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141.
This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity. First, the general asymptotic expansion of the inverse function at zero is derived, which can be used to approximate the inverse function when the variable is small. Second, an inversion algorithm is formulated by splitting the Bromwich integral into two parts. One is the main weakly oscillatory part, which is evaluated by a composite Gauss–Legendre rule and its Kronrod extension, and the other is the remaining strongly oscillatory part, which is integrated analytically using the Puiseux expansion of the transform at infinity. Finally, some typical tests show that the algorithm can be used to invert a wide range of Laplace transforms automatically with high accuracy and the output error estimator matches well with the true error. 相似文献
142.
Jakob Söhl 《Statistics & probability letters》2010,80(9-10):840-847
This paper studies polar sets for anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian random field is dominated by an anisotropic metric. We deduce an upper bound for the hitting probabilities and conclude that sets with small Hausdorff dimension are polar. Moreover, the results allow for a translation of the Gaussian random field by a random field, that is independent of the Gaussian random field and whose sample functions are of bounded Hölder norm. 相似文献
143.
Jakob Jonsson 《Discrete and Computational Geometry》2010,43(4):927-950
Let G be an infinite graph such that the automorphism group of G contains a subgroup K ?? d with the property that G/K is finite. We examine the homology of the independence complex Σ(G/I) of G/I for subgroups I of K of full rank, focusing on the case that G is the square, triangular, or hexagonal grid. Specifically, we look for a certain kind of homology cycles that we refer to as “cross-cycles,” the rationale for the terminology being that they are fundamental cycles of the boundary complex of some cross-polytope. For the special cases just mentioned, we determine the set Q(G,K) of rational numbers r such that there is a group I with the property that Σ(G/I) contains cross-cycles of degree exactly r?|G/I|?1; |G/I| denotes the size of the vertex set of G/I. In each of the three cases, Q(G,K) turns out to be an interval of the form [a,b]∩?={r∈?:a≤r≤b}. For example, for the square grid, we obtain the interval $[\frac{1}{5},\frac{1}{4}]\cap \mathbb{Q}Let G be an infinite graph such that the automorphism group of G contains a subgroup K
≅ℤ
d
with the property that G/K is finite. We examine the homology of the independence complex Σ(G/I) of G/I for subgroups I of K of full rank, focusing on the case that G is the square, triangular, or hexagonal grid. Specifically, we look for a certain kind of homology cycles that we refer to
as “cross-cycles,” the rationale for the terminology being that they are fundamental cycles of the boundary complex of some
cross-polytope. For the special cases just mentioned, we determine the set Q(G,K) of rational numbers r such that there is a group I with the property that Σ(G/I) contains cross-cycles of degree exactly r⋅|G/I|−1; |G/I| denotes the size of the vertex set of G/I. In each of the three cases, Q(G,K) turns out to be an interval of the form [a,b]∩ℚ={r∈ℚ:a≤r≤b}. For example, for the square grid, we obtain the interval
[\frac15,\frac14]?\mathbbQ[\frac{1}{5},\frac{1}{4}]\cap \mathbb{Q}. 相似文献
144.
Jakob Jonsson 《Annals of Combinatorics》2010,14(4):487-505
Let 1 ≤ m ≤ n. We prove various results about the chessboard complex M
m,n
, which is the simplicial complex of matchings in the complete bipartite graph K
m,n
. First, we demonstrate that there is nonvanishing 3-torsion in
[(H)\tilde]d(\sf Mm,n; \mathbb Z){{\tilde{H}_d({\sf M}_{m,n}; {\mathbb Z})}} whenever
\fracm+n-43 £ d £ m-4{{\frac{m+n-4}{3}\leq d \leq m-4}} and whenever 6 ≤ m < n and d = m − 3. Combining this result with theorems due to Friedman and Hanlon and to Shareshian and Wachs, we characterize all triples
(m, n, d ) satisfying
[(H)\tilde]d (\sf Mm,n; \mathbb Z) 1 0{{\tilde{H}_d \left({\sf M}_{m,n}; {\mathbb Z}\right) \neq 0}}. Second, for each k ≥ 0, we show that there is a polynomial f
k
(a, b) of degree 3k such that the dimension of
[(H)\tilde]k+a+2b-2 (\sf Mk+a+3b-1,k+2a+3b-1; \mathbb Z3){{\tilde{H}_{k+a+2b-2}}\,\left({{\sf M}_{k+a+3b-1,k+2a+3b-1}}; \mathbb Z_{3}\right)}, viewed as a vector space over
\mathbbZ3{\mathbb{Z}_3}, is at most f
k
(a, b) for all a ≥ 0 and b ≥ k + 2. Third, we give a computer-free proof that
[(H)\tilde]2 (\sf M5,5; \mathbb Z) @ \mathbb Z3{{\tilde{H}_2 ({\sf M}_{5,5}; \mathbb {Z})\cong \mathbb Z_{3}}}. Several proofs are based on a new long exact sequence relating the homology of a certain subcomplex of M
m,n
to the homology of M
m-2,n-1 and M
m-2,n-3. 相似文献
145.
146.
Andreas Herburger Dr. Milan Ončák Dr. Chi-Kit Siu Ephrem G. Demissie Jakob Heller Dr. Wai Kit Tang Prof. Dr. Martin K. Beyer 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(43):10165-10171
Understanding the intrinsic properties of the hydrated carbon dioxide radical anions CO2.−(H2O)n is relevant for electrochemical carbon dioxide functionalization. CO2.−(H2O)n (n=2–61) is investigated by using infrared action spectroscopy in the 1150–2220 cm−1 region in an ICR (ion cyclotron resonance) cell cooled to T=80 K. The spectra show an absorption band around 1280 cm−1, which is assigned to the symmetric C−O stretching vibration νs. It blueshifts with increasing cluster size, reaching the bulk value, within the experimental linewidth, for n=20. The antisymmetric C−O vibration νas is strongly coupled with the water bending mode ν2, causing a broad feature at approximately 1650 cm−1. For larger clusters, an additional broad and weak band appears above 1900 cm−1 similar to bulk water, which is assigned to a combination band of water bending and libration modes. Quantum chemical calculations provide insight into the interaction of CO2.− with the hydrogen-bonding network. 相似文献
147.
Jakob Knelles Dr. Stuart Beardsworth Korinna Bader Dr. Johanna R. Bruckner Andrea Bühlmeyer Robert Forschner Kevin Schweizer Dr. Wolfgang Frey Prof. Dr. Frank Giesselmann Prof. Dr. Yann Molard Prof. Dr. Sabine Laschat 《Chemphyschem》2019,20(17):2210-2216
A series of tetraguanidinium tetraphenylethene (TPE) arylsulfonates with different chain lengths was prepared via ionic self-assembly of tetraguanidinium TPE chloride and the respective methyl arylsulfonates. Liquid crystalline properties were studied by differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction. Tetraguanidinium TPE arylsulfonates with chain lengths of C8–C12 displayed hexagonal columnar mesophases over a broad temperature range, while derivatives with longer chains showed oblique columnar phases. In solution all compounds displayed aggregation-induced emission behaviour. Temperature-dependent luminescence spectra of the bulk phase of the tetraguanidinium TPE arylsulfonate with C14 side chains revealed a strong luminescence both in the solid state and the oblique columnar mesophase. The emission behaviour was rationalized by a unique combination of restriction of intramolecular rotation of the TPE core, Coulomb interaction between the guanidinium cations and π–π interactions of the anionic arylsulfonate moieties. 相似文献
148.
We consider the question whether, given a countable family of lattices in a locally compact abelian group G, there exist functions such that the resulting generalized shift-invariant system is a tight frame of . This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system. 相似文献
149.
150.
The Structure of the Cobalt Oxide/Au Catalyst Interface in Electrochemical Water Splitting
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