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Articles 31 - 60 of 343
Full-Text Articles in Mathematics
A Value For Digraph-Restricted Games, Oltion Voshtina
A Value For Digraph-Restricted Games, Oltion Voshtina
Mathematics Technical Papers - Archive
Digraph-restricted games model situations where some of the players, due to the lack of communication among them, are unable to cooperate. A digraph-restricted game v is defined as a function from the set of feasible coalitions to the reals. By strengthening the symmetry axiom we obtain an extension of the Shapley value for this class of games. Key words. Shapley value, cooperative game, directed graph.
A Quadratic Volterra Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari
A Quadratic Volterra Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Consider the Volterra integral equation [see pdf for notation], ^ is a parameter Solutions of this equation are discussed for separable and difference kernels using Laplace transform and differential equation techniques. Existence and uniqueness questions are explored for various assumptions on the kernel.
Geometry Of Post's Correspondence Problem, Mostafa Ghandehari
Geometry Of Post's Correspondence Problem, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Orthogonality of vectors with integer coordinates in an n-dimensional Euclidean space is used to show that Post's correspondence problem is solvable for words over a one-symbol alphabet. We also use orthogonality to discover a match for an instance of Post's correspondence problem with three symbols
New Mathematical Properties Of The Least Square Value, Irinel Dragan
New Mathematical Properties Of The Least Square Value, Irinel Dragan
Mathematics Technical Papers - Archive
The Least Square Values for cooperative TU games (briefly, LS-values) represent a family of solutions of the following family of optimization problems associated with a cooperative TU game: minimize the sum of weighted squares of deviations of the excesses from their average, on the preimputation set; the weights were positive numbers associated to the coalitions, depending only on their size. For each system of weights a LS-value is obtained by the Lagrange multipliers method; the Shapley value belongs to the family for specified weights. L. Ruiz, F. Valenciano and J. Zarzuelo who introduced this class of values (see[9]), gave two …
Continuous Deformation Of A Developable Surface, Chili Ping Hsu
Continuous Deformation Of A Developable Surface, Chili Ping Hsu
Mathematics Technical Papers - Archive
A developable surface can be developed from a piece of planar region, or vice versa. Several methods are known to construct an isometric mapping between the developable and the planar region. A simple and efficient algorithm based on the differential geometry and differential equations is presented to construct such an isometric mapping. This algorithm contains a deformation parameter ^, where ^ varies between 0 and 1, that can trace the development of the surface in a fashion that ^ = 0 corresponds to the planar region and ^ = 1 recovers the developable. An error estimation shows the error, in …
A Central Limit Theorem For Certain Nonlinear Statistics In Repeated Sampling Of A Finite Population, Chien-Pai Han, D. L. Hawkins
A Central Limit Theorem For Certain Nonlinear Statistics In Repeated Sampling Of A Finite Population, Chien-Pai Han, D. L. Hawkins
Mathematics Technical Papers - Archive
We prove a central limit theorem for the asymptotic joint distribution of non-linear statistics of the form [see pdf for notation] and linear statistics of the form [see pdf for notation], based on independent repeated samples of a finite population of size N with sample indicators [see pdf for notation] for the tth sample.
Minimum Path Problems In Normed Spaces, Reflection And Refraction, Michael Golomb, Mostafa Ghandehari
Minimum Path Problems In Normed Spaces, Reflection And Refraction, Michael Golomb, Mostafa Ghandehari
Mathematics Technical Papers - Archive
The main minimum (or extremum) path problem in this paper deals with the "law of refraction" at a curve separating the plane into two parts with different norms. Analytic and geometric characterization for the point at which refraction takes place and formulas for the angles that this incident and refracted rays make with a fixed axis or with the normal to the curve are established. The case where the unit circle of the two norms are Euclidean circles with different radii leads to the traditional Snell's Law. The other problem deals with the "law of reflection" from a curve in …
Conservative Motion Of Discrete, Hexahedral Gyroscope, Donald Greenspan
Conservative Motion Of Discrete, 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. Examples which included precession, nutation, and a combination of looping and cusp formation are described and discussed.
Conservative Motion Of Discrete, Tetrahedral Tops And Gyroscopes, Donald Greenspan
Conservative Motion Of Discrete, Tetrahedral Tops And Gyroscopes, Donald Greenspan
Mathematics Technical Papers - Archive
Tetrahedral tops and gyroscopes are simulated as discrete, rigid bodies in rotation by introducing a molecular mechanics formulation. The conservative, dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. Examples which include precession and nutation are described and discussed.
Dynamical Generation Of Electron Motions In Ground State H2+, In Ground State H2, And In The First Excited State Of H2, Donald Greenspan
Dynamical Generation Of Electron Motions In Ground State H2+, In Ground State H2, And In The First Excited State Of H2, Donald Greenspan
Mathematics Technical Papers - Archive
Using the recent formulation of Gell-Mann and Hartle for approximating quantum dynamical phenomena by means of classical equations, we simulate electron motions in ground state H2+, in ground state H2, and in the first excited state of H2. The approach develops approximate initial data first by mathematical bisection. The dynamical calculations are then carried out over short time intervals only, which is consistent with the Gell-Mann and Hartle theory and which is applicable because the phenomena to be studied are periodic. An energy conserving numerical scheme is used so that the energy of a given system will be a numerical …
Self-Circumference Of Rotors, Edward J. O'Neill, Mostafa Ghandehari
Self-Circumference Of Rotors, Edward J. O'Neill, Mostafa Ghandehari
Mathematics Technical Papers - Archive
The law of cosines from trigonometry is used to obtain elliptic integrals of the second kind to calculate the "self-circumference" of a Reuleaux triangle and the self-circumference of a rotor in an equilateral triangle. The Euclidean lengths of the polar duals of these sets with respect to their centers are expressed in terms of elliptic integrals of the second kind. Geometric inequalities for the polar duals of rotors in the plane are discussed.
Dynamical Simulation Of The Simplest Hydrides, Donald Greenspan
Dynamical Simulation Of The Simplest Hydrides, Donald Greenspan
Mathematics Technical Papers - Archive
In agreement with recent results of Gell-Mann and Hartle, we approximate electron motions in ground state Li7H1 and Li7H2 using an energy conserving numerical method for the solution of Newton's equations and a novel assumption about the interaction of the bonding electrons. Initial calculations for the first excited state of Li7H1 are also discussed. I. Introduction. Quantum dynamics is usually perceived through the time dependent Schrödinger equation, for which related analytical and computational problems appear to be insurmountable at the present time. There is however an alternate approach which can be implemented readily when the dynamical behavior is periodic. This …
Conservative Motion Of Discrete, Tetrahedral Top On A Smooth Horizontal Plane, Donald Greenspan
Conservative Motion Of Discrete, Tetrahedral Top On A Smooth Horizontal Plane, Donald Greenspan
Mathematics Technical Papers - Archive
Tetrahedral tops are simulated as discrete, rigid bodies in rotation by introducing a molecular mechanics formulation. The contact point of the top with the XY plane is allowed to move in the plane. The conservative, dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. Examples which include precession, nutation, cusp formation, and looping are described and discussed.
Two Remarks On Totally Balanced Games, Juan-Enrique Martínez-Legaz
Two Remarks On Totally Balanced Games, Juan-Enrique Martínez-Legaz
Mathematics Technical Papers - Archive
Two results on totally balanced TU games are presented. It is first shown that the core of any subgame of a non-negative totally balanced game can be easily obtained from the maximal average value function of the game. The second result is a characterization of convex games as those games all of whose marginal games are totally balanced.
Computer Experiments For Molecular Motions And Chemical Bonding, Donald Greenspan
Computer Experiments For Molecular Motions And Chemical Bonding, Donald Greenspan
Mathematics Technical Papers - Archive
It is shown how to simulate first the ground state molecule H. The correct bond length, period, and electron cloud result. The method is then extended to ground state H2 and it is shown that only a new model of the chemical bond can yield the correct bond length, period, and electron cloud.
New Mathematical Properties Of The Banzhaf Value, Irinel C. Dragan
New Mathematical Properties Of The Banzhaf Value, Irinel C. Dragan
Mathematics Technical Papers - Archive
In a paper by P. Dubey and L.S. Shapley an axiomatic definition of the Banzhaf value has been extracted from an axiomatic definition of the Banzhaf power index (see [6]). Briefly speaking, the Banzhaf value axioms can be obtained from the Shapley value axioms by replacing efficiency by a similar axiom. This fact suggest that other recently discovered properties of the Shapley value can lead to similar properties for the Banzhaf value and this is the motivation for the present work.
Heron's Problem In The Minkowski Plane, Mostafa Ghandehari
Heron's Problem In The Minkowski Plane, Mostafa Ghandehari
Mathematics Technical Papers - Archive
Heron's problem in the Euclidean plane is that of minimizing the length of a path that joins two points on one side of a line and intersects the line. A generalization in the Minkowski plane is given and used to discuss reflection properties of conics.
A Semiclassical, Dynamical Model Of The Water Molecule, Donald Greenspan
A Semiclassical, Dynamical Model Of The Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A model of the ground state water molecule is formulated dynamically and studied by computer simulations. Excellent approximations of NMR determined bond angles and bond lengths are achieved through electron pairing and simulation of ice I.
A New Method For Approximating Quantum Dynamical Phenomena Over Short (And Sometimes Long) Time Periods, Donald Greenspan
A New Method For Approximating Quantum Dynamical Phenomena Over Short (And Sometimes Long) Time Periods, Donald Greenspan
Mathematics Technical Papers - Archive
Approximate electron and proton motions are simulated for short time periods for using a special case of the quantum mechanical Ehrenfest equations. Attention is directed only to ground state. A numerical method is employed which conserves the ground state energy at all times. Large proton motions are found, with electron trajectories oscillating between the protons, but concentrating around them.
Computer Modelling Of A Dynamical Water Molecule, Donald Greenspan
Computer Modelling Of A Dynamical Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A model of a ground state water molecule is formulated dynamically and studied by computer simulations. The enigmatic 104.5° bond angle is approximated by introducing the effects of neighboring molecules in a crystaline state. The numerical methodology used conserves the system energy at all times. Illustrative examples are described and discussed.
Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures, D. L. Hawkins, Jerome Eisenfeld, C. P. Han
Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures, D. L. Hawkins, Jerome Eisenfeld, C. P. Han
Mathematics Technical Papers - Archive
Transition probabilities provide a convenient summary of changes in a categorical trait over time in a population. The difficulties of estimating such probabilities based on only aggregate data from repeated sampling are well known. We give here a method for augmenting aggregate data with haphazard recapture data, which can dramatically improve the estimation precision of transition probabilities. The method requires a rather high sampling fraction to provide sufficient numbers of recaptures. It is based on a generalized nonlinear least squares strategy which yields transition probability estimates preserving their natural parameter space, and which are asymptotically efficient. The asymptotic theory is …
Computer Study Of A Semiclassical Model Of The Dynamical Water Molecule, Donald Greenspan
Computer Study Of A Semiclassical Model Of The Dynamical Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A semiclassical model of the water molecule is formulated as an eleven-body problem. The stiff system of differential equations is run for two billion time steps using an energy conservative numerical method. The results are entirely consistent with the experimental bond length and bond angle measurements over the period considered.
On Nonlinear Parameter Estimation In Least Squares Approximation, Donald Greenspan
On Nonlinear Parameter Estimation In Least Squares Approximation, Donald Greenspan
Mathematics Technical Papers - Archive
A non-matrix form of Newton's method for systems of nonlinear equations is described for nonlinear parameter estimation in least squares approximation. Computer examples are described and discussed for the exponential functions [see pdf for notation] for which the method proves to be both easily implementable and exceptionally fast on both personal computers and main frames.
Particle Simulation Of Large Carbon Dioxide Bubbles In Water, Donald Greenspan
Particle Simulation Of Large Carbon Dioxide Bubbles In Water, Donald Greenspan
Mathematics Technical Papers - Archive
A method which can be applied to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, that is, the motion of carbon dioxide bubbles in water. The mathematical formulation uses classical molecular type formulas and results in an n-body problem which is solved numerically. The rise of the bubbles is described, as is the motion of the water near the bubbles. For variety, both H2O water and D20 heavy water are considered. Only workstation computer capabilities are required.
A Semiclassical, Dynamical Model Of Methane, Donald Greenspan
A Semiclassical, Dynamical Model Of Methane, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper we present a semiclassical, dynamical model of the ground state methane molecule. The resulting 13-body problem is solved numerically using energy conserving methodology. The bond length and bond angle results are in complete agreement with experimental results.
Electron Attraction As A Mechanism For The Chemical Bond Of Ground State H2, Donald Greenspan
Electron Attraction As A Mechanism For The Chemical Bond Of Ground State H2, Donald Greenspan
Mathematics Technical Papers - Archive
Previously, electron attraction, incorporated into classical models of the chemical bond, yielded correct bond lengths and vibrational frequencies for all the diatomic molecules through 02. In each case, maximally symmetric electron-nuclei configurations were utilized. In this paper, which concentrates only on ground state H2, it is shown that maximal symmetry is not necessary for the attainment of correct results.
Computer Studies Of A Semiclassical Model Of The Water Molecule, Donald Greenspan
Computer Studies Of A Semiclassical Model Of The Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A semiclassical model of the water molecule is formulated in ground state as an eleven-body problem. The stiff system of dynamical, nonlinear, ordinary differential equations is solved numerically on a CRAY YMP supercomputer. An energy conservative, implicit numerical method is used in order to assure invariance of the ground state energy. From selected initial data, the results of three examples, each run for 12 billion time steps, are shown to be entirely consistent with experimental bond angle measurements.
A Temperature-Adjusted Ozone Attainment Criterion Based On Extreme Value Regression Analysis, D. L. Hawkins
A Temperature-Adjusted Ozone Attainment Criterion Based On Extreme Value Regression Analysis, D. L. Hawkins
Mathematics Technical Papers - Archive
We propose a new statistical methodology to adjust observed peak ozone levels to "normal" meteorology (say, temperatures) across the year for a given site. The adjusted ozone levels can be used to establish a yearly ozone attainment criterion without undue influence of meteorology. They can also be used to estimate ozone trends resistant to meteorological influences. The adjustment process is based on an extreme value regression model of the relationship between peak ozone, temperature and various precursors of ozone. The proposed temperature-adjustment criterion is applied to data for seven sites in Los Angeles County for each of the years 1989-1993, …
Particle Modelling Of A Jiggling Gel, Donald Greenspan
Particle Modelling Of A Jiggling Gel, Donald Greenspan
Mathematics Technical Papers - Archive
Computer generated conical gels are constructed using classical molecular type formulas. Gravity is included in the modeling. Illustrative examples of gel jiggling are described and discussed. Only workstation capabilities are required.
Melting Points Of Atomic And Homogeneous, Diatomic Molecular Solids Via The Four-Body Problem, Donald Greenspan
Melting Points Of Atomic And Homogeneous, Diatomic Molecular Solids Via The Four-Body Problem, Donald Greenspan
Mathematics Technical Papers - Archive
For a regular tetrahedral arrangement of four identical atoms, the minimum velocity of one atom, required for that atom to pass through the plane of the other three, is used to define the melting point of any solid composed of such atoms. The formula which results is [see pdf for notation], in which h is Planck's constant. Computations and results are described for helium, neon, argon, krypton, xenon and copper. The methodology is then extended to homogeneous, diatomic molecular solids and results are described for H2, D2, N2, 02, and C12.