Sudoku Ripeto

ICGA Journal ◽  
2021 ◽  
pp. 1-24
Author(s):  
Miguel G. Palomo
Keyword(s):  
Sufficient Conditions ◽  
Proper Subset ◽  
Repetition Pattern

We present a variant of Sudoku called Sudoku Ripeto. It seems to be the first to admit any combination of repeated symbols, and includes Sudoku as a proper subset. We present other Sudoku Ripeto families, each with a different repetition pattern. We define Sudoku Ripeto squares and puzzles, prove several solving rules that generalize those for Sudoku, and give sufficient conditions to flexibly solve puzzles with rules only, without search.

scholarly journals On Magnifying Elements in E-Preserving Partial Transformation Semigroups

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 160
Author(s):  
Thananya Kaewnoi ◽  
Montakarn Petapirak ◽  
Ronnason Chinram
Keyword(s):  
Equivalence Relation ◽  
Transformation Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Necessary And Sufficient

Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X. In this paper, we consider the semigroup P ( X , E ) consisting of all E-preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X ) . The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X , E ) to be right or left magnifying.

scholarly journals Magnifiers in Some Generalization of the Full Transformation Semigroups

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 473
Author(s):  
Thananya Kaewnoi ◽  
Montakarn Petapirak ◽  
Ronnason Chinram
Keyword(s):  
Equivalence Relation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Necessary And Sufficient ◽  
Composition Of Functions

An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup of all transformations on a nonempty set X under the composition of functions, P = { X i ∣ i ∈ Λ } be a partition, and ρ be an equivalence relation on the set X. In this paper, we focus on the properties of magnifiers of the set T ρ ( X , P ) = { f ∈ T ( X ) ∣ ∀ ( x , y ) ∈ ρ , ( x f , y f ) ∈ ρ and X i f ⊆ X i for all i ∈ Λ } , which is a subsemigroup of T ( X ) , and provide the necessary and sufficient conditions for elements in T ρ ( X , P ) to be left or right magnifiers.

scholarly journals Left and Right Magnifying Elements in Generalized Semigroups of Transformations by Using Partitions of a Set

2018 ◽  
Vol 11 (3) ◽  
pp. 580-588
Author(s):  
Ronnason Chinram ◽  
Pattarawan Petchkaew ◽  
Samruam Baupradist
Keyword(s):  
Linear Transformation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Transformation Semigroups ◽  
Left And Right ◽  
Necessary And Sufficient ◽  
Composition Of Functions

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = Ma]. Let X be a nonempty set and T(X) be the semigroup of all transformation from X into itself under the composition of functions. For a partition P = {X_α | α ∈ I} of the set X, let T(X,P) = {f ∈ T(X) | (X_α)f ⊆ X_α for all α ∈ I}. Then T(X,P) is a subsemigroup of T(X) and if P = {X}, T(X,P) = T(X). Our aim in this paper is to give necessary and sufficient conditions for elements in T(X,P) to be left or right magnifying. Moreover, we apply those conditions to give necessary and sufficient conditions for elements in some generalized linear transformation semigroups.

scholarly journals Left and Right Magnifying Elements in the Semigroup of all Binary Relations

2020 ◽  
Vol 13 (4) ◽  
pp. 987-994
Author(s):  
Watchara Teparos ◽  
Soontorn Boonta ◽  
Thitiya Theparod
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Binary Relations ◽  
Left And Right ◽  
Necessary And Sufficient

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = M a]. Let X be a nonempty set and BX the semigroup of binary relations on X. In this paper, we give necessary and sufficient conditions for elements in BX to be left or right magnifying.

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.

Sign in / Sign up

Export Citation Format

Share Document