The Structure of Directed Forests of Minimal Weight: Algebra of Subsets

2021 ◽  
Author(s):  
V. A. Buslov
Keyword(s):  
Minimal Weight

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 $2$.

Antipsychotic and anticholinergic drugs

2020 ◽  
pp. 639-667
Author(s):  
Herbert Y. Meltzer ◽  
William V. Bobo
Keyword(s):  
Developmental Disorders ◽  
Negative Symptoms ◽  
Psychotic Disorders ◽  
Drug Action ◽  
Anticholinergic Drugs ◽  
Efficacy And Safety ◽  
Drug Induced ◽  
Minimal Weight ◽  
Long Acting

Antipsychotic drugs are utilized for far more than the treatment of psychosis in schizophrenia, their first indication. They now find wide use in a variety of psychotic disorders, mood disorders, developmental disorders, and drug-induced disorders. The classification of drugs as typical or atypical is based on their differences in extra-pyramidal side effects (EPS). This chapter emphasizes the greater diversity, efficacy, and safety of the atypical drugs, and the risk of tardive dyskinesia of the typical drugs. The atypical drug action may produce improvement in cognitive function and negative symptoms, as well as psychosis and mood in some patients. This diversity includes atypical drugs which produce minimal weight gain. Long-acting injectable formulations are recommended for non-adherent patients. The exceptional ability of clozapine to reduce the risk for suicide and to decrease mortality in schizophrenia is discussed. Anticholinergic and other drugs to treat EPS are also discussed.

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