Definition of Burning Velocity and a Geometric Interpretation of the Effects of Flame Curvature

1965 ◽  
Vol 8 (2) ◽  
pp. 273 ◽  
Author(s):  
R. M. Fristrom
Keyword(s):  
Burning Velocity ◽  
Geometric Interpretation ◽  
Definition Of ◽  
Flame Curvature

scholarly journals Point configurations, phylogenetic trees, and dissimilarity vectors

2021 ◽  
Vol 118 (12) ◽  
pp. e2021244118
Author(s):  
Alessio Caminata ◽  
Noah Giansiracusa ◽  
Han-Bom Moon ◽  
Luca Schaffler
Keyword(s):  
Phylogenetic Trees ◽  
Geometric Interpretation ◽  
Explicit Characterization ◽  
Point Configurations ◽  
Definition Of ◽  
Tropical Basis ◽  
The Way

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

scholarly journals GEOMETRIC BIJECTIONS FOR REGULAR MATROIDS, ZONOTOPES, AND EHRHART THEORY

2019 ◽  
Vol 7 ◽  
Author(s):  
SPENCER BACKMAN ◽  
MATTHEW BAKER ◽  
CHI HO YUEN
Keyword(s):  
Spanning Trees ◽  
Finite Abelian Group ◽  
Tutte Polynomial ◽  
Geometric Interpretation ◽  
Lattice Points ◽  
Combinatorial Interpretation ◽  
Ehrhart Polynomial ◽  
Ehrhart Theory ◽  
Regular Matroid ◽  
Definition Of

Let $M$ be a regular matroid. The Jacobian group $\text{Jac}(M)$ of $M$ is a finite abelian group whose cardinality is equal to the number of bases of $M$ . This group generalizes the definition of the Jacobian group (also known as the critical group or sandpile group) $\operatorname{Jac}(G)$ of a graph $G$ (in which case bases of the corresponding regular matroid are spanning trees of $G$ ). There are many explicit combinatorial bijections in the literature between the Jacobian group of a graph $\text{Jac}(G)$ and spanning trees. However, most of the known bijections use vertices of $G$ in some essential way and are inherently ‘nonmatroidal’. In this paper, we construct a family of explicit and easy-to-describe bijections between the Jacobian group of a regular matroid $M$ and bases of $M$ , many instances of which are new even in the case of graphs. We first describe our family of bijections in a purely combinatorial way in terms of orientations; more specifically, we prove that the Jacobian group of $M$ admits a canonical simply transitive action on the set ${\mathcal{G}}(M)$ of circuit–cocircuit reversal classes of $M$ , and then define a family of combinatorial bijections $\unicode[STIX]{x1D6FD}_{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70E}^{\ast }}$ between ${\mathcal{G}}(M)$ and bases of $M$ . (Here $\unicode[STIX]{x1D70E}$ (respectively $\unicode[STIX]{x1D70E}^{\ast }$ ) is an acyclic signature of the set of circuits (respectively cocircuits) of $M$ .) We then give a geometric interpretation of each such map $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FD}_{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70E}^{\ast }}$ in terms of zonotopal subdivisions which is used to verify that $\unicode[STIX]{x1D6FD}$ is indeed a bijection. Finally, we give a combinatorial interpretation of lattice points in the zonotope $Z$ ; by passing to dilations we obtain a new derivation of Stanley’s formula linking the Ehrhart polynomial of $Z$ to the Tutte polynomial of $M$ .

scholarly journals A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES

2013 ◽  
Vol 15 (02) ◽  
pp. 1250059 ◽  
Author(s):  
MICHAEL B. HENRY ◽  
DAN RUTHERFORD
Keyword(s):  
Standard Form ◽  
Geometric Interpretation ◽  
Graded Algebra ◽  
Legendrian Knots ◽  
Complex Sequence ◽  
Differential Graded Algebra ◽  
Legendrian Knot ◽  
Definition Of ◽  
Morse Complex ◽  
Differential Counts

For a Legendrian knot L ⊂ ℝ3, with a chosen Morse complex sequence (MCS), we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MCS arises from a generating family F, we give a geometric interpretation of our chord paths as certain broken gradient trajectories which we call "gradient staircases". Given two equivalent MCS's we prove the corresponding linearized complexes of the DGA are isomorphic. If the MCS has a standard form, then we show that our DGA agrees with the Chekanov–Eliashberg DGA after changing coordinates by an augmentation.

Design of Control System in the Class of Two-Parametric Structurally Stable Mappings

2015 ◽  
Vol 799-800 ◽  
pp. 1137-1141
Author(s):  
Leila Abdrakhmanova ◽  
Mamyrbek Beisenbi
Keyword(s):  
Control System ◽  
Control Systems ◽  
Robust Stability ◽  
Control Object ◽  
Geometric Interpretation ◽  
System Stability ◽  
Wide Range ◽  
Theoretical Fundamental ◽  
Definition Of ◽  
Structurally Stable

In this paper, we proposed a method for design of control systems with a high potential of robust stability in a class of two-parametric structurally stable mappings. Research of robust stability is based on the geometric interpretation of the second Lyapunov method, and also definition of system stability in the state space.We propose a method for construct the control system, designed in two-parametric class of structurally stable mappings, which will be sustained indefinitely in a wide range of uncertain parameters of the control object. This work presents novelty theoretical fundamental results assisting in analyzing of the behavior of control systems, meaning of robust stability.

scholarly journals Effects of the Flame Curvature on the Burning Velocity of Triple Flame

2004 ◽  
Vol 70 (691) ◽  
pp. 780-788 ◽  
Author(s):  
Yoshitaka NAGAI ◽  
Mitsutomo HIROTA ◽  
Masahiko MIZOMOTO
Keyword(s):  
Burning Velocity ◽  
Flame Curvature

scholarly journals METHOD OF PROTECTING SPECIALLY IMPORTANT OBJECTS BASED ON THE APPLICATION OF THE BISTATIC RADIOLOCATION TECHNIQUE

2019 ◽  
Vol 4 ◽  
pp. 63-75
Author(s):  
Aleksandr Kondratenko ◽  
Igor Boikov ◽  
Hennadii Marenko ◽  
Ivan Tsebriuk ◽  
Oleksandr Koval ◽  
...  
Keyword(s):  
Mobile Communications ◽  
National Guard ◽  
Geometric Interpretation ◽  
Signal Interference ◽  
Digital Television ◽  
Technical Equipment ◽  
Reflective Surface ◽  
Definition Of ◽  
Living Objects ◽  
Bistatic System

The solution of the tasks assigned to the National Guard of the state implies the presence of certain forces and means with the appropriate technical equipment. A well-known place among such tasks is security of important state facilities. Various physical effects and methods, including radar, are used to create security systems. The development of radar technology and technology made it possible to increase both the quantity and quality of the received information, as well as the use of radar stations for observing living objects. The industry today produces bioradioradars for detecting people and controlling their movements. All samples are made in a single-position version and have a relatively high cost, the fact of their work is easily detected, which facilitates their suppression, including force. In order to increase the secrecy of work, it is proposed to use the methods of separated, more precisely, bistatic location to control the area in front of particularly important objects. The defining detection index is the effective reflective surface (ERS), which is about 1 m2 for a person. Equipment, weapons and protective equipment contributes to the increase in the ERS. Given the small reflective surface of biological objects, it is proposed to limit the area of responsibility to the sector form in which, at a certain bistatic angle, the effect of a significant increase in the signal/(interference+noise) ratio is manifested. For a specific definition of the gain, it is necessary to choose the operating frequency of the bistatic system and its geometry. For greater secrecy, it is advisable to use the transmitters of radio and television broadcasting, mobile communications, etc. The estimates found, for example, when using digital television transmitters (T2), indicate that the creation of a secretive bistatic system is quite possible – at least in a geometric interpretation.

scholarly journals Econometric Models of Propensities

2007 ◽  
Vol 6 (1) ◽  
pp. 15-25
Author(s):  
Józef Hozer ◽  
Mariusz Doszyń
Keyword(s):  
Geometric Interpretation ◽  
Econometric Models ◽  
Alcoholic Beverages ◽  
Human Being ◽  
Manual Labour ◽  
Marginal Propensity ◽  
Definition Of ◽  
The Impact ◽  
Working Out

Econometric Models of Propensities Human being is one of the most important sources of causative forces of events that assemble economical processes. Working out the effective tools that enable measurement of the impact of people on socio-economic processes is necessary in analyzing, troubleshooting and forecasting. In the article the issues of calculating propensities by means of properly specified econometrics models were presented. The definition of propensity was introduced. Questions connected with topic of propensities were presented in context of concepts promoted by Szczecin school of econometrics (pentagon of sources of causative forces, types of relationships in economics, geometric interpretation of personality, broom of events). Econometric models, useful in analyzing propensities, were classified on primary models, econometrics models of average propensities and econometrics models of marginal propensities. Connections between the models were described. Settlement of analytical shapes of characterized models was mentioned. In an empirical example the presented methods were used to analyze average and marginal propensity to consumption of alcoholic beverages and tobacco in the households of employees in manual labour positions in Poland in years 1993-2005.

scholarly journals FRAÇÕES CONTÍNUAS, DETERMINANTES E EQUAÇÕES DIOFANTINAS LINEARES

2015 ◽  
Vol 37 ◽  
pp. 95
Author(s):  
Delfim Dias Bonfim ◽  
Gilmar Pires Novaes
Keyword(s):  
Diophantine Equation ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Diophantine Equations ◽  
Geometric Interpretation ◽  
Linear Diophantine Equation ◽  
Linear Diophantine Equations ◽  
Definition Of ◽  
Fundamental Theorems

http://dx.doi.org/10.5902/2179460X14468This article is intended to present a method for solving linear diophantine equations, using for this purpose, the concepts of continuous fractions and determinants. Initially we present the definition of simple continued fraction, geometric interpretation and some fundamental theorems related to this concept. Subsequently we relate the finite simple continued fractions with determinants. Finally we present the definition of linear Diophantine equation and we demonstrate the method to solve it using the concepts mentioned above.

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