Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Mathematics Research (195)
- Computer simulation (43)
- Banach spaces (30)
- Differential equations (25)
- Molecular mechanics (15)
-
- Ground state (14)
- Boundary value problems (13)
- Lyapunov functions (10)
- Statistics||Mathematics Research (10)
- Cooperative game (9)
- Differential inequalities (9)
- TU games (9)
- Abstract cones (8)
- Differential equations||Mathematics Research (8)
- Game theory||Mathematics Research (8)
- Mathematical statistics||Mathematics Research (8)
- Periodic solutions (8)
- Algorithm (7)
- Comparison theorems (7)
- Compartmental systems (7)
- Fluid drops (7)
- Molecular dynamics (7)
- Monotone iterative technique (7)
- Shapley value (7)
- Computer simulation||Mathematics Research (6)
- Dirichlet problem (6)
- Electrons (6)
- Lower and upper solutions (6)
- Mathematical models (6)
- Mathematical physics||Mathematics Research (6)
- Publication Year
Articles 1 - 30 of 343
Full-Text Articles in Mathematics
Geometrical Problems In Engineering Mechanics, Feraydune Kashefi, Mostafa Ghandehari
Geometrical Problems In Engineering Mechanics, Feraydune Kashefi, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Four problems in two dimensional geometry are presented, which are applicable to education of the basic courses, statics. These problems represent geometrical concepts that are understandable by engineering students. For example, consider a triangle made from a uniform rod. If we draw the inscribed circle of this triangle, and concentrate the weight of each side on the point at which in circle touches the side, center of the gravity of the three concentrated masses is located at the center.
The Reflection Property In Normed Linear Planes With Applications To Generalized Conics, Edward J. O'Neill, Mostafa Ghandehari
The Reflection Property In Normed Linear Planes With Applications To Generalized Conics, Edward J. O'Neill, Mostafa Ghandehari
Mathematics Technical Papers - Archive
The ancient Greek mathematician Heron was the first to solve the problem of finding the shortest path from point A to point B on one side of the line L, subject to the condition that the path goes from A to L and then to B (figure 1). Figure 1. His solution involved going from A to point R on L and then to B such that the line segments AR and BR make equal angles with L. This is exactly the path a light ray from A to B if L were a mirror. Heron included this proposition in …
The Least Square Values And The Shapley Value For Cooperative Tu Games, Irinel C. Dragan
The Least Square Values And The Shapley Value For Cooperative Tu Games, Irinel C. Dragan
Mathematics Technical Papers - Archive
The Least Square Values (briefly LS-values), represent a family of values for cooperative transferable utility games, introduced by L. Ruiz. F. Valenciano and J.Zarzuelo (1998). For a fixed set of players N, a set of weights [see pdf for notation], and any TU-game v , M.Keane (1968) has defined and solved a quadratic programming problem: minimize the sum of weighted squares of deviations of the excesses from their average, on the preimputation set. He has shown that this problem has a unique solution which depends on the weights and has also given the new computational formula. Further, Ruiz/Valenciano/Zarzuelo have called …
On The Inverse Problem For Semivalues Of Cooperative Tu Games, Irinel C. Dragan
On The Inverse Problem For Semivalues Of Cooperative Tu Games, Irinel C. Dragan
Mathematics Technical Papers - Archive
In the present paper, we define a basis of [see pdf for notation] relative to a Semivalue, we compute the potentials of the subgames of a given game, to show that the basis is a potential basis, from which we get the Semivalues of the basic vectors. In this way we discover a basis of the null space of a Semivalue and derive, as in the previous work, a solution of the inverse problem, this time for a Semivalue. As the Shapley value was considered in detail in the previous work, we give a complete description for the Banzhaf value. …
Fortran Program Hh1, Donald Greenspan
Fortran Program Hh1, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
On A New Mathematical Model Of The Molecular Bond, Donald Greenspan
On A New Mathematical Model Of The Molecular Bond, Donald Greenspan
Mathematics Technical Papers - Archive
Using a new model of the molecular bond, we produce a set of initial conditions for the ground state H2 molecule which yield, over one complete period, bond length and vibrational frequency which are identical to the experimental results.
Minkowski's Inequality For Convex Curves, Mostafa Ghandehari
Minkowski's Inequality For Convex Curves, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Minkowski's inequality is a relation between mixed areas of two curves and their respective areas. The concept of mixed area is defined. A variational technique is used to give a proof of Minkowski's inequality. As a special case the isoperimetric inequality is obtained.
Discrete Spring Solitons, Donald Greenspan
Discrete Spring Solitons, Donald Greenspan
Mathematics Technical Papers - Archive
A soliton is a local, traveling wave pulse. It is significant in a variety of unrelated areas, like studies of water waves, acoustic waves, electron transfer, gravity waves, plasmas, optics and condensed matter (Miura [4], Newell [5]). In this paper we will generate and study solitons in a new context, that is, from the point of view of discrete string motion in the XY plane. Our approach enables one to elucidate the complexities of soliton interactions easily using only a scientific personal computer and velocity profiles. Detailed examples are presented and displayed graphically.
A Geometric Inequality For Convex Polygons, Mostafa Ghandehari
A Geometric Inequality For Convex Polygons, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Consider a regular polygon with vertices P1, P2, , Pn. Assume P is an interior point. Let [see pdf for notation] denote the Euclidean distance from P to Pi, i = 1, ...., n. Let A denote the area of the polygon. It is shown that [see pdf for notation] special cases of the above inequality are proved for some nonregular convex polygons. An example is given to show that the above inequality is not true for a general convex polygon.
Estimating Change Over Time From Aggregate Samples Plus Partial Transition Data, Chien-Pai Han, D. L. Hawkins
Estimating Change Over Time From Aggregate Samples Plus Partial Transition Data, Chien-Pai Han, D. L. Hawkins
Mathematics Technical Papers - Archive
As such, the paper has two basic thrusts. The first is that to obtain efficient estimates of change measures (e.g. of transition probabilities) based on aggregate data, auxiliary data will in general be needed; several potentially useful auxiliary sampling schemes are discussed. The second thrust is the manner in which estimates from the such varied sampling schemes can be combined to achieve such efficient estimates. Since it either directly or indirectly suggests many possible longitudinal study designs, the paper necessarily cannot provide real examples of all (or even most) of the study designs considered. Indeed, the main point here is …
Banzhaf Permission Values For Games With Permission Structure, Rene Van Den Brink
Banzhaf Permission Values For Games With Permission Structure, Rene Van Den Brink
Mathematics Technical Papers - Archive
A game with a permission structure describes a situation in which cooperation possibilities in a cooperative game with transferable utility are limited because there are players that need permission from other players before they are allowed to cooperate. In the conjunctive approach it is assumed that every player needs permission from all its direct superiors. In the disjunctive approach it is assumed that each player only needs permission from at least one of its direct superiors. Both approaches yield different modified games which take account of the limited cooperation possibilities. Applying the Banzhaf value to these modified games yields allocation …
Molecular Study Of Turbulence In Three Dimensional Cavity Flow, Donald Greenspan
Molecular Study Of Turbulence In Three Dimensional Cavity Flow, Donald Greenspan
Mathematics Technical Papers - Archive
Three dimensional molecular cavity problems are formulated and solved numerically. The fluid considered is water at 15°C. The turbulent flows generated are characterized by strong crosscurrents over the usual primary vortex direction.
On The Semivalues And The Power Core Of Cooperative Tu Games, Juan-Enrique Martínez-Legaz, Irinel C. Dragan
On The Semivalues And The Power Core Of Cooperative Tu Games, Juan-Enrique Martínez-Legaz, Irinel C. Dragan
Mathematics Technical Papers - Archive
The Semivalues were introduced axiomatically by P.Dubey, A.Neyman and R.J.Weber (1981) as an important class of values for cooperative TU games. This class contains the Shapley value, the Banzhaf value, and many other values. For the Shapley value characterizations of games for which the Shapley value is coalitionally rational are due to Inarra and Usategui (1993), Izawa and Takahashi (1998), and Marin-Solano and Rafels (1999). In this paper the same problem of coalitional rationality is discussed for Semivalues, by using special formulas for the computation of Semivalues. The characterization shows that this is a prosperity property as defined by Van …
Particle Simulation In Contact Mechanics Of A Bouncing Elastic Ball, Donald Greenspan
Particle Simulation In Contact Mechanics Of A Bouncing Elastic Ball, Donald Greenspan
Mathematics Technical Papers - Archive
An elastic ball is simulated by considering lumped mass molecular sets called particles. Particles are allowed to interact only locally in a fashion similar to that employed in molecular mechanics. Under local and gravity forces an n-body problem results when initial data are prescribed. By scaling the forces, the resulting n-body problem is solved numerically using only a scientific personal computer. A variety of examples of bouncing balls are described and discussed.
Molecular Mechanics Simulations Of The Three Dimensional Cavity Problem, Donald Greenspan
Molecular Mechanics Simulations Of The Three Dimensional Cavity Problem, Donald Greenspan
Mathematics Technical Papers - Archive
The rapid development of computer technology has resulted in broad interest in three dimensional fluid simulation, which is known to have more complex force interactions than occur in two dimensions (see, e.g., refs. [1-6], [9], [11-15], [17], [18] and the additional references therein). In this paper we develop and analyze some molecular mechanics simulations of the three dimensional cavity problem. The fluid considered is water at 15° C.
Tennis, Geometric Progression, Probability And Basketball, Mostafa Ghandehari
Tennis, Geometric Progression, Probability And Basketball, Mostafa Ghandehari
Mathematics Technical Papers - Archive
The following problem about a tennis match is well—known. See Halmos [1, 2]. Consider 2n tennis players playing a single elimination match. Ask the question: what are the number of games played? The answer can be obtained in two ways. First using the geometric progression 2n-1 + 2n-2 + • • • -2+1 we find that the answer is 2n — 1. We can also explain the answer as follows: for each game played there is a loser. Thus the total number of games played is equal to the number of losers. Since there is only one winner the total …
A Quadratic Fredholm Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari
A Quadratic Fredholm Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Consider the Fredholm integral equation [see pdf for notation], a parameter. The solution of this equation is discussed for separable, difference and distribution kernels. Existence, uniqueness and bifurcation questions are explored for various assumptions on the kernel.
Heating Water Vapor In A Square Cavity Using Molecular And Particle Mechanics, Donald Greenspan
Heating Water Vapor In A Square Cavity Using Molecular And Particle Mechanics, Donald Greenspan
Mathematics Technical Papers - Archive
This paper explores the computer simulation of heating water vapor in a square cavity. Both molecular and particle mechanics are applied. A particular parameter called vel, found on the micro level, is shown to be applicable on the macro level in generating both laminar and turbulent flows.
A Molecular Mechanics Simulation Of Cracks And Fractures In A Sheet Of Ice, Donald Greenspan
A Molecular Mechanics Simulation Of Cracks And Fractures In A Sheet Of Ice, Donald Greenspan
Mathematics Technical Papers - Archive
Rectangular, two dimensional sheets of ice molecules are both stressed and compressed. Computer examples compare dynamical responses when the plate has a slot or does not have a slot. The mechanisms for both crack and fracture development are clearly delineated on the molecular level.
Potential And Consistency For Semivalues Of Finite Cooperative Tu Games, Irinel C. Dragan
Potential And Consistency For Semivalues Of Finite Cooperative Tu Games, Irinel C. Dragan
Mathematics Technical Papers - Archive
A new axiomatic characterization of the semivalues of finite cooperative n-person games with transferable utilities is given, by using a potential function. The semivalues are proved to be the unique functionals on the space of such games, which are consistent relative to a Hart/Mas Colell type of reduced game and weighted standard for two person games. The potential is also used to prove the validity of a recursive definition of semivalues, as well as the fact that the semivalues are Shapley values of the so called Power Game.
Molecular Cavity Flow, Donald Greenspan
Molecular Cavity Flow, Donald Greenspan
Mathematics Technical Papers - Archive
Using molecular mechanics, cavity flow is studied in a basin of 4235 water molecules at 15°C. Primary vortices are generated with wallspeeds [see pdf for notation]. The vortex motions agree with experimental results in the large. Fully turbulent flow is generated with wallspeed .V = 3000°A/ps. The mechanisms for primary vortex generation are clearly delineated, as are those for turbulent flow.
On A Proximal Point Method For Optimization In Banach Spaces, Alfredo N. Iusem, Dan Butnariu
On A Proximal Point Method For Optimization In Banach Spaces, Alfredo N. Iusem, Dan Butnariu
Mathematics Technical Papers - Archive
We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of …
Some Recursive Definitions Of The Shapley Value And Other Linear Values Of Cooperative Tu Games, Irinel C. Dragan
Some Recursive Definitions Of The Shapley Value And Other Linear Values Of Cooperative Tu Games, Irinel C. Dragan
Mathematics Technical Papers - Archive
Let N be a finite set of players, |N| = n; a cooperative TU game in coalitional form is a function v : P(N) -> R, with v(ø) = 0. It is well known that the set of all games with the set of players N, denoted below G(N), is a space of dimension 2n - 1. Let S be any coalition in v E G(N) and denote by G(S) the space of games with the set of players S. If v E G(N), then the restriction of v to S is a game in G(S). To avoid a notation …
The Generation Of Turbulence In A Compressed Gas, Donald Greenspan
The Generation Of Turbulence In A Compressed Gas, Donald Greenspan
Mathematics Technical Papers - Archive
A molecular mechanics type formulation is applied to generate turbulence in a compressed gas. Turbulence is defined in terms of the rapid appearance and disappearance of many small vortices. The generating mechanism lies in the large repulsive forces between particles.
Conservative Motion Of A Discrete, Nonsymmetric, Hexahedral Gyroscope, Donald Greenspan
Conservative Motion Of A Discrete, Nonsymmetric, Hexahedral Gyroscope, Donald Greenspan
Mathematics Technical Papers - Archive
Gyroscopic motion is simulated by applying a molecular dynamics formulation to a rigid hexahedron. The conservative dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. The difficult problem of nonsymmetry is emphasized. Examples of the complex motions which result are described and discussed.
A Molecular Mechanics Type Approach To Turbulence, Donald Greenspan
A Molecular Mechanics Type Approach To Turbulence, Donald Greenspan
Mathematics Technical Papers - Archive
A molecular mechanics type formulation is applied to the cavity problem to generate primary vortices, secondary vortices, and turbulent flow. The fluid considered is water. Turbulence is defined in terms of the absence of a primary vortex and the rapid appearance and disappearance of many small vortices. The mechanism for generating turbulent flow lies in the generation of large repulsive forces between the particles of the model. This results from the increase in particle speeds due to the increase in wall speed.
Controlling Curvature In The Minkowski Plane, Mostafa Ghandehari
Controlling Curvature In The Minkowski Plane, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Pontryagin's maximum principle is used to find the curve of shortest length with bounded Minkowskian curvature passing through two points with given initial and terminal tangents.
Ray Optics On Surfaces, Mostafa Ghandehari
Ray Optics On Surfaces, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Variational techniques are used to find path of light rays on surfaces. Using Fermat's principle of least time the problem is treated as a constraint optimization to obtain a system of partial differential equations.
Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures Ii. The Case Of Covariates., Chien-Pai Han, D. L. Hawkins
Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures Ii. The Case Of Covariates., Chien-Pai Han, D. L. Hawkins
Mathematics Technical Papers - Archive
The paper extends the authors' earlier methods for estimating transition probabilities, by combining aggregate and haphazard recapture data, to the case of categorical covariates. Both fixed and time-dependent covariates are considered. A two-stage estimation procedure is proposed. The first stage uses a Markov model to estimate multivariate transition probabilities for the response and all covariates. The second stage uses the Stage 1 estimates to model covariate effects. The required number of sampling waves depends only on the number of response levels and time-dependent covariate levels — and not on the number of fixed covariate levels. Recommendations are given for the …
Snell's Law In Normed Linear Planes, Mostafa Ghandehari
Snell's Law In Normed Linear Planes, Mostafa Ghandehari
Mathematics Technical Papers - Archive
The method of Lagrange multipliers is used to find a reflection principle in a real normed linear plane with smooth unit circle. A generalization of Snell's law of refraction with two different norms is given. The case where the unit circles of the two norms are Euclidean circles with different radii leads to Snell's law.