Kurtosis of each Marriage Function
102(1)
4.5 Late-Marriage Trend in Japan from SDSMF
103(3)
4.5.1 Earlier-than-Expected Outset of Late-Marriage Trend
103(1)
4.5.2 Late-Marriage Trend from the Perspective of Marriage Functions
104(1)
4.5.2.1 Temporal Backward or Stationary Trends
104(1)
4.5.3 Limitations of SDSMF
105(1)
5 Marriage Function in High-Dimensional Space
106(37)
5.1 Diffusion of Late-Marriage Trend
106(1)
5.2 Formulation
107(11)
5.2.1 Unification of Cohort and Period
111(1)
5.2.2 Baby Boom
112(2)
5.2.2.1 Boom or Boomlet
114(2)
5.2.2.2 Baby Boom as a Chain Reaction
116(1)
5.2.2.3 Boomlet or No Boom Following World War I
117(1)
5.3 Extension to Geographical Dimensions
118(12)
5.3.1 Purposes of Extension
118(1)
5.3.2 Marriage Function as a Hypersurface
119(1)
5.3.2.1 Formulation
119(1)
5.3.3 Marriage Function in Tokyo
120(1)
5.3.3.1 Fit Marriage Function to Observed Data
121(2)
5.3.3.2 1970--1975
123(1)
5.3.3.3 1975--1980
124(1)
5.3.3.4 1980--1985
125(1)
5.3.3.5 1985--1990
126(1)
5.3.3.6 1990--1995
127(2)
5.3.3.7 1995--2000
129(1)
5.3.3.8 2000--2005
129(1)
5.3.3.9 2005--2010
129(1)
5.3.3.10 2010--2015
129(1)
5.4 Drawing the Three-Dimensional Surface via Interpolation
130(2)
5.5 Time-Space Pattern Caused by Geographical Extension
132(11)
5.5.1 Fundamental Instability
133(2)
5.5.2 Brief Convergence of Patterned Undulations
135(1)
5.5.2.1 Initial Heterogeneity
136(1)
5.5.2.2 Pattern Dynamics
137(2)
5.5.2.3 Qualitative Analysis of the Alteration of the Hypersurface
139(1)
5.5.3 Fixed Undulated Surfaces Remain
140(3)
6 To Alter Marriage Function
143(23)
6.1 Dynamics of the Hypersurface
144(4)
6.1.1 Simulation Settings
144(1)
6.1.2 Slight Marriage Delays at Young Ages Caused Every Delay
145(1)
6.1.2.1 Beginning of the Late-Marriage Trend in Japan in 1950
146(2)
6.2 Constancy of Undulation of Hypersurface
148(1)
6.3 Altering the Hypersurface
149(5)
6.3.1 Flattening Effect vs Ripple Effect
150(1)
6.3.1.1 Ineffectiveness of Raising the Marriage Probability of Older Individuals
150(1)
6.3.2 Quest for a Relatively More Effective Convex Surface
151(1)
6.3.2.1 No Progressive Wave in the Geographical Dimensions
152(1)
6.3.2.2 Progressive Wave in the Age Dimension
153(1)
6.4 Revisiting the Baby Boom from the Perspective of the Extended Marriage Function
154(9)
6.4.1 American Baby Boom---not the Kuznets Cycle
154(1)
6.4.2 Geographical Extension for Radicalizing the Chain Reaction
155(1)
6.4.2.1 Simulation Settings
156(1)
6.4.2.2 How Marriage Probabilities Increase
156(1)
6.4.2.3 Two-Sex Problem---Marriage Squeeze Hypothesis
157(1)
6.4.3 Artificial Baby Boom in High-Dimensional Space
158(1)
6.4.3.1 Simulation Results
159(2)
6.4.4 Effectiveness of the Artificial Baby Boom
161(1)
6.4.4.1 What Increases the Sparsity of Increments?
162(1)
6.5 To End This
Chapter
163(3)
Section III Birth Function in High Dimensional Space
7 No Individual Birth Functions Exist
166(32)
7.1 Quasi Linearity of the Expected Number of Children Based on Marriage Duration
166(7)
7.1.1 Stochastic Variable
167(1)
7.1.1.1 Indistinguishability Based on Socioeconomic Conditions
168(2)
7.1.2 (Class) Differential Fertility
170(1)
7.1.2.1 Number of Children---Indefinite Solution
170(3)
7.2 Negation of the Existence of the Function of the Number of Children by the Diagonal Method
173(2)
7.2.1 Contradiction by the Diagonal Method
173(2)
7.2.1.1 Function as an Assumption
175(1)
7.3 Statistical Test of the Randomness of the Number of Children
175(12)
7.3.1 Sorting by Independent Variables
176(1)
7.3.1.1 List of Statistical Tests
176(4)
7.3.1.2 Result of the Statistical Test of GSS 1950s Data
180(1)
7.3.1.3 Sequence by Another Sorting Method
181(1)
7.3.2 Statistical Tests for Number of Japanese Children
182(1)
7.3.2.1 SSM Survey Data
182(1)
7.3.2.2 JGSS Data
183(1)
7.3.2.3 Comparison with the Hierarchical Differential Sequence
184(1)
7.3.3 Older (Partial) Sequences
185(1)
7.3.3.1 U.S. 1930--1939 Cohort
186(1)
7.3.3.2 U.S. 1910--1919 Cohort
186(1)
7.4 Irreducibility of the Sequence of the Number of Children
187(1)
7.4.1 Evaluation of the Function Using Information Theory
187(1)
7.5 Conscious Choice of Birth---Distribution of the Number of Children
188(5)
7.5.0.1 Free Choices are Random
188(1)
7.5.0.2 Ideal Number of Children and the Number of Children in America
189(1)
7.5.0.3 Ideal Versus Actual Number of Children in Japan
190(3)
7.5.0.4 Ideal Number of Children is a Response to the Number of Children in High Dimensional Space
193(1)
7.6 Necessity of Multi-Dimensional Space
193(4)
7.6.1 Necessity of Geographical Dimensions
194(1)
7.6.1.1 Consideration of Geographical Dimensions
195(1)
7.6.2 Necessity of Time Dimension for Observation
196(1)
7.7 Conjecture
197(1)
8 Birth Function for a Cohort
198(44)
8.1 Only One Birth Function Exists
198(1)
8.1.1 Birth Process
199(1)
8.2 Calculation of Birth Probabilities by Age and Specific Age at Marriage
199(9)
8.2.1 Birth Probabilities in 1939 in Japan
202(3)
8.2.1.1 England-Wales in 1939
205(3)
8.3 Regularity of Birth Probabilities
208(2)
8.3.1 Precise Computation of Birth Probability by the Birth Function
209(1)
8.3.1.1 Quasi-Replication
210(1)
8.4 Fecundability
210(1)
8.5 Regularity of Birth
211(6)
8.5.1 1965 Cohort in Japan
213(1)
8.5.1.1 Idiosyncrasy
214(1)
8.5.2 1970 Cohort in Japan
215(1)
8.5.3 1975 and 1980 Cohorts in Japan
215(1)
8.5.4 1939 and 1985 Cohorts in Japan
215(1)
8.5.5 England-Wales---C. Clark's Data
216(1)
8.5.6 General Law
216(1)
8.6 Birth Function for a Cohort
217(6)
8.6.1 Virtual 1985 Cohort
218(1)
8.6.1.1 Model Zero
218(1)
8.6.1.2 Model One
219(1)
8.6.1.3 Model Two
220(1)
8.6.1.4 Model-Three
221(1)
8.6.1.5 Model-Four and Model-Five
221(1)
8.6.1.6 Model Six
222(1)
8.7 Integration of Birth Function with 1985 (Virtual) Cohort
223(10)
8.7.1 Idiosyncrasy Rates of 1985
223(1)
8.7.2 Model-Six for 1985
223(3)
8.7.3 Model Eight
226(1)
8.7.3.1 Coefficient of Catch-up
227(1)
8.7.3.2 Analysis of the Derivatives of the Birth Function
228(2)
8.7.3.3 Effect of Infertility Treatment
230(2)
8.7.4 Randomness of the Sequence of the Number of Children
232(1)
8.8 Statistical Test of Birth Function for a Cohort
233(2)
8.9 Fixed Point of Birth Function for a Cohort
235(1)
8.10 Strong Relation between Late Marriage Tendency and Birth Function
236(4)
8.10.1 The Reverse is not Always True
238(1)
8.10.1.1 Effectiveness of Pronatalist Policy Measures
238(2)
8.11 Limitations of the Birth Function for a Cohort
240(2)
9 Necessity of Extending the Birth Function
242(36)
9.1 Need for Geographical Factors
242(12)
9.1.1 Religious Differential Fertility Explained by Spatial Differentials
243(1)
9.1.1.1 Jewish Fertility Decline in 19th-Century Venice
244(2)
9.1.1.2 True Nature of Difference Between a Ghetto and Elsewhere
246(1)
9.1.2 End of American Catholic Fertility
247(3)
9.1.3 Inability of Explaining Fertility Undulations through Socioeconomic Differences
250(1)
9.1.3.1 Universality of Fertility Undulation
251(3)
9.2 Equivalent Principle of Time and Distance
254(12)
9.2.1 Effect of High-Speed Mobility on the Equivalent Principle
255(1)
9.2.1.1 High-Speed Mobility is not Destroying the Equivalent Principle
255(2)
9.2.2 Effect of Network Communication on the Equivalent Principle
257(1)
9.2.2.1 Present-Day No-acceleration of the Tempo of Fertility Undulation
258(1)
9.2.2.2 High-Speed Mobility and Networks Transmit Conscious Information but cannot Alter Demographic Behaviors
258(1)
9.2.3 Diffusion of Low Fertility in Spaces in Japan
258(1)
9.2.3.1 Failure of the Will Alteration Hypothesis
259(2)
9.2.4 Verification of the Principle by Historical Data
261(1)
9.2.4.1 Colyton
261(1)
9.2.4.2 Bottesford
262(2)
9.2.4.3 Terling
264(2)
9.2.4.4 Falsifiable Theory
266(1)
9.3 Alteration of Values does not Cause Human Behaviors
266(4)
9.3.1 Alteration of Fertility Before Change in the Value of Childbearing
266(4)
9.4 Decline of the Number of Children by Unconscious Parents
270(1)
9.5 Unconscious Birth Control
271(5)
9.5.1 Failed Efforts of the Third Reich
272(1)
9.5.2 Unconscious Alteration of the Number of Children per Family in Japan
273(1)
9.5.2.1 Childbearing and Increased Fertility Until the Defeat in World War II
273(2)
9.5.2.2 Antinatalist Policy in Japan Following World War II
275(1)
9.6 Birth Function as a General Law
276(2)
10 Partial Constant Birth Probability
278(9)
10.1 Idiosyncratic Teenagers
278(6)
10.1.1 Teenage Pregnancy in The United States
279(2)
10.1.2 Teenage Pregnancy in France
281(1)
10.1.3 Teenage Pregnancy in Sweden
282(1)
10.1.4 Teenage Pregnancy in Canada
283(1)
10.2 Effect of Teenage Marriage Rate on Birth
284(1)
10.2.1 Turn in the Trend
284(1)
10.2.1.1 Reasons for the Fertility Decline of Teenagers
284(1)
10.2.2 Idiosyncrasy of Teenage Marriage
284(1)
10.3 Choosing Initial Constant Values?
285(2)
10.3.1 Distinctive Features
286(1)
10.3.2 End of Teenage Birth Probabilities
286(1)
11 Birth Function for High-Dimensional Space
287(34)
11.1 Age and Marriage-Age Dimensions
287(5)
11.1.1 Causes of Dynamics are Birth Probabilities and Background Independence
288(1)
11.1.1.1 Sensitive Range of a Female
288(3)
11.1.1.2 Self-Reconditioning is Ignored
291(1)
11.1.1.3 Diffusion Model
291(1)
11.2 Initial Values of the Birth Function
292(1)
11.3 Idiosyncratic Birth Behaviors
293(5)
11.3.1 Features of Birth Functions
294(2)
11.3.2 Age of 18 as a Turning Point in the Birth Function for Japan
296(1)
11.3.2.1 Modification of Initial Values and Destinations
297(1)
11.3.3 Dynamics of the Birth Function for Japan
297(1)
11.4 Addition of Geographical Dimensions
298(3)
11.4.1 Extension in Lattice Space
299(1)
11.4.1.1 Endogenously Computed n(tk)--Expected Number of Children
300(1)
11.4.1.2 Difference Equation in the Extended Space
301(1)
11.5 Benefit of Extending the Birth Function
301(7)
11.5.1 Significance of Four Dimensions
302(1)
11.5.2 Original Values of Coefficients
303(1)
11.5.2.1 Elimination of Alternative Reference
303(1)
11.5.2.2 Infinite Transportation
304(1)
11.5.2.3 Considering μ = 1.0 for the Diagonal Elements
304(1)
11.5.3 Changes in the Neighboring Function
305(1)
11.5.3.1 How is the First Birth Function Altered?
305(1)
11.5.3.2 Rapid Alteration by the First Married Population
306(1)
11.5.4 Ground of β, γ
307(1)
11.6 Origin of the Hole of Low Fertility
308(1)
11.6.1 What Constitutes the Hole of Low Fertility?
308(1)
11.6.2 Peculiar Pattern of the Birth Function
309(1)
11.7 Magnificent Metamorphosis
309(3)
11.7.1 Schema of the Dynamics of the Birth Function
310(1)
11.7.1.1 Resemblance with the Birth Function of England-Wales
311(1)
11.8 Strange Ripples Following the Development of the Hole of Low Fertility
312(8)
11.8.1 Birth Function as a Reaction-Diffusion System
315(1)
11.8.1.1 Mechanism of the Strange Patterns
316(1)
11.8.1.2 Reason for the Preservation of Convexoconcave Undulations
317(1)
11.8.1.3 Individual Cut Sections
317(2)
11.8.1.4 Transcendental Others
319(1)
11.9 Birth Behaviors are not Individualistic
320(1)
12 Distribution of the Numbers of Children
321(8)
12.1 Validity of the Extended Birth Function
321(1)
12.2 Distribution of the Number of Children
322(7)
12.2.1 Number of Children Based on the Birth Function
322(1)
12.2.2 Distribution of the Number of Children at the Beginning of Fertility Decline---Japan, 1939
323(1)
12.2.3 Distribution of the Number of Children During the Process of Fertility Decline---Japan, 1985
324(1)
12.2.3.1 Test by Variance and Non-parametric Values
325(1)
12.2.4 Prediction and Test by Non-Parametric Statistics
325(1)
12.2.4.1 Gradual Variation of Birth Function Between Fixed Points
326(3)
13 Conclusion---to End This Book
329(2)
13.1 End of Eclecticism
329(1)
13.2 Time and Space
330(1)
Appendix 331(2)
Bibliography 333(8)
Index 341
Shuichirou Ike is a mathematical sociologist. His specialty is demography, social psychology, and social research. He obtained his Ph.D. Sociology from Tokyo University and is a professor in the Department of Sociology, Faculty of Letter of Teikyo University, Japan. He has been the chief of the Information Processing Center of Teikyo University, Hachioji since 2011. He is a member of the Public Information Committee of the Population Association of Japan and explores society as a stochastic process.
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