scholarly journals Crossing-Symmetric Decomposition of then-Point Veneziano Formula into Tree-Graph Integrals. I

1971 ◽  
Vol 45 (2) ◽  
pp. 451-470 ◽  
Author(s):  
Noboru Nakanishi
Keyword(s):  
Tree Graph ◽  
Symmetric Decomposition ◽  
Veneziano Formula

Evaluation of TiO2 nanotubes array ordering in tree-graph representation

2017 ◽  
Author(s):  
P. L. Titov ◽  
S. A. Schegoleva ◽  
N. B. Kondrikov
Keyword(s):  
Tio2 Nanotubes ◽  
Graph Representation ◽  
Tree Graph

Application of Tree Graph Method for Reducing the Total Time of Tool Changing in Milling and Boring Machine Tools

2013 ◽  
Vol 371 ◽  
pp. 431-435 ◽  
Author(s):  
Claudiu Obreja ◽  
Gheorghe Stan ◽  
Lucian Adrian Mihaila ◽  
Marius Pascu
Keyword(s):  
Machine Tools ◽  
Design Method ◽  
Machining Process ◽  
Cnc Machine Tools ◽  
Tree Graph ◽  
Cnc Machine ◽  
High Productivity ◽  
Automatic Tool Changer ◽  
Automatic Tool ◽  
Set Up

With a view of increasing the productivity on CNC machine tools one of the main solution is to reduce, as much as possible, the auxiliary time consumed with the set-up and replacement of the tools and work pieces engaged in the machining process. Reducing the total time of the tool changing process by the automatic tool changer system can be also achieved through minimizing the number of movements needed for the actual exchange of the tool, from the tool magazine to the machine spindle (the optimization of the tool changing sequences). This paper presents a new design method based on the tree-graph theory. We consider an existing automatic tool changing system, mounted on the milling and boring machining centre, and by applying the new method we obtain all the possible configurations to minimize the tool changing sequence of the automatic tool changer system. By making use of the method proposed we obtain the tool changing sequences with minimum necessary movements needed to exchange the tool. Reconfiguring an existing machine tool provided with an automatic tool changer system by making use of the proposed method leads to obtaining the smallest changing time and thus high productivity.

scholarly journals The $1/k$-Eulerian Polynomials of Type $B$

10.37236/9313 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Shi-Mei Ma ◽  
Jun Ma ◽  
Jean Yeh ◽  
Yeong-Nan Yeh
Keyword(s):  
Recurrence Relations ◽  
Type B ◽  
Eulerian Polynomials ◽  
Combinatorial Interpretations ◽  
Symmetric Decomposition

In this paper, we define the $1/k$-Eulerian polynomials of type $B$. Properties of these polynomials, including combinatorial interpretations, recurrence relations and $\gamma$-positivity are studied. In particular, we show that the $1/k$-Eulerian polynomials of type $B$ are $\gamma$-positive when $k>0$. Moreover, we define the $1/k$-derangement polynomials of type $B$, denoted $d_n^B(x;k)$. We show that the polynomials $d_n^B(x;k)$ are bi-$\gamma$-positive when $k\geq 1/2$. In particular, we get a symmetric decomposition of the polynomials $d_n^B(x;1/2)$ in terms of the classical derangement polynomials.

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