scholarly journals Improved Bounds on mr(2,q) q=19,25,27

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rumen Daskalov ◽  
Elena Metodieva
Keyword(s):  
Projective Plane ◽  
Maximum Size ◽  
Upper Bounds ◽  
Computer Search ◽  
Lower And Upper Bounds ◽  
Local Computer

An (n,r)-arc is a set of n points of a projective plane such that some r, but no r+1 of them, are collinear. The maximum size of an (n,r)-arc in PG(2, q) is denoted by mr(2, q). In this paper, a new (286, 16)-arc in PG(2,19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2,27). Tables with lower and upper bounds on mr(2, 25) and mr(2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.

Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search

2015 ◽  
Vol 107 (1) ◽  
pp. 89-117 ◽  
Author(s):  
Daniele Bartoli ◽  
Alexander A. Davydov ◽  
Giorgio Faina ◽  
Alexey A. Kreshchuk ◽  
Stefano Marcugini ◽  
...  
Keyword(s):  
Projective Plane ◽  
Upper Bounds ◽  
Computer Search ◽  
Desarguesian Projective Plane ◽  
Complete Arc ◽  
Finite Desarguesian Projective Plane

scholarly journals Induced and Non-induced Forbidden Subposet Problems

10.37236/4644 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Balázs Patkós
Keyword(s):  
Asymptotic Behavior ◽  
Boolean Lattice ◽  
Maximum Size ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Extra Condition ◽  
Multi Level

The problem of determining the maximum size $La(n,P)$ that a $P$-free subposet of the Boolean lattice $B_n$ can have, attracted the attention of many researchers, but little is known about the induced version of these problems. In this paper we determine the asymptotic behavior of $La^*(n,P)$, the maximum size that an induced $P$-free subposet of the Boolean lattice $B_n$ can have for the case when $P$ is the complete two-level poset $K_{r,t}$ or the complete multi-level poset $K_{r,s_1,\dots,s_j,t}$ when all $s_i$'s either equal 4 or are large enough and satisfy an extra condition. We also show lower and upper bounds for the non-induced problem in the case when $P$ is the complete three-level poset $K_{r,s,t}$. These bounds determine the asymptotics of $La(n,K_{r,s,t})$ for some values of $s$ independently of the values of $r$ and $t$.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number

scholarly journals Lower and upper bounds of quantum battery power in multiple central spin systems

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Li Peng ◽  
Wen-Bin He ◽  
Stefano Chesi ◽  
Hai-Qing Lin ◽  
Xi-Wen Guan
Keyword(s):  
Upper Bounds ◽  
Spin Systems ◽  
Lower And Upper Bounds ◽  
Battery Power
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