Limit Design of Perforated Cylindrical Shells per ASME Code

1977 ◽  
Vol 99 (4) ◽  
pp. 646-651 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell ◽  
J. R. Farr
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
The Other ◽  
Safety Factors ◽  
Design Standards ◽  
Asme Code ◽  
Optimal Spacing ◽  
Circular Holes ◽  
Margin Of Safety ◽  
Actual Limit

Limit pressures are evaluated for cylindrical perforated shells containing circular holes arranged in the various penetration patterns typically found in practice. Statically admissible discontinuous fields of stress are used to obtain rigorous lower-bound limit pressures. These solutions are shown to be quite close to the actual limit pressures based on the efficiency of the discontinuous fields of stress and a comparison with upper-bound solutions. The optimal spacing parameters are obtained over the interesting range of ligament efficiencies for both the diamond (romboidal) and rectangular penetration patterns. The results of this work show that for most penetration configurations, the present ASME standards require substantially thicker shells than would be needed to maintain the same safety factors that are used for unperforated shells. On the other hand, the British and German standards allow the use of thinner shells than would be needed to maintain the safety factors for unperforated shells. Revised design curves which provide the same margin of safety for all configurations are derived and are proposed for use in design standards.

scholarly journals Nano topology induced by Lattices

2019 ◽  
Vol 38 (5) ◽  
pp. 197-204
Author(s):  
M. Lellis Thivagar ◽  
V. Sutha Devi
Keyword(s):  
Lower Bound ◽  
19Th Century ◽  
Upper Bound ◽  
Lattice Theory ◽  
Ordered Set ◽  
Equivalence Classes ◽  
The Other ◽  
Five Elements ◽  
Lower And Upper Approximations ◽  
The 19Th Century

Lattice is a partially ordered set in which all finite subsets have a least upper bound and greatest lower bound. Dedekind worked on lattice theory in the 19th century. Nano topology explored by Lellis Thivagar et.al. can be described as a collection of nano approximations, a non-empty finite universe and empty set for which equivalence classes are buliding blocks. This is named as Nano topology, because of its size and what ever may be the size of universe it has atmost five elements in it. The elements of Nano topology are called the Nano open sets. This paper is to study the nano topology within the context of lattices. In lattice, there is a special class of joincongruence relation which is defined with respect to an ideal. We have defined the nano approximations of a set with respect to an ideal of a lattice. Also some properties of the approximations of a set in a lattice with respect to ideals are studied. On the other hand, the lower and upper approximations have also been studied within the context various algebraic structures.

Automorphism Groups of Homogeneous Semilinear Orders: Normal Subgroups and Commutators

1991 ◽  
Vol 43 (4) ◽  
pp. 721-737 ◽  
Author(s):  
M. Droste ◽  
W. C. Holland ◽  
H. D. Macpherson
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Partially Ordered Set ◽  
Automorphism Groups ◽  
Ordered Set ◽  
Infinite Chain ◽  
The Other ◽  
Normal Subgroups ◽  
Partially Ordered

A partially ordered set (T, ≤) is called a tree if it is semilinearly ordered, i.e. any two elements have a common lower bound but no two incomparable elements have a common upper bound, and contains an infinite chain and at least two incomparable elements. Let k ∈ ℕ. We say that a partially ordered set (T, ≤) is k-homogeneous, if each isomorphism between two k-element subsets of T extends to an automorphism of (T, ≤), and weakly k-transitive, if for any two k-element subchains of T there exists an automorphism of (T, ≤) taking one to the other.

Upward directedness of the Rudin-Keisler ordering of p-points

1990 ◽  
Vol 55 (2) ◽  
pp. 449-456
Author(s):  
Claude Laflamme
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Related Question ◽  
The Other ◽  
Other Hand ◽  
New Construction

It has been proven by Blass [1973] that any two P-points which have a P-point as a common upper bound in the Rudin-Keisler (RK) ordering necessarily have a common lower bound (necessarily a P-point). Hence two nonisomorphic Ramsey ultrafilters have neither a common lower nor a common upper bound which is a P-point. So in a model of CH for example (or MA, P(c),…), the RK ordering restricted to P-points is neither upward nor downward directed, since it is well known that nonisomorphic Ramsey ultrafilters exist in such models. On the other hand, we will see that in the model for “near coherence of filters” (NCF) produced by Blass and Shelah [1985], the RK ordering of P-points is upward, hence downward directed. This shows that the question of directedness of the RK ordering of P-points, upward or downward, cannot be decided in ZFC.There is a related question, asked by Blass in [1973], whether two P-points which have a common lower bound necessarily have a common upper bound which is a P-point. Our main result establishes the independence of this statement relative to ZFC. Its consistency will follow as soon as we show that the RK ordering of P-points is upward directed in the NCF model mentioned above, which we do in §2. But its independence will require a new construction, and will be given in §3.

scholarly journals The length of an s-increasing sequence of r-tuples

2021 ◽  
pp. 1-36
Author(s):  
W. T. Gowers ◽  
J. Long
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Ramsey Theory ◽  
The Other ◽  
Simple Construction ◽  
Extremal Combinatorics ◽  
Removal Lemma

Abstract We prove a number of results related to a problem of Po-Shen Loh [9], which is equivalent to a problem in Ramsey theory. Let a = (a1, a2, a3) and b = (b1, b2, b3) be two triples of integers. Define a to be 2-less than b if a i < b i for at least two values of i, and define a sequence a1, …, a m of triples to be 2-increasing if a r is 2-less than a s whenever r < s. Loh asks how long a 2-increasing sequence can be if all the triples take values in {1, 2, …, n}, and gives a log* improvement over the trivial upper bound of n2 by using the triangle removal lemma. In the other direction, a simple construction gives a lower bound of n3/2. We look at this problem and a collection of generalizations, improving some of the known bounds, pointing out connections to other well-known problems in extremal combinatorics, and asking a number of further questions.

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.

Non-homogeneous binary cubic forms

1951 ◽  
Vol 47 (3) ◽  
pp. 457-460 ◽  
Author(s):  
R. P. Bambah
Keyword(s):  
Lower Bound ◽  
Finite Volume ◽  
Upper Bound ◽  
The Other ◽  
Real Numbers ◽  
Cubic Form ◽  
Homogeneous Form ◽  
Other Hand ◽  
Image Position ◽  
Cubic Forms

1. Let f(x1, x2, …, xn) be a homogeneous form with real coefficients in n variables x1, x2, …, xn. Let a1, a2, …, an be n real numbers. Define mf(a1, …, an) to be the lower bound of | f(x1 + a1, …, xn + an) | for integers x1, …, xn. Let mf be the upper bound of mf(a1, …, an) for all choices of a1, …, an. For many forms f it is known that there exist estimates for mf in terms of the invariants alone of f. On the other hand, it follows from a theorem of Macbeath* that no such estimates exist if the regionhas a finite volume. However, for such forms there may be simple estimates for mf dependent on the coefficients of f; for example, Chalk has conjectured that:If f(x,y) is reduced binary cubic form with negative discriminant, then for any real a, b there exist integers x, y such that

scholarly journals NOTE ON THE NUMBER OF OBTUSE ANGLES IN POINT SETS

2014 ◽  
Vol 24 (03) ◽  
pp. 177-181 ◽  
Author(s):  
RUY FABILA-MONROY ◽  
CLEMENS HUEMER ◽  
EULÀLIA TRAMUNS
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
General Position ◽  
Crossing Number ◽  
The Other ◽  
Point Sets ◽  
Convex Position ◽  
Minimum Number

In 1979 Conway, Croft, Erdős and Guy proved that every set S of n points in general position in the plane determines at least [Formula: see text] obtuse angles and also presented a special set of n points to show the upper bound [Formula: see text] on the minimum number of obtuse angles among all sets S. We prove that every set S of n points in convex position determines at least [Formula: see text] obtuse angles, hence matching the upper bound (up to sub-cubic terms) in this case. Also on the other side, for point sets with low rectilinear crossing number, the lower bound on the minimum number of obtuse angles is improved.

scholarly journals Density Guarantee on Finding Multiple Subgraphs and Subtensors

2021 ◽  
Vol 15 (5) ◽  
pp. 1-32
Author(s):  
Quang-huy Duong ◽  
Heri Ramampiaro ◽  
Kjetil Nørvåg ◽  
Thu-lan Dam
Keyword(s):  
Lower Bound ◽  
State Of The Art ◽  
The State ◽  
The Other ◽  
Exact Methods ◽  
Practical Solution ◽  
Novel Approach ◽  
Wide Range ◽  
Real World Datasets ◽  
Tensor Data

Dense subregion (subgraph & subtensor) detection is a well-studied area, with a wide range of applications, and numerous efficient approaches and algorithms have been proposed. Approximation approaches are commonly used for detecting dense subregions due to the complexity of the exact methods. Existing algorithms are generally efficient for dense subtensor and subgraph detection, and can perform well in many applications. However, most of the existing works utilize the state-or-the-art greedy 2-approximation algorithm to capably provide solutions with a loose theoretical density guarantee. The main drawback of most of these algorithms is that they can estimate only one subtensor, or subgraph, at a time, with a low guarantee on its density. While some methods can, on the other hand, estimate multiple subtensors, they can give a guarantee on the density with respect to the input tensor for the first estimated subsensor only. We address these drawbacks by providing both theoretical and practical solution for estimating multiple dense subtensors in tensor data and giving a higher lower bound of the density. In particular, we guarantee and prove a higher bound of the lower-bound density of the estimated subgraph and subtensors. We also propose a novel approach to show that there are multiple dense subtensors with a guarantee on its density that is greater than the lower bound used in the state-of-the-art algorithms. We evaluate our approach with extensive experiments on several real-world datasets, which demonstrates its efficiency and feasibility.

scholarly journals Tripartite entropic uncertainty relation under phase decoherence

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. A. Abdelghany ◽  
A.-B. A. Mohamed ◽  
M. Tammam ◽  
Watson Kuo ◽  
H. Eleuch
Keyword(s):  
Lower Bound ◽  
Uncertainty Relation ◽  
Nearest Neighbors ◽  
The Other ◽  
Uncertainty In Measurement ◽  
Entropic Uncertainty Relation ◽  
Specific Choice ◽  
Phase Decoherence ◽  
Time Invariant ◽  
Incompatible Observables

AbstractWe formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

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