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  • Articles  (11)
  • Applied Mathematics  (9)
  • petroleum
  • 2020-2023
  • 2010-2014
  • 1990-1994  (9)
  • 1970-1974  (2)
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  • Mathematics  (11)
  • Geosciences  (2)
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  • Articles  (11)
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  • Mathematics  (11)
  • Geosciences  (2)
  • 1
    Electronic Resource
    Electronic Resource
    A lithologic data-recording form for a computer-based well-data system (1972)
    Springer
    Mathematical geology 4 (1972), S. 61-72 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; data recording ; data files ; lithology ; petroleum ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Well-data files maintained by petroleum companies and service companies are important sources of data for exploration geologists. To make these data readily accessible and useful for computer studies, three preliminary steps are necessary: (1) systematic data gathering and recording, (2) storage for ready retrieval, and (3) preparation of analysis programs. One important source of geologic data is lithologic descriptions of well cuttings and cores. The practical lithologic data-recording form described here is used routinely at the well site and in the laboratory. It is designed in an 80-column format and uses codes for lithologic characteristics, porosity, and hydrocarbon shows, and forms part of an integrated well-data file. This datarecording form has the advantages that descriptions are made according to a standardized format convenient to use at the well site, and the data are subsequently available in raw form relatively free from interpretive bias. A library of analysis and display programs can be assembled for utilization of the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083194
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  • 2
    Electronic Resource
    Electronic Resource
    A piecewise exponential model for seismic well-logging data (1974)
    Springer
    Mathematical geology 6 (1974), S. 33-45 
    Details
    ISSN: 1573-8868
    Keywords: inversion of data ; mathematics ; numerical analysis ; regression analysis ; geophysics ; petroleum ; well logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Conventional methods of analyzing sonic log data do not always yield accurate information on each velocity segment of a well. It is shown here that the velocity-depth parameters and the sections of approximately constant velocity may be more precisely defined by using an exponential spline to model the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111925
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  • 3
    Electronic Resource
    Electronic Resource
    Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita-type systems (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 1005-1016 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita-type systems are considered leading to global existence and finite time blow-up results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171302
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  • 4
    Electronic Resource
    Electronic Resource
    Diffraction by an acoustically transmissive or an electromagnetically dielectric half-plane (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 387-402 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half-plane. An approximate boundary condition is used that depends on the thickness of, and the material constants for, the half-plane. A solution is obtained, by using the approximate boundary condition, for the problem of a line source field diffracted by a penetrable/dielectric half-plane. The asymmetry of the approximate boundary condition results in a matrix Wiener-Hopf problem, which is solved explicitly.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140603
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  • 5
    Electronic Resource
    Electronic Resource
    Minimal-energy splines: I. Plane curves with angle constraints (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 351-372 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This is the first in a series of papers on minimal-energy splines. The paper is devoted to plane minimal-energy splines with angle constraints. We first consider minimal-energy spline segments, then general minimal-energy spline curves. We formulate problems for minimal-energy spline segments and curves, prove the existence of solutions, justify the Lagrange multiplier rules, and obtain some nice properties (e.g., the infinite smoothness). Finally, we report our computational experience on minimal-energy splines.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130407
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  • 6
    Electronic Resource
    Electronic Resource
    A tracking method for gas flow into vacuum based on the vacuum Riemann problem (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 597-612 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, a tracking method is proposed for the expansion of gas flow into vacuum which may be combined with numerical methods for the equations of gas dynamics, the Euler equations. This tracking prevents the difficulties of the numerical approximation introduced by the vacuum as a region where the Euler equations are not valid due to the failure of the continuum assumption. The tracking algorithm is based on the exact or an approximate solution of the vacuum Riemann problem. This is the initial value problem with two constant states, one being the gas and the other the vacuum state, and a limit case of the usual Riemann problem. In this approach, the gas-vacuum boundary is sharply resolved within one mesh interval. For a test problem, the numerical results of gas flow into vacuum are presented which indicate that the gas vacuum boundary is captured very well.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170803
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  • 7
    Electronic Resource
    Electronic Resource
    Regularity of solutions and approximate inertial manifolds for von Karman evolution equations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 667-680 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The necessary and sufficient conditions of regularity of solutions of von Karman evolution equations are derived. It is proved that a global attractor consists of smooth functions for these evolution equations. The results obtained are used to construct a family of approximate inertial manifolds. These finite dimensional manifolds approximate the global attractor and are determined by a simple iterative procedure. Their use makes it possible to suggest a new method of numerical investigation of long-time behaviour and limit regimes of the equations in question. In particular, this method can be applied for studying a non-linear flutter problem in real air space systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170902
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  • 8
    Electronic Resource
    Electronic Resource
    Approximation of solutions to evolution equations (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 753-763 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form u′(t)= - Au(t) + M(u(t)) is shown. Here A is a closed, positive definite, self-adjoint linear operator with domain D(A) dense in a Hilbert space H and M is a non-linear map defined on D(A½) which satisfies a Lipschitz condition on balls in D(A½).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171002
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  • 9
    Electronic Resource
    Electronic Resource
    Dynamical stability of an elastic column and the phenomenon of bifurcation (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 855-875 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The article studies the stability of rectilinear equilibrium shapes of a non-linear elastic thin rod (column or Timoshenko's beam), the ends of which are pressed. Stability is studied by means of the Lyapunov direct method with respect to certain integral characteristics of the type of norms in Sobolev spaces. To obtain equations of motion, a model suggested in [16] is used. Furta [6] solved the problem of stability for all values of the parameter except bifurcational ones. When values of the system's parameter become bifurcational, the study of stability is more complicated already in a finite-dimensional case. To solve a problem like that, one often has to use a procedure of solving the singularities described in [1], for example. In this paper a change of variables is made which, in fact, is the first step of the procedure mentioned. To prove instability, we use a Chetaev function which can be considered as an infinite-dimensional analogue of functions suggested in [14, 9]. The article also investigates a linear problem on the stability of adjacent shapes of equilibrium when the parameter has supercritical values (post-buckling).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171103
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  • 10
    Electronic Resource
    Electronic Resource
    A free boundary problem and stability for the rectangular plate (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 129-138 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the recent paper [13] we have answered the question of stability for the linear circular plate which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. In this case there are radially symmetric solutions and the contact region is a disk of a smaller radius. This simplified the determination of the critical parameter values for which the plane jumps to another state. For the rectangular plate continuation has to be applied to the variational inequality in order to determine the contact region and evalute the stability criterion. A numerical method is developed for a discretization of the problem and is used to compute the critical load both in the simply supported and the clamped case.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120204
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