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Articles 61 - 90 of 343
Full-Text Articles in Mathematics
An Average Per Capita Formula For The Shapely Value, Irinel C. Dragan
An Average Per Capita Formula For The Shapely Value, Irinel C. Dragan
Mathematics Technical Papers - Archive
A new formula for the Shapley value is given which does not require the storage of the [see pdf for notation] values of the characteristic function in the computer, and avoids the search in the memory for such data.
On Electron Attraction & Newtonian Methodology For Approximating Quantum Mechanical Phenomena, Donald Greenspan
On Electron Attraction & Newtonian Methodology For Approximating Quantum Mechanical Phenomena, Donald Greenspan
Mathematics Technical Papers - Archive
Classical dynamical computations for ground state [see pdf for notation], and [see pdf for notation] have been shown to yield correct vibrational frequencies and molecular diameters under an assumption of electron attraction for bonding electrons. In this paper, it is shown that such a mechanism also extends to [see pdf for notation] and to the nonhomogeneous molecules [see pdf for notation] and [see pdf for notation]. The vibrational motions are, apparently, quasi-periodic rather than periodic.
Multiweighted Shapley Values And Random Order Values, Irinel C. Dragan
Multiweighted Shapley Values And Random Order Values, Irinel C. Dragan
Mathematics Technical Papers - Archive
Recently, R. J. Weber introduced axiomatically in [14] the concept of random order value, an operator from [see pdf for notation], the space of TU games, to [see pdf for notation], satisfying linearity, dummy, efficiency and monotonicity axioms. In the present paper, we consider the concept of multiweighted Shapley value (MWSV), an operator from [see pdf for notation], satisfying linearity and carrier axioms. In the first section, we show that a MWSV is defined by its matrix representation relative to the unanimity basis for [see pdf for notation] and the standard basis for [see pdf for notation], if and only …
Completely Conservative And Covariant Numerical Methodology For N-Body Problems With Distance-Dependent Potentials, Donald Greenspan
Completely Conservative And Covariant Numerical Methodology For N-Body Problems With Distance-Dependent Potentials, Donald Greenspan
Mathematics Technical Papers - Archive
We consider a general class of N-body problems for arbitrary, distance-dependent potentials. Completely conservative, covariant numerical methodology is established for their solution and an example is provided in which energy conservation is essential.
Inference About The Transition-Point In Nbue-Nwue Or Nwue-Nbue Models, Subhash Kochar, D. L. Hawkins
Inference About The Transition-Point In Nbue-Nwue Or Nwue-Nbue Models, Subhash Kochar, D. L. Hawkins
Mathematics Technical Papers - Archive
e(t) < e(0) for [see pdf for notation]. If the inequalities for e(t) are reversed on these time intervals, it is called NWUE-NBUE. Using a characterization of such distributions in terms of the scaled total-time-on-test transform (STTT), we first give tests of exponentiality versus NBUE-NWUE or NWUE-NBUE with to unknown. This extends the work of Klefsjo (1989), who devised tests assuming that [see pdf for notation] is known. Then, assuming that F is either NBUE-NWUE or NWUE-NBUE, we give point estimates and asymptotic confidence intervals for to and [see pdf for notation]. The point estimates are asymptotically normal. We rely heavily on the theory of the empirical STTT process discussed in Csorgo, Csorgo and Horvith (1986). Two examples of real-data applications are provided.
Allocations To Discriminated Players In Discriminatory Von Neumann-Morgenstern Solutions, J. G. C. Heijmans
Allocations To Discriminated Players In Discriminatory Von Neumann-Morgenstern Solutions, J. G. C. Heijmans
Mathematics Technical Papers - Archive
Von Neumann-Morgenstern solutions (stable sets) for cooperative sidepayment games are notoriously difficult to find. This paper provides guidelines on how to find discriminatory vN-M solutions and exhibits some difficulties one may encounter. Easy to use necessary restrictions on the allocations to the discriminated players are derived. Easy to use complete characterisations of discriminatory vN-M solutions for simple games and of discriminatoy vN-M solutions with some additional structure for arbitrary games are provided.
Classical, Computer Studies Of One-Electron And Two-Electron Atoms And Ions, Donald Greenspan
Classical, Computer Studies Of One-Electron And Two-Electron Atoms And Ions, Donald Greenspan
Mathematics Technical Papers - Archive
A geometrical, computer-oriented method is utilized to generate circular orbits of electrons in one-electron and two-electron atoms and ions. The radii of these orbits are defined to be the radii of the atoms or ions. Only energy conserving computer methodology is used. The results suggest a natural modification of the Bohr approach to hydrogen which is then applied heuristically to helium.
On A Class Of Bargaining Schemes For Points In The Core Of A Cooperative N-Person Game, Yair Censor, Dan Butnariu
On A Class Of Bargaining Schemes For Points In The Core Of A Cooperative N-Person Game, Yair Censor, Dan Butnariu
Mathematics Technical Papers - Archive
Projection methods of solving convex feasibility problems lead naturally to a class of bargaining scheme's for points in the core of cooperative n-person games. Each such bargaining scheme is by itself a mathematical model of "rational behavior" describing a specific way of achieving "equilibrated" payoff vectors. We show that many of these bargaining schemes are "stable"' and have meaningful heuristic interpretations.
On Attractive Force Between Electrons In The Same Molecular Orbital, Donald Greenspan
On Attractive Force Between Electrons In The Same Molecular Orbital, Donald Greenspan
Mathematics Technical Papers - Archive
Is is assumed, on the basis of recent studies in particle theory, that two electrons in the same molecular orbital attract, rather than repel, and the consequences are explored by means of three dimensional, supercomputer, molecular mechanics type simulations of ground state H2 and D2. Using spectroscopic data, it is shown that, in every case, the resulting vibrational frequency and molecular diameter are entirely in agreement with experiment.
Testing Exponentiality Against Idmrl Distributions With Unknown Change Point, D. L. Hawkins, Clive Loader, Subhash Kochar
Testing Exponentiality Against Idmrl Distributions With Unknown Change Point, D. L. Hawkins, Clive Loader, Subhash Kochar
Mathematics Technical Papers - Archive
Guess, Hollander and Proschan (1986) proposed tests for exponentiality versus IDMRL (increasing initially and then decreasing mean residual life) distributions when the change point, or corresponding quantile, is known. In this paper we propose two tests which do not require such knowledge of the change point. The tests are based on estimates of functionals of the cdf which discriminate between the exponential and IDMRL families.
On Electron Attraction In The Diatomic Bond, Donald Greenspan
On Electron Attraction In The Diatomic Bond, Donald Greenspan
Mathematics Technical Papers - Archive
Previously, it was shown that classical simulation of the ground state diatomic hydrogen, deuterium and tritium molecules yielded the correct vibrational frequencies and average molecular diameters under the assumption that the bonding electrons attracted, rather than repelled. It is shown here that the assumption of electron attraction also yields the correct vibrational frequencies and average molecular diameters for [see pdf for notation].
A New Model Of The Molecular Bond, Donald Greenspan
A New Model Of The Molecular Bond, Donald Greenspan
Mathematics Technical Papers - Archive
It is assumed, on the basis of recent supercomputer calculations, that electrons attract, rather than repel. The consequences are explored by means of three dimensional, molecular mechanics type simulations of ground state [see pdf for notation]. Using spectroscopic data, it is shown that, in every case, the resulting vibrational frequencies and molecular diameters are entirely in agreement with experiment.
Studies In Rapid Kinetic Reactions By Quasi-Quantum Mechanical, Conservative Methodology, Donald Greenspan
Studies In Rapid Kinetic Reactions By Quasi-Quantum Mechanical, Conservative Methodology, Donald Greenspan
Mathematics Technical Papers - Archive
Simulations are made of prototype, ground state, rapid kinetic reactions for A+BC, in which B, and C are hydrogen atoms and BC is a hydrogen molecule. We study cases in which B and C first unbind, and then A, B, and C undergo complex, three-body, oscillatory behavior in accordance with the Morse potential. It is shown that, in every case, one of A, or C is ejected and the remaining two atoms form an H2 bond with precisely correct ground state energy, frequency, and bond length. Pico second trajectories are described and discussed. The numerical method employed conserves the system's …
A Method For Approximating The Solution Set Of A System Of Convex Inequalities By Polytopes, Yair Censor, Dan Butnariu
A Method For Approximating The Solution Set Of A System Of Convex Inequalities By Polytopes, Yair Censor, Dan Butnariu
Mathematics Technical Papers - Archive
In this note a method for computing approximations by polytopes of the solution set [see pdf for notation] of a system of convex inequalities is presented. It is shown that such approximations can be determined by an algorithm which converges in finitely many steps when the solution set of the given system of inequalities is bounded. In this case, the algorithm generates "inner" and "outer' approximations having the Hausdorff distance to each other (and to the set [see pdf for notation]) not greater than an a priori fixed [see pdf for notation] and having their extremal points in [see pdf …
Generalized Gradient Methods For Solving Locally Lipschitz Feasibility Problems, Dan Butnariu
Generalized Gradient Methods For Solving Locally Lipschitz Feasibility Problems, Dan Butnariu
Mathematics Technical Papers - Archive
In this paper we study the behavior of a class of iterative algorithms for solving feasibility problems, that is finite systems of inequalities [see pdf for notation], where each [see pdf for notation] is a locally Lipschitz functional on a Hilbert space X. We show that, under quite mild conditions, the algorithms studied in this note, if converge, then they approximate a solution of the feasibility given problem, provided that the feasibility problem is consistent. We prove several convergence criteria showing that, when the envelope of the functionals [see pdf for notation], is sufficiently "regular", then the algorithms converge. The …
Accurate Quasi-Quantum Mechanical Numerical Methodology, Donald Greenspan
Accurate Quasi-Quantum Mechanical Numerical Methodology, Donald Greenspan
Mathematics Technical Papers - Archive
A quasi-quantum mechanical method in which energy is determined by quantum mechanics and motion by Newtonian mechanics is studied by combining it with numerical methodology which conserves energy exactly at each time step. Application is made to the study of the diameter and vibrational frequency of the ground state H2 molecule. The numerical results agree exactly with experimental and quantum mechanical results.
Supercomputer Simulation Of The Modes Of Colliding Microdrops Of Water, Larry F. Heath, Donald Greenspan
Supercomputer Simulation Of The Modes Of Colliding Microdrops Of Water, Larry F. Heath, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
On The Error In Quasi-Quantum Mechanical Calculations, Donald Greenspan
On The Error In Quasi-Quantum Mechanical Calculations, Donald Greenspan
Mathematics Technical Papers - Archive
A numerical simulation of the vibration of a ground state H2 molecule is made from a quasi-quantum mechanical point of view, that is, energy has been determined by quantum mechanics and trajectories determined by Newtonian mechanics. The numerical method used is implicit and conserves the energy exactly at each time step. A variety of CRAY X-MP/SE14 calculations are described and discussed. Comparisons are made with correct oscillation and diameter values.
A Particle Model Of Ground State H2, Donald Greenspan
A Particle Model Of Ground State H2, Donald Greenspan
Mathematics Technical Papers - Archive
A particle model is developed for the ground state H2 molecule. Interparticle forces are formulated which are noncoulombic, but nearly coulombic. The vibration is simulated by a numerical method which conserves the molecule's energy exactly. Numerical examples are described and discussed.
Discriminatory Von Neumann-Morgenstern Solutions, J. G. C. Heijmans
Discriminatory Von Neumann-Morgenstern Solutions, J. G. C. Heijmans
Mathematics Technical Papers - Archive
The von Neumann-Morgenstern solution (vN-M solution) or stable set is arguably the most dynamic and flexible solution concept for cooperative games with side-payments. Perhaps the most striking phenomenon is that vN-M solutions often suggest intricate coalition formation processes and corresponding payoffs. Why this occurs is not well understood. On the other hand, vN-M solutions are difficult to find. This paper deals with the class of discriminatory vN-M solutions and presents results that give insights in the corresponding coalition formation process. A computationally effective procedure is presented to answer the decision problem whether or not a proposed set of imputations to …
Supercomputer Simulation Of Liquid Drop Formation On A Solid Surface, Donald Greenspan
Supercomputer Simulation Of Liquid Drop Formation On A Solid Surface, Donald Greenspan
Mathematics Technical Papers - Archive
Using a molecular dynamics type approach, we show how to simulate the formation of a liquid drop on a solid surface. Application is made to the case in which the liquid is water and the solid is graphite. The dynamical equations are large systems of nonlinear, ordinary differential equations which must be solved numerically. CRAY X-MP/ 24 simulations and related contact angle calculations are described and discussed.
Particle Modelling Of Combustion, Donald Greenspan
Particle Modelling Of Combustion, Donald Greenspan
Mathematics Technical Papers - Archive
Combustion is simulated by a molecular type model using classical molecular type interaction formulas. Supercomputer examples which emphasize turbulent motion are described and discussed.
Arbitrary Order, Hamiltonian Conserving Numerical Solutions Of Calogero And Toda Systems, Donald Greenspan, Andrzej Marciniak
Arbitrary Order, Hamiltonian Conserving Numerical Solutions Of Calogero And Toda Systems, Donald Greenspan, Andrzej Marciniak
Mathematics Technical Papers - Archive
For Calogero and Toda dynamical equations two numerical methods of arbitrary high order, conserving the Hamiltonian are developed. The methods consist of modifications of conventional polynomial extrapolation with the Gragg method used as a basic method. The theoretical study is confirmed by a number of numerical examples.
Energy Conserving Numerical Solutions Of Simplified Turbulence Equations, Donald Greenspan, Andrzej Marciniak
Energy Conserving Numerical Solutions Of Simplified Turbulence Equations, Donald Greenspan, Andrzej Marciniak
Mathematics Technical Papers - Archive
The purpose of this paper is to develop some numerical methods for solving non-Hamiltonian nonintegrable simplified turbulence equations which conserve the energy. We present two kinds of conservative methods for solving these equations: a second order method which uses simple differences, and an arbitrary high order method based on a modification of conventional polynomial extrapolation.
Local Molecular Temperature, Donald Greenspan
Local Molecular Temperature, Donald Greenspan
Mathematics Technical Papers - Archive
For the study of phase-transition by molecular dynamics, the concept of local temperature is desirable. Such a concept, defined and studied previously for atoms, is extended in this paper to molecules. The fundamental formula involves Planck's constant, not Boltzmann's. Related dynamical calculations are described for approximating, theoretically, the melting points of N2, 02, CO, NO, and CH4, and the results are compared with those available experimentally.
Local Atomic Temperature, Donald Greenspan
Local Atomic Temperature, Donald Greenspan
Mathematics Technical Papers - Archive
For the study of phase-transition by molecular dynamics, the concept of local temperature is desirable. Such a concept is defined and studied in this paper. From computer studies of tetrahedral arrangements of four atoms, the constant which results in the formulation is Planck's constant, not Boltzmann's. Related dynamical calculations reveal that the approach yields good approximations for the melting point of the Noble gases, copper and alpha-iron.
The Compensatory Bargaining Set Of A Big Boss Game, Gianfranco Gambarelli, Irinel C. Dragan
The Compensatory Bargaining Set Of A Big Boss Game, Gianfranco Gambarelli, Irinel C. Dragan
Mathematics Technical Papers - Archive
The bargaining sets have been introduced as concepts of solution for cooperative n—person games with side payments by R.J.Aumann and M. Maschler (1964) and studied further by many authors. A comparison of various solutions for games with coalition structures has been done by R.J.Aumann and J.Dreze (1974). In a previous paper of one of the authors I.Dragan (1988), a modified concept of bargaining set, called the compensatory bargaining set, has been introduced and a combinatorial characterization of the noncore elements in the compensatory bargaining set has been obtained. This characterization becomes particularly simple for some classes of games. One of …
Software For The Computation Of The Capacity Of The Polyhedra, C. Sue Brown
Software For The Computation Of The Capacity Of The Polyhedra, C. Sue Brown
Mathematics Technical Papers - Archive
This program computes the boundary values for a selected function and then computes the values on an interior domain by solving the governing dirichlet problem. The boundary is defined by the inverted tetrahedron with an insphere of unit radius, centered at the origin.
Supercomputer Simulation Of Cracks And Fractures By Quasimolecular Dynamics, Donald Greenspan
Supercomputer Simulation Of Cracks And Fractures By Quasimolecular Dynamics, Donald Greenspan
Mathematics Technical Papers - Archive
The gross physical behavior of solids and liquids is the result of atomic or molecular reactions to external forces. Using molecular dynamics, we can study such reactions in the small, on the molecular level. In quasimolecular dynamics, molecules are aggregated into larger units, called quasimolecules, in order to simulate behavior in the large. Mass and energy conservation considerations are fundamental in this approach. In particular, we will simulate the generation of cracks in a slotted plate which, for illustrative purposes, is chosen to be of pure copper. CRAY X—MP/24 supercomputer examples are described and discussed.
Quantitative, Quasimolecular Modelling Of The Fall Of A Drop Into A Basin Of Water, Donald Greenspan, Mohsen Mahmoudi
Quantitative, Quasimolecular Modelling Of The Fall Of A Drop Into A Basin Of Water, Donald Greenspan, Mohsen Mahmoudi
Mathematics Technical Papers - Archive
The fall of a drop into a basin of water is simulated by a molecular aggregate approach. The dynamical equations are large systems of nonlinear, ordinary differential equations which are derived using conservation of mass and total energy. These equations have to be solved numerically. Supercomputer examples of backdrop and wave simulations are described and discussed.