On small covering codes in arbitrary mixed hamming spaces

2007 ◽  
Vol 44 (4) ◽  
pp. 517-534
Author(s):  
Gerzson Kéri
Keyword(s):  
Sufficient Conditions ◽  
Covering Codes ◽  
Quaternary Codes

Some results of Kéri and Östergård [3] regarding mixed binary/ternary covering codes are extended a) for mixed binary/ternary/quaternary codes, b) for codes in arbitrary mixed Hamming spaces. Some other results (sufficient conditions and examples of solved and unsolved cases) regarding 5-word codes in Z2bZ3tZ4q and Z2bZ3tZ4qZ5f are also provided in the paper.

On the covering radius of small codes

2003 ◽  
Vol 40 (1-2) ◽  
pp. 242-256 ◽  
Author(s):  
G. Kéri ◽  
P. R. J. Östergård
Keyword(s):  
Lower Bounds ◽  
Sufficient Conditions ◽  
Covering Radius ◽  
Necessary And Sufficient Conditions ◽  
New Methods ◽  
Quaternary Codes ◽  
Minimum Number ◽  
Necessary And Sufficient

The minimum number of codewords in a code with t ternary and b binary coordinates and covering radius R is denoted by K(t,b,R). In this paper, necessary and sufficient conditions for K(t,b,R)=M are given for all M = 5. By the help of generalized s-surjective codes, we develop new methods for finding bounds for K(t,b,R). These results are used to prove the equality K(9,0,5)=6 as well as some new lower bounds such as K(2,7,3) =7,  K(3,6,3)=8,  K(5,3,3)=8, and K(9,0,4)=9. Some bounds for (nonmixed) quaternary codes are also obtained.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

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