scholarly journals Tiling the Line with Triples

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Aaron Meyerowitz
Keyword(s):  
Greedy Algorithm ◽  
Direct Proof ◽  
Open Problems ◽  
One Dimensional ◽  
Proof By Contradiction ◽  
International Audience ◽  
The Subject ◽  
The One ◽  
Finite Digraph ◽  
Elegant Proof

International audience It is known the one dimensional prototile $0,a,a+b$ and its reflection $0,b,a+b$ always tile some interval. The subject has not received a great deal of further attention, although many interesting questions exist. All the information about tilings can be encoded in a finite digraph $D_{ab}$. We present several results about cycles and other structures in this graph. A number of conjectures and open problems are given.In [Go] an elegant proof by contradiction shows that a greedy algorithm will produce an interval tiling. We show that the process of converting to a direct proof leads to much stronger results.

scholarly journals Explicit Numerical Solution of High - Dimensional Advection - Diffusion

2013 ◽  
Vol 2 (3) ◽  
pp. 17-22
Author(s):  
Elham Bayatmanesh
Keyword(s):  
High Dimensional ◽  
Numerical Techniques ◽  
Science And Engineering ◽  
Numerical Examples ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Constant Coefficients ◽  
The Subject ◽  
The One

The Several numerical techniques have been developed and compared for solving the one-dimensional and three-dimentional advection-diffusion equation with constant coefficients. the subject has played very important roles to fluid dynamics as well as many other field of science and engineering. In this article, we will be presenting the of n-dimentional and we neglect the numerical examples.

scholarly journals A stronger recognizability condition for two-dimensional languages

2013 ◽  
Vol Vol. 15 no. 2 (Automata, Logic and Semantics) ◽  
Author(s):  
Marcella Anselmo ◽  
Maria Madonia
Keyword(s):  
Finite Automata ◽  
The Other ◽  
Two Dimensional ◽  
Minimal Size ◽  
One Dimensional ◽  
Tiling System ◽  
International Audience ◽  
The One

Automata, Logic and Semantics International audience The paper presents a condition necessarily satisfied by (tiling system) recognizable two-dimensional languages. The new recognizability condition is compared with all the other ones known in the literature (namely three conditions), once they are put in a uniform setting: they are stated as bounds on the growth of some complexity functions defined for two-dimensional languages. The gaps between such functions are analyzed and examples are shown that asymptotically separate them. Finally the new recognizability condition results to be the strongest one, while the remaining ones are its particular cases. The problem of deciding whether a two-dimensional language is recognizable is here related to the one of estimating the minimal size of finite automata recognizing a sequence of (one-dimensional) string languages.

scholarly journals Alternating and variable controls for the wave equation

2020 ◽  
Vol 26 ◽  
pp. 38 ◽  
Author(s):  
Antonio Agresti ◽  
Daniele Andreucci ◽  
Paola Loreti
Keyword(s):  
Wave Equation ◽  
Sufficient Conditions ◽  
Dimensional Case ◽  
Equivalent Condition ◽  
Open Problems ◽  
One Dimensional ◽  
Constant Rate ◽  
Exact Observability ◽  
Single Exchange ◽  
The One

The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which takes into account only the location in time of the observation. To this end we use Fourier series. Then we investigate the two specific cases of single exchange of the control position, and of exchange at a constant rate. In the multi-dimensional case, we analyse sufficient conditions for the exact observability relying on the multiplier method. In the last section, the multi-dimensional results are applied to specific settings and some connections between the one and multi-dimensional case are discussed; furthermore some open problems are presented.

An Improved Method for Simulating Ideal Low-Tension Flooding Processes

1976 ◽  
Vol 16 (02) ◽  
pp. 53-55 ◽  
Author(s):  
H.B. Hales ◽  
A.S. Odeh
Keyword(s):  
Finite Difference ◽  
Relative Permeability ◽  
Surfactant Concentration ◽  
Finite Difference Methods ◽  
Time Step ◽  
One Dimensional ◽  
The Subject ◽  
The One ◽  
Low Tension ◽  
Polymer Surfactant

Introduction Most reservoir simulators employ finite-difference methods to solve the appropriate set of equations. Variables that influence the accuracy of the results are the time-step size and the cell dimensions. While the effects of these variables on the results of conventional simulators can be significant, they can be even more important with chemical-flooding models. This is because of the presence of an additional phase, such as a surfactant slug that is moving with time and that can occupy part of, or all of, a cell. Within this slug, fluid saturations and relative permeability relations are different than those ahead or behind it. This causes a mathematical problem that is the subject of this work. problem that is the subject of this work. DESCRIPTION OF THE PROBLEM Simulation of the low-tension flooding process involves calculating the three unknown variables, pressure, saturation, and surfactant concentration, pressure, saturation, and surfactant concentration, as a function of time and space. The pressure and saturation distributions can be calculated using the usual finite-difference methods of solution of the equations for immiscible flow. The surfactant concentration distribution can be determined by tracking the surfactant slug boundaries analogous to the scheme proposed by Vela et al. for polymerflood simulation. However, the surfactant slug polymerflood simulation. However, the surfactant slug maintains a fairly sharp boundary as it moves through the reservoir. Therefore, in some finite-difference cells, two distinct parts may exist, one with and one without surfactant. Each part is different from the other in fluid saturations and relative permeability relations. However, the finite-difference method of solution requires that the two parts be represented by one average saturation and by one relative permeability value. Thus, the problem is how to average the two parts and to determine how sensitive the results of simulation are to the averaging scheme, to the cell size, and to the time step. METHOD OF ATTACK Ideally, one wants an averaging scheme that (1) gives answers that are not sensitive to the time step or to the cell size, and (2) gives correct answers. The second criterion is the most difficult to check since no exact solution to the surfactant flood is reported in the literature. The work was started by developing an analytic solution (Buckley-Leverett type) to a one-dimensional surfactant flood. The solution is analogous to solutions for other tertiary recovery projects. It combines the relationship for the normalized motion of a point of constant saturation, with expressions for the dimensionless velocity of each phase, and vw = (1-fo)/(1-So). (fo is fractional flow of oil; So is oil saturation.) Saturations throughout the one-dimensional reservoir are thereby obtained. Several solution regimes result. (1) For oil-water viscosity ratios greater than unity, oil moves exclusively in front of the surfactant, forming a bank, and all the oil is produced. (2) For slightly unfavorable viscosity ratios, an oil bank is still formed, but the oil gradually invades the surfactant and may result in reduced production. (3) Highly unfavorable viscosity ratios cause all the oil to move through the surfactant, and no bank is formed. The one-dimensional surfactant flood was then simulated using an incompressible, two-dimensional, polymer-surfactant model that solves for the polymer-surfactant model that solves for the concentration using a point-tracking scheme based on the method of characteristics. This method eliminates numerical dispersion and results in sharp surfactant-slug interfaces. Several sets of runs were made, with each set using a different averaging scheme. The various schemes used are described in the next section. SPEJ P. 53

scholarly journals A Survey on Extremal Problems of Eigenvalues

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Ping Yan ◽  
Meirong Zhang
Keyword(s):  
Variational Method ◽  
Lebesgue Space ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Lower And Upper Bounds ◽  
Open Problems ◽  
One Dimensional ◽  
Sturm Liouville ◽  
The One ◽  
Neumann Eigenvalues

Given an integrable potentialq∈L1([0,1],ℝ), the Dirichlet and the Neumann eigenvaluesλnD(q)andλnN(q)of the Sturm-Liouville operator with the potentialqare defined in an implicit way. In recent years, the authors and their collaborators have solved some basic extremal problems concerning these eigenvalues when theL1metric forqis given;∥q∥L1=r. Note that theL1spheres andL1balls are nonsmooth, noncompact domains of the Lebesgue space(L1([0,1],ℝ),∥·∥L1). To solve these extremal problems, we will reveal some deep results on the dependence of eigenvalues on potentials. Moreover, the variational method for the approximating extremal problems on the balls of the spacesLα([0,1],ℝ),1<α<∞will be used. Then theL1problems will be solved by passingα↓1. Corresponding extremal problems for eigenvalues of the one-dimensionalp-Laplacian with integrable potentials have also been solved. The results can yield optimal lower and upper bounds for these eigenvalues. This paper will review the most important ideas and techniques in solving these difficult and interesting extremal problems. Some open problems will also be imposed.

scholarly journals Deterministic Random Walks on the Integers

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Joshua Cooper ◽  
Benjamin Doerr ◽  
Joel Spencer ◽  
Gábor Tardos
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Deterministic Process ◽  
One Dimensional ◽  
Space And Time ◽  
Dimensional Version ◽  
International Audience ◽  
The One

International audience We analyze the one-dimensional version of Jim Propp's $P$-machine, a simple deterministic process that simulates a random walk on $\mathbb{Z}$. The "output'' of the machine is astonishingly close to the expected behavior of a random walk, even on long intervals of space and time.

Heat-Transfer for Fins with Two-Port Theory

1996 ◽  
Vol 24 (1) ◽  
pp. 61-72 ◽  
Author(s):  
C. Lombard
Keyword(s):  
Heat Transfer ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Flow Structures ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
The Matrix ◽  
The Subject ◽  
Complicated Geometry ◽  
The One

Fin heat transfer is an essential part of the education of mechanical engineers. It represents the simplest application of the heat conduction equation: the one-dimensional, steady, case. The usual presentation of the subject involves solving the conduction equation for various boundary conditions. In this paper, two-port techniques are applied to fin heat transfer. This concept is more suitable for the training of engineers because it emphasizes the importance of the boundaries rather than the internal conduction. Besides this important conceptual aid, the matrix is a powerful aid in computations; making it much easier to solve arrangements with complicated geometry. In fact, the two-port representation makes it possible to use graph theory for the automatic solution of complicated heat-flow structures.

INNOVATION AND BARRIERS OF INNOVATION IN PERSONNEL PROCESSES OF THE ORGANIZATION

2018 ◽  
Vol 19 (4) ◽  
pp. 51-60
Author(s):  
Teresa Myjak
Keyword(s):  
Statistical Method ◽  
Dimensional Analysis ◽  
Literature Analysis ◽  
One Dimensional ◽  
Barriers To Innovation ◽  
Survey Technique ◽  
The Subject ◽  
The One

The aim of the publication is to present the issues of innovation and its barriers and to show barriers to innovation and directions of activities undertaken by the organization, so that personnel processes are innovative. The theoretical aspects of the personnel processes of the organization are presented, as well as the nature and barriers to innovation in the organization. The results of my own research are presented below. In the study I have used literature analysis of the subject and the survey technique, as well as the one- dimensional analysis statistical method

REPETITIONS, FULLNESS, AND UNIFORMITY IN TWO-DIMENSIONAL WORDS

2004 ◽  
Vol 15 (02) ◽  
pp. 355-383 ◽  
Author(s):  
ARTURO CARPI ◽  
ALDO de LUCA
Keyword(s):  
Essential Role ◽  
Finite Alphabet ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Fixed Size ◽  
Open Problems ◽  
One Dimensional ◽  
Combinatorial Properties ◽  
The Difference ◽  
The One

We consider some combinatorial properties of two-dimensional words (or pictures) over a given finite alphabet, which are related to the number of occurrences in them of words of a fixed size (m,n). In particular a two-dimensional word (briefly, 2D-word) is called (m,n)-full if it contains as factors (or subwords) all words of size (m,n). An (m,n)-full word such that any word of size (m,n) occurs in it exactly once is called a de Bruijn word of order (m,n). A 2D-word w is called (m,n)-uniform if the difference in the number of occurrences in w of any two words of size (m,n) is at most 1. A 2D-word is called uniform if it is (m,n)-uniform for all m,n>0. In this paper we extend to the two-dimensional case some results relating the notions above which were proved in the one-dimensional case in a preceding article. In this analysis the study of repeated factors in a 2D-word plays an essential role. Finally, some open problems and conjectures are discussed.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sign in / Sign up

Export Citation Format

Share Document