scholarly journals ON THE REMAK HEIGHT, THE MAHLER MEASURE AND CONJUGATE SETS OF ALGEBRAIC NUMBERS LYING ON TWO CIRCLES

2001 ◽  
Vol 44 (1) ◽  
pp. 1-17 ◽  
Author(s):  
A. Dubickas ◽  
C. J. Smyth
Keyword(s):  
Lower Bounds ◽  
Height Function ◽  
Complete Characterization ◽  
Mahler Measure ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Algebraic Numbers ◽  
Salem Numbers ◽  
Primary 11R06

AbstractWe define a new height function $\mathcal{R}(\alpha)$, the Remak height of an algebraic number $\alpha$. We give sharp upper and lower bounds for $\mathcal{R}(\alpha)$ in terms of the classical Mahler measure $M(\alpha)$. Study of when one of these bounds is exact leads us to consideration of conjugate sets of algebraic numbers of norm $\pm 1$ lying on two circles centred at 0. We give a complete characterization of such conjugate sets. They turn out to be of two types: one related to certain cubic algebraic numbers, and the other related to a non-integer generalization of Salem numbers which we call extended Salem numbers.AMS 2000 Mathematics subject classification: Primary 11R06

Stochastic inequalities for an overflow model

1987 ◽  
Vol 24 (3) ◽  
pp. 696-708 ◽  
Author(s):  
Arie Hordijk ◽  
Ad Ridder
Keyword(s):  
Failure Rate ◽  
Lower Bounds ◽  
Approximation Method ◽  
Queueing Networks ◽  
Upper And Lower Bounds ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Decreasing Failure Rate ◽  
General Method

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

LOWER BOUNDS FOR THE NORMALIZED HEIGHT AND NON-DENSE SUBSETS OF SUBVARIETIES OF ABELIAN VARIETIES

2010 ◽  
Vol 06 (03) ◽  
pp. 471-499 ◽  
Author(s):  
EVELINA VIADA
Keyword(s):  
Lower Bound ◽  
Elliptic Curve ◽  
Abelian Variety ◽  
Lower Bounds ◽  
Finite Rank ◽  
Height Function ◽  
Algebraic Numbers ◽  
Algebraic Subgroup ◽  
Rank Zero ◽  
The Third

This work is the third part of a series of papers. In the first two, we considered curves and varieties in a power of an elliptic curve. Here, we deal with subvarieties of an abelian variety in general. Let V be a proper irreducible subvariety of dimension d in an abelian variety A, both defined over the algebraic numbers. We say that V is weak-transverse if V is not contained in any proper algebraic subgroup of A, and transverse if it is not contained in any translate of such a subgroup. Assume a conjectural lower bound for the normalized height of V. Then, for V transverse, we prove that the algebraic points of bounded height of V which lie in the union of all algebraic subgroups of A of codimension at least d + 1 translated by the points close to a subgroup Γ of finite rank, are non-Zariski-dense in V. If Γ has rank zero, it is sufficient to assume that V is weak-transverse. The notion of closeness is defined using a height function.

scholarly journals Bounds for the Collapse Load of a Beam Compressed by Three Dies

1956 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
W Freiberger
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Plastic Yielding ◽  
Plane Plastic

This paper deals with the problem of the plastic deformation of a beam under the action of three perfectly rough rigid dies, two dies applied to one side, one die to the other side of the beam, the single die being situated between the two others. It is treated as a problem of plane plastic flow. Discontinuous stress and velocity fields are assumed and upper and lower bounds for the pressure sufficient to cause pronounced plastic yielding determined by limit analysis.

scholarly journals Locating Chromatic Number of Powers of Paths and Cycles

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 389
Author(s):  
Manal Ghanem ◽  
Hasan Al-Ezeh ◽  
Ala’a Dabbour
Keyword(s):  
Chromatic Number ◽  
Lower Bounds ◽  
Minimum Distance ◽  
Upper And Lower Bounds ◽  
Color Code ◽  
Partition Class ◽  
Distinct Color

Let c be a proper k-coloring of a graph G. Let π = { R 1 , R 2 , … , R k } be the partition of V ( G ) induced by c, where R i is the partition class receiving color i. The color code c π ( v ) of a vertex v of G is the ordered k-tuple ( d ( v , R 1 ) , d ( v , R 2 ) , … , d ( v , R k ) ) , where d ( v , R i ) is the minimum distance from v to each other vertex u ∈ R i for 1 ≤ i ≤ k . If all vertices of G have distinct color codes, then c is called a locating k-coloring of G. The locating-chromatic number of G, denoted by χ L ( G ) , is the smallest k such that G admits a locating coloring with k colors. In this paper, we give a characterization of the locating chromatic number of powers of paths. In addition, we find sharp upper and lower bounds for the locating chromatic number of powers of cycles.

scholarly journals TOTAL CURVATURES OF HOLONOMIC LINKS

2000 ◽  
Vol 09 (07) ◽  
pp. 893-906 ◽  
Author(s):  
TOBIAS EKHOLM ◽  
OLA WEISTRAND
Keyword(s):  
Lower Bounds ◽  
Total Curvature ◽  
Geometric Characterization ◽  
Upper And Lower Bounds ◽  
Braid Index

A differential geometric characterization of the braid-index of a link is found. After multiplication by 2π, it equals the infimum of the sum of total curvature and total absolute torsion over holonomic representatives of the link. Upper and lower bounds for the infimum of the total curvature over holonomic representatives of a link are given in terms of its braid- and bridge-index. Examples showing that these bounds are sharp are constructed.

Minimal Reversible Deterministic Finite Automata

2018 ◽  
Vol 29 (02) ◽  
pp. 251-270 ◽  
Author(s):  
Markus Holzer ◽  
Sebastian Jakobi ◽  
Martin Kutrib
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Transition Function ◽  
Upper And Lower Bounds ◽  
State Graph ◽  
Deterministic Finite Automata ◽  
Injective Mapping ◽  
Pattern Approach ◽  
Almost All

We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on the absence of a forbidden pattern in the (minimal) deterministic state graph. Again with a forbidden pattern approach, we also show that the minimality of REV-DFAs among all equivalent REV-DFAs can be decided. Both forbidden pattern characterizations give rise to [Formula: see text]-complete decision algorithms. In fact, our techniques allow us to construct the minimal REV-DFA for a given minimal DFA. These considerations lead to asymptotic upper and lower bounds on the conversion from DFAs to REV-DFAs. Thus, almost all problems that concern uniqueness and the size of minimal REV-DFAs are solved.

Can letter position encoding be modified by visual perceptual elements?

2018 ◽  
Vol 72 (6) ◽  
pp. 1344-1353 ◽  
Author(s):  
Ana Marcet ◽  
Manuel Perea ◽  
Ana Baciero ◽  
Pablo Gomez
Keyword(s):  
Lexical Decision ◽  
Letter Position ◽  
Complete Characterization ◽  
The Other ◽  
Letter Position Coding ◽  
Position Coding ◽  
Visual Characteristics ◽  
Abstract Component ◽  
Perceptual Locus

A plethora of studies has revealed that letter position coding is relatively flexible during word recognition (e.g., the transposed-letter [TL] pseudoword CHOLOCATE is frequently misread as CHOCOLATE). A plausible explanation of this phenomenon is that letter identity and location are not perfectly bound as a consequence of the limitations of the visual system. Thus, a complete characterization of letter position coding requires an examination of how letter position coding can be modulated by visual perceptual elements. Here we conducted three lexical decision experiments with TL and replacement-letter pseudowords that manipulated the visual characteristics of the stimuli. In Experiment 1, each syllable was presented either in a different colour or monochromatically (e.g., [Formula: see text] vs. [Formula: see text]) with the transposition occurring across syllables. In Experiment 2, the critical letters had a consistent contrast or not (e.g., [Formula: see text] vs. [Formula: see text]). In Experiment 3, the stimuli were presented either simultaneously or serially, letter by letter (i.e., as occurs in braille reading). Results showed that whereas colouring differently each syllable only produced a small nonsignificant reduction of the TL effect, the other two manipulations—presenting the two critical letters with an altered contrast and presenting the letters one at a time—reduced, but did not eliminate, the magnitude of the TL effect relative to the regular format. Although these findings are consistent with models that postulate an early perceptual locus of the TL effect, the robustness of the TL effect suggests that letter position coding also has an orthographic abstract component.

Upper and Lower Bounds for the Number of Conjugated Patterns in Carbocyclic and Heterocyclic Compounds

1994 ◽  
Vol 49 (10) ◽  
pp. 973-976
Author(s):  
Tetsuo Morikawa
Keyword(s):  
Lower Bounds ◽  
Special Class ◽  
Heterocyclic Compounds ◽  
The Other ◽  
Upper And Lower Bounds ◽  
The One

Abstract It is possible to regard two polygonal skeletons as the same in a special class of carbocyclic and heterocyclic compounds, if the one is reducible to the other by means of the contraction of cyclic subskeletons, and if the numbers of conjugated patterns in them are equal to each other. In such polygonal skeletons, three forms of cyclic subskeletons are defined; the one is called “alternate”, and the others, involving the one called “inclusive”, have a path (b, b), where (b) is a conjugated vertex connecting with three vertices. Successive eliminations of the cyclic subskeletons enable to estimate the upper and lower bounds for the number of conjugated patterns in a given polygonal skeleton.

scholarly journals Chemical characterization of commercial and single-variety avocado oils

2018 ◽  
Vol 69 (2) ◽  
pp. 256 ◽  
Author(s):  
G. D. Fernandes ◽  
R. B. Gómez-Coca ◽  
M. C. Pérez-Camino ◽  
W. Moreda ◽  
D. Barrera-Arellano
Keyword(s):  
Fatty Acids ◽  
Chemical Characterization ◽  
Complete Characterization ◽  
The Other ◽  
Principal Minor ◽  
Avocado Oil ◽  
Terpenic Alcohols ◽  
Minor Compounds ◽  
Single Variety

This work aimed to determine the major and minor compounds of avocado oils. Mono-varietal oils from the Bacon, Fuerte, Hass, and Pinkerton cultivars were obtained by means of an Abencor® system, while commercial oils from Brazil, Chile, Ecuador and New Zealand were purchased locally. The content of triacylglycerols, fatty acids, aliphatic and terpenic alcohols, desmethyl- methyl- and dimethyl-sterols, squalene and tocopherols were determined. The main triacylglycerols were those with ECN48. In addition, the oleic, palmitic and linoleic acids prevailed. Desmethyl-sterols were the principal minor compounds. Low amounts of aliphatic and terpenic alcohols were also found. Squalene concentrations were higher in Bacon, Fuerte and Pinkerton oils than in the other oils. The most abundant tocopherol was α-tocopherol. Partial least squares discriminant analysis made it possible to express the differences among the samples. To summarize, this work brings a different approach to the complete characterization of avocado oil.

scholarly journals Maximal prime gaps bounds

2021 ◽  
Author(s):  
Jan Feliksiak
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Estimation Error ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Close Approximation ◽  
Implicit Constant ◽  
Error Cost ◽  
Prime Gaps

This paper presents research results, pertinent to the maximal prime gaps bounds. Four distinct bounds are presented: Upper bound, Infimum, Supremum and finally the Lower bound. Although the Upper and Lower bounds incur a relatively high estimation error cost, the functions representing them are quite simple. This ensures, that the computation of those bounds will be straightforward and efficient. The Lower bound is essential, to address the issue of the value of the lower bound implicit constant C, in the work of Ford et al (Ford, 2016). The concluding Corollary in this paper shows, that the value of the constant C does diverge, although very slowly. The constant C, will eventually take any arbitrary value, providing that a large enough N (for p <= N) is considered. The Infimum/Supremum bounds on the other hand are computationally very demanding. Their evaluation entails computations at an extreme level of precision. In return however, we obtain bounds, which provide an extremely close approximation of the maximal prime gaps. The Infimum/Supremum estimation error gradually increases over the range of p and attains at p = 18361375334787046697 approximately the value of 0.03.

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