Results 131 to 140 of about 618,259 (179)
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New anisotropic a priori error estimates
Numerische Mathematik, 2001We prove a priori anisotropic estimates for the $L^2$ and $H^1$ interpolation error on linear finite elements. The full information about the mapping from a reference element is employed to separate the contribution to the elemental error coming from different directions. This new
FORMAGGIA, LUCA, PEROTTO, SIMONA
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2012
In this chapter we determine a priori estimates on the behavior at infinity of positive solutions of the equation $$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$ (4.1) on M under assumptions on \( a(x) \) and \( b(x) \) related to the geometrical requirement $$ \mathrm{Ric} \geq-(m-1)H^{2}(1+r(x)^{2})^{\frac{\delta}{2}} $
Paolo Mastrolia +2 more
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In this chapter we determine a priori estimates on the behavior at infinity of positive solutions of the equation $$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$ (4.1) on M under assumptions on \( a(x) \) and \( b(x) \) related to the geometrical requirement $$ \mathrm{Ric} \geq-(m-1)H^{2}(1+r(x)^{2})^{\frac{\delta}{2}} $
Paolo Mastrolia +2 more
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A Priori Estimation of Organic Reaction Yields
Angewandte Chemie, 2015AbstractA thermodynamically guided calculation of free energies of substrate and product molecules allows for the estimation of the yields of organic reactions. The non‐ideality of the system and the solvent effects are taken into account through the activity coefficients calculated at the molecular level by perturbed‐chain statistical associating ...
Emami, Fateme S. +6 more
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Volume growth, ?a priori? estimates, and geometric applications
Geometric And Functional Analysis, 2003Let \((M,\langle\;,\;\rangle)\) be a smooth, connected, non-compact, complete Riemannian manifold of dimension \(m\geq 2\), \(\nabla\) (resp. div) the gradient (resp. divergence) operator, \(| \;| \) the norm corresponding to \(\langle\;,\;\rangle\) and the \(\varphi\)-Laplacian \(L_\varphi\) defined, for \(u\in C^1(M)\), by \(L_\varphi (u) := \text ...
PIGOLA, STEFANO +2 more
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Weak Solutions, A Priori Estimates
2017The fundamental laws of continuum mechanics that can be interpreted as infinite families of integral identities equivalent to systems of partial differential equations give rise to the concept of weak (or variational) solutions that can be vastly extended to extremely divers physical systems of various sorts.
Eduard Feireisl, Antonín Novotný
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1991
This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral
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This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral
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1982
As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on R(A), i.e., if one has the estimate $$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$ (7.1) then the adjoint equation (A*) is everywhere solvable.
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As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on R(A), i.e., if one has the estimate $$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$ (7.1) then the adjoint equation (A*) is everywhere solvable.
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2011
In this chapter we obtain a priori estimates for elliptic operators in bounded or unbounded domains. We will use the spaces of functions introduced in Chapter 2.
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In this chapter we obtain a priori estimates for elliptic operators in bounded or unbounded domains. We will use the spaces of functions introduced in Chapter 2.
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Estimating semantic content: An A priori approach
International Journal of Intelligent Systems, 1988We present our research into the use of the logical structure of natural language discourse to generate estimates of the quantity of semantic content contained within a passage. These estimates of the degree of meaningfulness are recovered from the logical form of the passage, without actually recovering its meaning or necessitating real understanding.
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