scholarly journals Unbalanced digit sets and the closest choice strategy for minimal weight integer representations

2009 ◽  
Vol 52 (2) ◽  
pp. 185-208 ◽  
Author(s):  
Clemens Heuberger ◽  
James A. Muir
Keyword(s):  
Minimal Weight ◽  
Choice Strategy

Wrestlers?? minimal weight

1991 ◽  
Vol 23 (2) ◽  
pp. 247???253 ◽  
Author(s):  
ROBERT A. OPPLIGER ◽  
DAVID H. NIELSEN ◽  
CAROL G. VANCE
Keyword(s):  
Minimal Weight

Selection of the Optimal Structural Design of a Spar Composite Wing

2021 ◽  
pp. 90-99
Author(s):  
O.V. Tatarnikov ◽  
W.A. Phyo ◽  
Lin Aung Naing
Keyword(s):  
Optimal Design ◽  
Element Analysis ◽  
Minimal Weight ◽  
Wing Structures ◽  
Optimization Parameters ◽  
Nonlinear Static ◽  
Wing Structure ◽  
Pareto Method ◽  
Selection Of ◽  
Composite Wing

This paper describes a method for optimizing the design of a spar-type composite aircraft wing structure based on multi-criterion approach. Two types of composite wing structures such as two-spar and three-spar ones were considered. The optimal design of a wing frame was determined by the Pareto method basing on three criteria: minimal weight, minimal wing deflection, maximal safety factor and minimal weight. Positions of wing frame parts, i.e. spars and ribs, were considered as optimization parameters. As a result, an optimal design of a composite spar-type wing was proposed. All the calculations necessary to select the optimal structural and design of the spar composite wing were performed using nonlinear static finite element analysis in the FEMAP with NX Nastran software package.

scholarly journals Constructions of vector-valued modular forms of rank four and level one

2020 ◽  
Vol 16 (05) ◽  
pp. 1111-1152
Author(s):  
Cameron Franc ◽  
Geoffrey Mason
Keyword(s):  
Irreducible Representation ◽  
Differential Equations ◽  
Modular Forms ◽  
Modular Group ◽  
Tensor Products ◽  
Two Dimensional ◽  
Minimal Weight ◽  
Graded Module ◽  
Holomorphic Modular Forms ◽  
Vector Valued

This paper studies modular forms of rank four and level one. There are two possibilities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we describe when each case occurs for general choices of exponents for the [Formula: see text]-matrix. In the remaining sections we describe how to write down the corresponding differential equations satisfied by minimal weight forms, and how to use these minimal weight forms to describe the entire graded module of holomorphic modular forms. Unfortunately, the differential equations that arise can only be solved recursively in general. We conclude the paper by studying the cases of tensor products of two-dimensional representations, symmetric cubes of two-dimensional representations, and inductions of two-dimensional representations of the subgroup of the modular group of index two. In these cases, the differential equations satisfied by minimal weight forms can be solved exactly.

scholarly journals Minimal Weight in Union-Closed Families

10.37236/582 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Victor Falgas-Ravry
Keyword(s):  
Lower Bound ◽  
Related Question ◽  
Average Degree ◽  
Additional Information ◽  
Minimal Weight ◽  
Multiplicative Factor ◽  
Finite Set

Let $\Omega$ be a finite set and let $\mathcal{S} \subseteq \mathcal{P}(\Omega)$ be a set system on $\Omega$. For $x\in \Omega$, we denote by $d_{\mathcal{S}}(x)$ the number of members of $\mathcal{S}$ containing $x$. A long-standing conjecture of Frankl states that if $\mathcal{S}$ is union-closed then there is some $x\in \Omega$ with $d_{\mathcal{S}}(x)\geq \frac{1}{2}|\mathcal{S}|$. We consider a related question. Define the weight of a family $\mathcal{S}$ to be $w(\mathcal{S}) := \sum_{A \in \mathcal{S}} |A|$. Suppose $\mathcal{S}$ is union-closed. How small can $w(\mathcal{S})$ be? Reimer showed $$w(\mathcal{S}) \geq \frac{1}{2} |\mathcal{S}| \log_2 |\mathcal{S}|,$$ and that this inequality is tight. In this paper we show how Reimer's bound may be improved if we have some additional information about the domain $\Omega$ of $\mathcal{S}$: if $\mathcal{S}$ separates the points of its domain, then $$w(\mathcal{S})\geq \binom{|\Omega|}{2}.$$ This is stronger than Reimer's Theorem when $\vert \Omega \vert > \sqrt{|\mathcal{S}|\log_2 |\mathcal{S}|}$. In addition we construct a family of examples showing the combined bound on $w(\mathcal{S})$ is tight except in the region $|\Omega|=\Theta (\sqrt{|\mathcal{S}|\log_2 |\mathcal{S}|})$, where it may be off by a multiplicative factor of $2$. Our proof also gives a lower bound on the average degree: if $\mathcal{S}$ is a point-separating union-closed family on $\Omega$, then $$ \frac{1}{|\Omega|} \sum_{x \in \Omega} d_{\mathcal{S}}(x) \geq \frac{1}{2} \sqrt{|\mathcal{S}| \log_2 |\mathcal{S}|}+ O(1),$$ and this is best possible except for a multiplicative factor of $2$.

Research on Network-on-Chip Dynamic and Adaptive Algorithm and Choice Strategy

2014 ◽  
Vol 539 ◽  
pp. 296-302
Author(s):  
Dong Li
Keyword(s):  
Energy Consumption ◽  
Execution Time ◽  
Adaptive Algorithm ◽  
Network On Chip ◽  
Time Dimension ◽  
Choice Strategy ◽  
Bus Structure ◽  
On Chip ◽  
Mapping Scheme ◽  
Single Objective

With further increase of the number of on-chip device, the bus structure has not met the requirements. In order to make better communication between each part, the chip designers need to explore a new structure to solve the interconnection of on-chip device. The paper proposes a network-on-chip dynamic and adaptive algorithm which selects NoC platform with 2-dimension mesh as the carrier, incorporates communication energy consumption and delay into unified cost function and uses ant colony optimization to realize NOC map facing energy consumption and delay. The experiment indicates that compared with random map, single objective optimization can separately saves (30%~47 %) and ( 20%~39%) in communication energy consumption and execution time compared with random map, and joint objective optimization can further excavate the potential of time dimension in mapping scheme dominated by the energy.

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