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430
THE COMPLEX INVERSION FORMULA REVISITED
"... Abstract. We give a simplified proof of the complex inversion formula for semigroups and — more generally — solution families for scalartype Volterra equations, including the stronger versions on UMD spaces. Our approach is based on (elementary) Fourier analysis. 1. ..."
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Abstract. We give a simplified proof of the complex inversion formula for semigroups and — more generally — solution families for scalartype Volterra equations, including the stronger versions on UMD spaces. Our approach is based on (elementary) Fourier analysis. 1.
THE SUM OF INVERSES OF BINOMIAL COEFFICIENTS REVISITED
, 1996
"... The aim of this note is to generalize the work on finite sums of inverses of binomial coefficients that are part of a paper by Andrew Rockett [1] which was published in this Quarterly in 1981. Our work rests on the following lemma. Lemma 1: For any positive integers n and/?, with p < n\ i n + \\P ..."
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+ \\P, (n \ l Proof: Use the wellknown formulas of Euler, f t u\\t) v l dt = T ^ Y{y} Jo T(u + v) = jV(i0"^. and T(k + \) = k\, that are valid for any positive real numbers u and v, and any positive integer k. Now we define q0 = l and ^(*, j) — I ^ W ^ for arbitrary nonzero complex numbers
Zeno product formula revisited
, 2008
"... We introduce a new product formula which combines an orthogonal projection with a complex function of a nonnegative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operatornorm convergence ..."
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Cited by 1 (1 self)
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We introduce a new product formula which combines an orthogonal projection with a complex function of a nonnegative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operatornorm convergence
Zeno product formula revisited
, 2006
"... Abstract: We introduce a new product formula which combines an orthogonal projection with a complex function of a nonnegative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operatornorm con ..."
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Abstract: We introduce a new product formula which combines an orthogonal projection with a complex function of a nonnegative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operator
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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reconstruction from multiple receiver data. Using the framework of linear algebra, two different reconstruction strategies have been derived. In their general forms the resulting formulae hold for arbitrary sampling patterns in kspace. A detailed discussion is dedicated to the most practical case, namely
Monte Carlo sampling of solutions to inverse problems
 J. geophys. Res
, 1995
"... Probabilistic formulation of inverse problems leads to the definition of a probability distribution in the model space. This probability distribution combines a priori information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linkin ..."
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Cited by 104 (10 self)
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no explicit formula for the a priori distribution is available. The most well known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex a priori information and data
Lowcomplexity transform and quantization in H.264/AVC
 IEEE Trans. Circuits Syst. Video Technol
, 2003
"... Abstract—This paper presents an overview of the transform and quantization designs in H.264. Unlike the popular 8 8 discrete cosine transform used in previous standards, the 4 4 transforms in H.264 can be computed exactly in integer arithmetic, thus avoiding inverse transform mismatch problems. The ..."
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Cited by 101 (0 self)
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. The new transforms can also be computed without multiplications, just additions and shifts, in 16bit arithmetic, thus minimizing computational complexity, especially for lowend processors. By using short tables, the new quantization formulas use multiplications but avoid divisions. Index Terms
C.: Revisiting histograms and isosurface statistics
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract—Recent results have shown a link between geometric properties of isosurfaces and statistical properties of the underlying sampled data. However, this has two defects: not all of the properties described converge to the same solution, and the statistics computed are not always invariant unde ..."
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Cited by 19 (3 self)
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under isosurfacepreserving transformations. We apply Federer’s Coarea Formula from geometric measure theory to explain these discrepancies. We describe an improved substitute for histograms based on weighting with the inverse gradient magnitude, develop a statistical model that is invariant under
A Note on the Inversion Complexity of Boolean Functions in Boolean Formulas
, 811
"... In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f. In 1958, Markov determined th ..."
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In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f. In 1958, Markov determined
The Higher Derivatives Of The Inverse Tangent Function Revisited
, 2010
"... A closedform formula for all derivatives of the real arctangent function is presented. In addition a curious series expansion for the function is obtained and one of its speci…c consequences is given. 1 ..."
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A closedform formula for all derivatives of the real arctangent function is presented. In addition a curious series expansion for the function is obtained and one of its speci…c consequences is given. 1
Results 1  10
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