On the Scattering on a Loop-shaped Graph

2012 ◽  
pp. 227-245 ◽  
Author(s):  
K. Mochizuki ◽  
I. Yu. Trooshin
Keyword(s):  
Shaped Graph

Easy Absolute Values? Absolutely

2015 ◽  
Vol 21 (1) ◽  
pp. 49-52
Author(s):  
Sharon E. Taylor ◽  
Kathleen Cage Mittag
Keyword(s):  
Absolute Value ◽  
Algebra Students ◽  
Advanced Students ◽  
Solving Equations ◽  
The Absolute ◽  
Shaped Graph

When we ask algebra students to tell us about absolute value, we usually get an answer along the lines of “something that is always positive.” Students immediately question their answer when asked about the absolute value of zero (0). Sometimes our more advanced students say that it has a V-shaped graph or mention the piecewise definition. Despite the varied answers given by our students, seldom do we hear the answer “distance from 0.” However, using distance from 0 is the perfect way to help students understand absolute-value computations. Distance from 0 also provides a foundation for solving equations and inequalities.

Structural Design Exploration for Product Architecture Design

2020 ◽  
Author(s):  
Masato Toi ◽  
Yutaka Nomaguchi ◽  
Kikuo Fujita
Keyword(s):  
Modular Design ◽  
Design Method ◽  
Critical Issue ◽  
Product Architecture ◽  
Architecture Design ◽  
Hierarchical Tree ◽  
Design Structure ◽  
Representative Model ◽  
Shaped Graph ◽  
Mathematical Operations

Abstract This paper proposed a design support method based on structuralization and analysis of various design candidates of product architecture design. The product architecture is a basic scheme that assigns the function of the product to physical components. In the conventional modular design method, a concise model, i.e., a graph or a matrix, is used to express the interactions of the system’s components and aims to support the designer grasping the system behavior. The Design Structure Matrix (DSM) is a representative model of system architecture and enables quantitative evaluation of design candidates. While various design candidates are generated through mathematical operations, it is difficult to understand their relationships from simple comparisons because of discrete behavior and the size of the problem. It must be a critical issue at the stage of selecting and interpreting the design candidates. In the proposed method, the design candidates are classified and structuralized as a dendrogram by the hierarchical clustering method. The comparison of clusters of each branch of dendrogram clarifies the system leverage points. The information of the system is summarized into the hierarchical tree-shaped graph that corresponds to the dendrogram. The designer can explore the design candidates with such a graph-based based interpretation of underlying structures effectively.

Partial inverse nodal problems for differential pencils on a star‐shaped graph

2020 ◽  
Vol 43 (15) ◽  
pp. 8841-8855
Author(s):  
Yu Ping Wang ◽  
Chung‐Tsun Shieh ◽  
Xianbiao Wei
Keyword(s):  
Partial Inverse ◽  
Inverse Nodal Problems ◽  
Shaped Graph ◽  
Differential Pencils

On an equation connected with the theory of triode oscillations

1952 ◽  
Vol 48 (4) ◽  
pp. 698-717 ◽  
Author(s):  
R. A. Smith
Keyword(s):  
Electrical Circuit ◽  
Forced Oscillations ◽  
Qualitative Behaviour ◽  
Current Voltage Characteristic ◽  
Van Der Pol ◽  
Flat Bottom ◽  
Near Resonance ◽  
Current Voltage ◽  
Image Position ◽  
Shaped Graph

This discussion is concerned with the periodic solutions of the differential equationwhere the parameter k is small. The equation arises from an investigation of the forced oscillations of a simple electrical circuit (6) containing a triode. The function f(x) is derived from the current-voltage characteristic of the triode and it has a roughly ⊂-shaped graph, with a flat bottom and some slight asymmetry. For a regenerative circuit, we have f(0) < 0. Van der Pol (5) considered the equation with f (x) = x2 − 1, and he and later writers (1, 2, 4) have built up an extensive theory of triode oscillations for this ideal case. In practice, the graph of f(x) has a much flatter bottom than that of the function x2 − 1, and it was asked by Cartwright ((3), p. 214) whether this flattening would alter the qualitative behaviour of the circuit near resonance. The main part of this paper is an attempt to answer this question.

scholarly journals Green's function of differential operators on a star-shaped graph with common boundary conditions

2019 ◽  
Vol 101 (1) ◽  
pp. 48-58
Author(s):  
D. B. Zharullayev ◽  
◽  
B. E. Kanguzhin ◽  
M. N. Konyrkulzhayeva ◽  
◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Differential Operators ◽  
Common Boundary ◽  
Shaped Graph

Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions

2018 ◽  
Vol 26 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Liouville Operator ◽  
Mixed Boundary ◽  
Constructive Method ◽  
Asymptotic Formulas ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph

AbstractThe Sturm–Liouville operator on a star-shaped graph with different types of boundary conditions (Robin and Dirichlet) in different vertices is studied. Asymptotic formulas for the eigenvalues are derived and partial inverse problems are solved: we show that the potential on one edge can be uniquely determined by different parts of the spectrum if the potentials on the other edges are known. We provide a constructive method for the solution of the inverse problems, based on the Riesz basis property of some systems of vector functions.

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