Calculation of stresses in a coal seam in presence of gas diffusion

Analytical expressions are obtained for calculating the stresses in a coal seam in presence of gas diffusion. The solution is given as a sum whose four terms are convergent series. All functions in the relevant expressions can easily be computed either separately or successively; i.e., it is not required to solve infinite systems of equations.     

Using population of models to investigate and quantify gas production in a spatially heterogeneous coal seam gas field

In this work, we discuss the use of a local model developed previously [1] that describes the multiphase flow of gaseous species and liquid water within a single coal seam to investigate the gas production from a spatially heterogeneous production field. The field is located within the Surat Basin in Queensland, and is composed of a total of 80 production wells spread over a region covering approximately 36 km². However, not every well is producing gas at any one time and so in this work we take a subset of 42 wells that are the top-producing wells in terms of total gas volume.We utilise a population of models approach to understand the variability in the underlying physical processes, and as a mechanism for dealing with the spatial heterogeneity that arises due to geological variation across the field. We are able to simultaneously obtain a family of parameter sets for each of these wells, in which each set in the family yields a predicted cumulative total gas production curve that matches the measured cumulative production curve for a given well to within an allowable limit of error.By analysing the results of this population of models approach we can identify the similarities between wells based on the parameter distributions, and understand the sensitivity of key model parameters. We show by example that high correlation between wells based on their parameter values may be an indicator of their similarity. A combinatorial sum of the predicted gas production is compared against the individual gas volumes (given in terms of percentage of the total volume) measured at the compression facility as a way of further calibrating a subpopulation of models.     

On the specificity of a possibility distribution

The specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation. As such it is a measure of amount of uncertainty or information. We investigate a number of issues related to specificity measures. We discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution. We describe unifying view for constructing specificity measures. We look at the relationship of the specificity of a distribution and its negation. We consider the case where the base set is continuous.     

Effect of property anisotropy of a rock mass on its stressed state and length of the plastic region of an excavated seam

The solution of the mixed problem of the theory of elasticity for a half plane modeling the stress-strain state of an anisotropic rock mass during the excavation of a seam is constructed. The results of numerical investigation of the length of the neardrift plastic zone of the seam being excavated as a function of the anisotropy of its plastic properties are given. Diagrams showing the stress distribution in the mass are presented.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 38–43, 1987.     

Fuzzy sets as a basis for a theory of possibility

The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U={u} which is characterized by its membership function μ_F, then a proposition of the form “X is F,” where X is a variable taking values in U, induces a possibility distribution ∏X which equates the possibility of X taking the value u to μF(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution ∏_x in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle.A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form “X is F is α-possible,” where α is a number in the interval [0, 1], is formulated and illustrated by examples.     

Fuzzy sets as a basis for a theory of possibility

The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U = {u} which is characterized by its membership function μ_F, then a proposition of the form $\text{“X}\text{is}\text{F”}$, where X is a variable taking values in U, induces a possibility distribution $\text{t}\text{?}{}_{\mathrm{x}}$ which equates the possibility of X taking the value u to μ_F(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution $\text{t}\text{?}{}_{\mathrm{x}}$ in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle.A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form $\text{“X}\text{is}\text{F}$ is α-possible”, where α is a number in the interval [0,1], is formulated and illustrated by examples.     

Best possibility of the Furuta inequality

Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but .

     

On possibility of refining bounds for the delay of a parallel adder

A nontrivial lower bound to the delay of a parallel adder over the classical basis B₀ = {&; V, ^?} is obtained with the additive remainder term of order log log log n.     

Semideviations of reduced fuzzy variables: a possibility approach

This paper proposes new methods to reduce the uncertain information embedded in the secondary possibility distribution of a type-2 fuzzy variable. Based on possibility measure, we define the lower value-at-risk (VaR) and upper VaR of a regular fuzzy variable, and develop the VaR-based reduction methods for type-2 fuzzy variables. The proposed VaR-based reduction methods generalize some existing reduction methods by introducing possibility level parameter in distribution functions. For VaR reduced fuzzy variables, we employ Lebesgue–Stieltjes (L–S) integral to define three $n$ th semideviations to gauge the risk resulted from asymmetric fuzzy uncertainty. Furthermore, we compute the mean values and semideviations of the VaR reduced fuzzy variables, and derive some useful analytical expressions. The theoretical results obtained in this paper have potential applications in practical risk management and engineering optimization problems.     

On the possibility of simplifying the thermoelastic equation

By some very simple algebraic manipulations, it is shown as the linear thermoelastic equation can be solved by looking for the solutions of much simpler vectorial equations. As an example the displacements of the reflecting surface of a mirror illuminated by a high power laser beam have been evaluated.

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Sommario Utilizzando alcuni semplici passaggi algebrici, viene mostrato come l'equazione degli spostamenti termoelastici possa essere risolta cercando le soluzioni di equazioni vettoriali molto più semplici. Come esempio vengono calcolate le deformazioni della superficie riflettente di uno specchio investito da un fascio laser di grande potenza.

     

On the possibility of strengthening the Lieb-Thirring inequality

In 1976, Lieb and Thirring obtained an upper bound for the square of the normon L ²(?²) of the sum of the squares of functions from finite orthonormal systems via the sum of the squares of the norms of their gradients. Later, a series of Lieb-Thirring inequalities for orthonormal systems was established by many authors. In the present paper, using the standard theory of functions, we prove Lieb-Thirring inequalities, which have applications in the theory of partial differential equations.     

Cooling of a cylindrical container blasted into the rock

An upright cylindrical container blasted into the rock is filled instantaneously with a warm liquid. Heat is transferred from the liquid into the surrounding rock and the open air. The temperature of the liquid and the surrounding rock is determined as a function of time.The differential equation and the auxiliary conditions of the transient heat conduction problem are Laplace transformed, the subsidiary equations are solved by two-dimensional relaxation, and the resulting temperature is obtained by means of numerical inversion of the Laplace transform.The results are presented numerically and graphically.     

Collateral in banking policy: On the possibility of signaling

In this paper we study the validity of the assertion that collateral is in a position to signal the degree of borrowers’ riskiness. We use a framework in which the cash flow from the risky project is described by means of a continuous density and projects are classified by second-order stochastic dominance. We show that if collateral is assumed bounded by the initial project outlay the positive role of collateral, namely truthfully conveying the private information about the project risk by the collateral amount, can no longer be ensured.     

A slow wave in a fluid layer simulating an oil-saturated seam

A simple model of an oil-saturated layer is proposed. A slow wave propagating in a fluid layer sandwiched between two elastic half-spaces is studied. For this wave the phase and group velocities and also the horizontal and vertical components of the displacement are presented. The theoretical results are in good agreement with the experimental data obtained. Bibliography:4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 101–112. Translated by P. V. Krauklis.     

The best possibility of the grand Furuta inequality

Let be invertible bounded linear operators on a Hilbert space satisfying , and let be real numbers satisfying Furuta showed that if , then . This inequality is called the grand Furuta inequality, which interpolates the Furuta inequality
and the Ando-Hiai inequality ( ).

In this paper, we show the grand Furuta inequality is best possible in the following sense: that is, if , then there exist invertible matrices with which do not satisfy .

     

On the possibility of gravitational collapse in the relativistic theory of gravity

In the example of dust matter, it is shown that a gravitational attractive force does not lead to the formation of “black holes” in the relativistic theory of gravity. It is proved that in the absence of matter, the gravitational field is also absent. Therefore, a vacuum is not a source of a gravitational field. The mechanism of energy production in the process of the accumulation of matter into massive objects is discussed.     

On the possibility of globally stabilizing invariant sets

In this paper we study the possibility of globally stabilizinginvariant sets of autonomous continuous nonlinear systems bythe state (output) feedback control law. We show that the topologicalstructure of invariant sets can give rise to obstruction tothe existence of a continuous control law for global stabilizationof invariant sets.     

Centralized DEA models with the possibility of downsizing

While traditional data envelopment analysis (DEA) models assess the relative efficiency of similar, independent decision making units (DMUs) centralized DEA models aim at reallocating inputs and outputs among the units setting new input and output targets for each one. This system point of view is appropriate when the DMUs belong to a common organization that allocates their inputs and appropriates their outputs. This intraorganizational perspective opens up the possibility that greater technical efficiency for the organization as a whole might be achieved by closing down some of the existing DMUs. In this paper, we present three centralized DEA models that take advantage of this possibility. Although these models involve some binary variables, we present efficient solution approaches based on Linear Programming. We also present some numerical results of the proposed models for a small problem from the literature.     

Externalities and the possibility of pareto- satisfactory decentralization

This paper shows that the (New)² Welfare Economics provides interesting new ways of classifying externalities in terms of the complexity of messages required to equate equilibria and optima; and in which, at the end, it is shown that the study of externalities provides useful new insights into the (New)² Welfare Economics by showing problems with the definition of satisfactory informationally decentralized resource allocation mechanisms.