scholarly journals On the density and the structure of the Peirce-like formulae

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Antoine Genitrini ◽  
Jakub Kozik ◽  
Grzegorz Matecki
Keyword(s):  
Finite Number ◽  
Upper Bound ◽  
Large Family ◽  
Partial Answer ◽  
International Audience ◽  
Almost All

International audience Within the language of propositional formulae built on implication and a finite number of variables $k$, we analyze the set of formulae which are classical tautologies but not intuitionistic (we call such formulae - Peirce's formulae). We construct the large family of so called simple Peirce's formulae, whose sequence of densities for different $k$ is asymptotically equivalent to the sequence $\frac{1}{ 2 k^2}$. We prove that the densities of the sets of remaining Peirce's formulae are asymptotically bounded from above by $\frac{c}{ k^3}$ for some constant $c \in \mathbb{R}$. The result justifies the statement that in the considered language almost all Peirce's formulae are simple. The result gives a partial answer to the question stated in the recent paper by H. Fournier, D. Gardy, A. Genitrini and M. Zaionc - although we have not proved the existence of the densities for Peirce's formulae, our result gives lower and upper bound for it (if it exists) and both bounds are asymptotically equivalent to $\frac{1}{ 2 k^2}$.

Characteristics and attitudes of family planners in Khartoum, Sudan

1982 ◽  
Vol 14 (1) ◽  
pp. 7-16 ◽  
Author(s):  
M. A. Khalifa
Keyword(s):  
Family Planning ◽  
Birth Control ◽  
Early Stage ◽  
Significant Proportion ◽  
Large Family ◽  
Capital City ◽  
Age Group ◽  
African Countries ◽  
The Mean ◽  
Almost All

SummaryIn a survey of 1475 urban Moslem wives in the age group 15–49 living in the capital city of the Sudan, knowledge of birth control was reported by almost all respondents while a significant proportion had used contraception at least once. The mean age of the users was 32·8 years, their duration of marriage was 15·1 years and their mean number of surviving children was 4·6. Those who had never used contraception had a higher mean age, a longer duration of marriage and more surviving children. Most of the users had an urban residential background and belonged to the high socioeconomic class. They held favourable attitudes to family planning. Although they thought that having a large family (more than five children) was not desirable, their mean preferred family size was no different from that of the never users.The results indicate that contraception is used for the purpose of spacing births rather than limiting their ultimate number. At this early stage of contraceptive adoption in Sudan, the characteristics of the pioneer acceptors are similar to those observed in other African countries.

scholarly journals The Fundamental Group of Balanced Simplicial Complexes and Posets

10.37236/73 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Steven Klee
Keyword(s):  
Fundamental Group ◽  
Upper Bound ◽  
Large Family ◽  
Simplicial Complexes ◽  
Generating Set ◽  
Minimal Generating Set

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

scholarly journals Graphs with many vertex-disjoint cycles

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Dieter Rautenbach ◽  
Friedrich Regen
Keyword(s):  
Graph Theory ◽  
Upper Bound ◽  
Linear Time ◽  
Simple Extension ◽  
Disjoint Cycles ◽  
Cyclomatic Number ◽  
Finite Set ◽  
Extension Rule ◽  
International Audience ◽  
Vertex Disjoint

Graph Theory International audience We study graphs G in which the maximum number of vertex-disjoint cycles nu(G) is close to the cyclomatic number mu(G), which is a natural upper bound for nu(G). Our main result is the existence of a finite set P(k) of graphs for all k is an element of N-0 such that every 2-connected graph G with mu(G)-nu(G) = k arises by applying a simple extension rule to a graph in P(k). As an algorithmic consequence we describe algorithms calculating minmu(G)-nu(G), k + 1 in linear time for fixed k.

scholarly journals Optimal and Nonoptimal Gronwall Lemmas

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1728
Author(s):  
Daniela Marian ◽  
Sorina Anamaria Ciplea ◽  
Nicolaie Lungu
Keyword(s):  
Upper Bound ◽  
Partial Answer ◽  
Optimal Inequalities

In this paper, we study some optimal inequalities of the Riccati type and of the Bihari type. We also consider nonoptimal inequalities of the Wendorf type. At the same time, we get a partial answer to Problems 5 and 9, formulated by I. A. Rus. This paper is also motivated by the fact that, in many inequalities, the upper bound is not an optimal one.

Dominance Relationships and Agonistic Behavior of Canada Geese in Winter

Behaviour ◽  
1970 ◽  
Vol 37 (3-4) ◽  
pp. 291-318 ◽  
Author(s):  
Dennis G. Raveling
Keyword(s):  
Individual Recognition ◽  
Rank Order ◽  
Large Family ◽  
Dominance Order ◽  
Canada Geese ◽  
Erect Posture ◽  
Dominance Relationships ◽  
Rank Orders ◽  
Violent Attack ◽  
Almost All

AbstractThe dominance relationships and associated agonistic postures of Canada geese were studied during the winters 1963-64 and 1964-65 by observation of the behavior of radio-and color-marked families and individuals living in a large, wild flock in southern Illinois. Part I I. Behavior was not significantly altered by color-marking and attachment of trausmitters. 2. Hostile encounters occurred during almost all activities. They varied widely in frequency and intensity and were especially associated with feeding. 3. Success in hostile encounters was directly related to family size, i.e., large family> smaller family > pair > single. 4. Unified action by all members of a family occurred in 8.5 percent of victories and T5 percent of defeats. 5. All members of a family shared equal dominance status but the success of a family in the rank order was most dependent upon the gander. 6. Only once in 26 fights between unmarked family ganders did the gander of the largest family lose. 7. Dominance position of family individuals decreased immediately upon separation and increased upon reunification of family members. 8. Large families were engaged in significantly more conflicts per unit time than were singles, pairs, and small families. 9. Exceptions to the usual dominance hierarchy occurred after pairs were newly formed. The gander of a newly formed pair could dominate family ganders. 10. Intrafamily aggression was rare and of low intensity. 11. Fights rarely occurred; threats and chases were common. 12. In some instances, rank orders based upon individual recognition could exist. However, stable rank orders in most large flocks appear to be based on recognition of different postures and levels of intensity of threat. 13. The dominance order of geese yields benefit in terms of food and space acquisition and freedom from defeat in aggressive encounters for the pairs and their young in direct relation to those most successful at raising a brood. Part II 1. Postures associated with attack or fleeing or simultaneous tendencies to do both are described. These include actual fleeing or attack, Submissive attitude, Erect, Head-pumping, Rolling, Bent-neck, and Forward postures. 2. The Submissive attitude is exhibited mostly by single geese and probably results from the conflicting tendency to approach (but not attack) and flee from other geese at the same time. This posture functions to identify single geese, allow approach, habituation, and ultimately pair formation, and inhibits violent attack. 3. The Erect posture may take either the form of intention movements of escape or attack and represents an ambivalent motivation between these two tendencies. 4. Head-pumping contains alternating intention movements of attacking and fleeing and represents almost a perfect balance between these two tendencies but is of higher intensity and ritualization than the Erect position. 5. Rolling is a complex portion of the Triumph Ceremony but also serves as the most intense threat of Canada geese and is highly ritualized. The spatial relationships of a gander to his mate and family appear most important in motivating Rolling. Intrusion of another high ranking gander or family on those boundaries may result in violent attack. 6. Erect, Head-pumping, and Rolling serve as three different intensity threats which are recognized by other geese and serve to maintain and establish the rank order of geese without undue fighting. 7. Bent-neck and Forward postures may occasionally represent conflicting attack and flee tendencies but often appear to represent a conflict of attack and remain doing another activity such as feeding or preening. These postures serve to maintain and reinforce a rank order but are probably not very important in initial establishment of rank.

Children who work in the street in Izmir, Turkey

2011 ◽  
Vol 39 (1) ◽  
pp. 129-144 ◽  
Author(s):  
Hatice Bal Yilmaz ◽  
Şeyda Dülgerler
Keyword(s):  
Risk Factors ◽  
Large Family ◽  
Great Majority ◽  
School Age ◽  
The Family ◽  
Big City ◽  
Economic Contribution ◽  
Almost All ◽  
Primary School Age

Using Izmir, Turkey as a case study the risk factors leading children to work in the streets were identified. Participants in the study were 226 children working in the streets, average age 10.35±2.21 who worked 6.8±2.11 hours per day. The great majority of the children were boys (90.2%), 77.9% were of primary school age; two-thirds of the children were working to provide an economic contribution to the family; 86.6% were from a large family; 78.8% were from a family that migrated to a big city. Almost all did not find working in the street safe; and nearly half were not hopeful about the future. It was established that frequent problems in the children's families include poverty, unemployment, poor education, having a large family, poor family functioning, migration, limited possibilities of shelter, and domestic violence, including the beating of wives and children. Although nearly all the children still lived with their families, a small percentage of the children (5.8%) had begun living permanently on the streets and then cut ties with their families. A significant relationship was found between living on the streets and the age of the child, the father's education, and the father's use of alcohol.

The Measure of Plane Sets

1943 ◽  
Vol 39 (1) ◽  
pp. 51-53
Author(s):  
P. A. P. Moran
Keyword(s):  
Finite Number ◽  
Coordinate System ◽  
Lebesgue Measure ◽  
Upper Bound ◽  
Two Dimensional ◽  
Image Position ◽  
Bounded Sets ◽  
Dimensional Lebesgue Measure

We consider bounded sets in a plane. If X is such a set, we denote by Pθ(X) the projection of X on the line y = x tan θ, where x and y belong to some fixed coordinate system. By f(θ, X) we denote the measure of Pθ(X), taking this, in general, as an outer Lebesgue measure. The least upper bound of f (θ, X) for all θ we denote by M. We write sm X for the outer two-dimensional Lebesgue measure of X. Then G. Szekeres(1) has proved that if X consists of a finite number of continua,Béla v. Sz. Nagy(2) has obtained a stronger inequality, and it is the purpose of this paper to show that these results hold for more general classes of sets.

scholarly journals A Hypothetical Upper Bound on the Heights of the Solutions of a Diophantine Equation with a Finite Number of Solutions

2018 ◽  
Author(s):  
Apoloniusz Tyszka
Keyword(s):  
Positive Integer ◽  
Finite Number ◽  
Diophantine Equation ◽  
Upper Bound ◽  
Diophantine Equations ◽  
Rational Solution ◽  
Infinitely Many Solutions ◽  
Rational Solutions ◽  
Number Of Solutions ◽  
Integer Solutions

Let f ( 1 ) = 1 , and let f ( n + 1 ) = 2 2 f ( n ) for every positive integer n. We consider the following hypothesis: if a system S ⊆ {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x1, . . . , xn, then each such solution (x1, . . . , xn) satisfies x1, . . . , xn ≤ f (2n). We prove:   (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set M ⊆ N has a finite-fold Diophantine representation, then M is computable.

scholarly journals On Compact Encoding of Pagenumber $k$ Graphs

2008 ◽  
Vol Vol. 10 no. 3 ◽  
Author(s):  
Cyril Gavoille ◽  
Nicolas Hanusse
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Constant Time ◽  
Worst Case ◽  
Encoding Scheme ◽  
Information Theoretic ◽  
Auxiliary Table ◽  
Minimum Number ◽  
International Audience

International audience In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(kn) bits in the worst-case. For m-edge graphs of pagenumber k (with multi-edges and loops), we propose a 2mlog2k + O(m) bits encoding improving the best previous upper bound of Munro and Raman whenever m ≤ 1 / 2kn/log2 k. Actually our scheme applies to k-page embedding containing multi-edge and loops. Moreover, with an auxiliary table of o(m log k) bits, our coding supports (1) the computation of the degree of a node in constant time, (2) adjacency queries with O(logk) queries of type rank, select and match, that is in O(logk *minlogk / loglogm, loglogk) time and (3) the access to δ neighbors in O(δ) runs of select, rank or match;.

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