| He gave a wonderful series of lectures on special functions, asymptotic analysis, and approximation theory. |
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| The process of becoming healthy is like some kind of asymptotic aim towards an unachievable end. |
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| For these data, the linear and asymptotic curves were nearly indistinguishable. |
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| Other topics in the large range of applied mathematics topics which he studied were existence theorems and asymptotic expansions. |
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| Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure. |
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| Gromov brought his geometric intuition to group theory and told us to look at the asymptotic properties of the Cayley graph. |
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| Aleksandrov further developed the integral transform method and used asymptotic methods to solve the problem for a finite thickness layer. |
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| According to asymptotic theory, the distribution of maximum-likelihood estimates can be approximated by a multivariate normal distribution. |
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| First, the asymptotic results provide a very reasonable approximation for the velocity even for a much lower level of cooperativity. |
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| He also worked on asymptotic analysis, fractional integration and singular partial differential equations. |
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| He often returned to the topic of his first research paper on the error term in an asymptotic formula discovered by Gauss. |
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| They are more interested in the qualitative properties, which are often deduced from complex asymptotic results. |
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| That asymptotic rise of the stock markets since WWII has flattened out. |
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| The asymptotic course of the stress-number curve offers an explanation for this drop in fatigue strength. |
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| This takes advantage of the better asymptotic properties of the difference in the log variances, as well as of the monotonicity of the transformation. |
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| Experiments were subsequently designed to find the point at which the asymptotic limit had been attained at each bleaching stage. |
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| Only at infinitely close distances are quarks free, an effect known as asymptotic freedom. |
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| Unfortunately, the asymptotic properties of IV estimators in the presence of non-stationary instruments are not known. |
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| Keywords Smarandache LCM dual function, Dirichlet series, exact calculating formula, asymptotic formula. |
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| Grabner, Numerical integration, energy and asymptotic equidistribution on the sphere, submitted. |
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| Then consistency and asymptotic distribution for the microergodic parameters are established. |
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| Partial-state asymptotic stability is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state. |
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| A bootstrap algorithm is used to approximate the distribution of the test statistic in finite samples and show that the bootstrapped distribution converges to the asymptotic distribution in probability. |
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| The opening paper presents results on the asymptotic stabilization of systems of conservation laws by controls acting at a single boundary point. |
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| Due to the nonlinearity of the brightness vs. concentration profile, a minimum of three mill trials would be needed to determine the graphical relationship for the asymptotic curve. |
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| This condition is called asymptotic freedom. |
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| This again sets the star evolving toward the red giant stage along what is called the asymptotic giant branch, located slightly above the main region of giants in the Hertzsprung-Russell diagram. |
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| In a sample of near or less than 100 observations, as is the case in McPhail's paper, the tabulated asymptotic critical values may be inappropriate. |
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| These are universal laws, and their existence means that even if we do not know the law of the phenomenon, we can still say a number of things about its behaviour thanks to these asymptotic results. |
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| The convergence properties and the asymptotic distributions of the proposed non-parametric estimators of the diffusion functions with multivariate dimensions are also obtained. |
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| The first-order asymptotic validity of the proposed procedure is proven, and a series of Monte Carlo experiments show it may improve test sizes over conventional block bootstrapping. |
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| With this type of specification, short rates necessarily converge towards the asymptotic long rate, i.e. the asymptotic curve is necessarily, in mean, flat. |
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| The elements of such a correlation matrix do not have asymptotic variances and covariances of the form, even if S has a Wishart distribution. |
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| In addition, a paper by Bayes on asymptotic series was published posthumously. |
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| In some cases, Maxwell's equations are solved through infinite space, and boundary conditions are given as asymptotic limits at infinity. |
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| The proposed controllers provide asymptotic attitude stabilization with complete rejection of unknown external disturbances. |
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| In that paper, we started asymptotic analysis of the correlation kernel and computed the limit shape as a result. |
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| The real situation is slightly more complicated since we must symmetrize the asymptotic basis with respect to exchange of t he identical nuclei. |
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| The approximations approach is founded on asymptotic analysis and perturbation theory, which deal with the study of applied mathematical systems in limiting cases. |
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| In the rest of this abstract we will state our asymptotic results and then explain in more detail how they are applied to solve the limit problems listed above. |
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| Exercises and problems also explain how Borel summability can be used to solve problems concerning formal expansions as well as improving the accuracy of asymptotic estimates. |
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| Any attempt to grasp truth is, therefore, relativized in view of the fact that human perspectives and representations are always asymptotic to it. |
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| Asymptotic prey profitability drives star-nosed moles to the foraging speed limit. |
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