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11.
Ville H. Pettersson Helge A. Tverberg Patric R. J. Östergård 《Discrete and Computational Geometry》2014,51(3):722-728
In 1911, Toeplitz made a conjecture asserting that every Jordan curve in $\mathbb{R}^{2}$ contains four points forming the corners of a square. Here Conjecture C is presented, which states that the side length of the largest square on a closed curve that consists of edges of an n×n grid is at least $1/\sqrt{2}$ times the side length of the largest axis-aligned square contained inside the curve. Conjecture C implies Toeplitz’ conjecture and is verified computationally for n≤13. 相似文献
12.
Klika KD Kivelä H Ovcharenko VV Nieminen V Sillanpää R Arpalahti J 《Dalton transactions (Cambridge, England : 2003)》2007,(35):3966-3970
The reaction of tetrapyrazine Pt(II) with adenine under basic conditions yielded two products both disubstituted by adenine and bound in all cases to the N-9 nitrogen of adenine. Crystals amenable to X-crystallographic analysis were obtained for one product which was consequently identified as trans-[Pt(II)(N9-adeH)2(pz)2](NO3)(4).H2O. The other product, though, was identified as the cis isomer based on extensive and comparative NMR structural studies whereby the two compounds were examined as both neutral and tetraprotonated species in solution. The major product of the reaction was unexpectedly the cis isomer, thus obtained in contrast to the trans effect, and the reason for this result is speculated on. Computational calculations using DFT at the B3LYP/TZVP-MARI-J level of theory provided the head-to-tail conformer as the overwhelmingly more stable species over the head-to-head conformer for both compounds whilst the trans product was found to be more stable than the cis. Thus the reaction does not follow a thermodynamic course and rather is kinetically controlled in concert with the speculated mode of reaction. 相似文献
13.
Noora Virtanen Ville Nevalainen Taru Lehtinen Satu Mikkola 《Journal of Physical Organic Chemistry》2007,20(1):72-82
Transesterification of a phosphodiester bond of RNA models has been studied in various buffer solutions, under neutral and slightly alkaline conditions in H2O and D2O. The results show that imidazole is the only buffer system where a clear buffer catalysis on the cleavage of a phosphodiester bond is observed. The rate enhancement in sulphonic acid buffers is smaller, and a sulphonate base, particularly, is inactive as a catalyst. The rate‐enhancing effect of imidazole is, however, catalytic, and the catalytic inactivity of sulphonate buffers can be attributed to their structure and/or charge. The catalysis by imidazole is a complex system which, in addition to first‐order reactions, involves a process that shows a second‐order dependence in imidazole concentration. The latter reaction becomes significant in acidic imidazole buffers (pH < pKa), as the buffer concentration increases. The kinetic solvent deuterium isotope effect kH/kD, referring to first‐order catalysis by imidazole base, is 2.3 ± 0.3. That referring to second‐order catalysis is most probably much larger, but an accurate value could not be obtained. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
14.
Michael Ruzhansky Ville Turunen Jens Wirth 《Journal of Fourier Analysis and Applications》2014,20(3):476-499
In this paper we give several global characterisations of the Hörmander class \(\Psi ^m(G)\) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols. 相似文献
15.
The insect population in grain stores can be kept under control by maintaining a high concentration of CO2 gas (greater than 35%) throughout the grain bed. In this paper the initial phase of this process is considered, where the gas is introduced into the bed. The flow of CO2 through the grain bulk is modelled as fluid flow in a porous medium and the effect of advection, dispersion, sorption and curvilinear isobars and streamlines are considered. An analytic solution to this problem is developed using perturbation expansions and the analysis is restricted to the dominant term in each expansion. In curvilinear flow, a useful variable is the traverse time; the time taken for the gas to travel from the inlet duct. It is shown that lines of constant traverse time are also lines of constant CO2 concentration throughout the grain bed except in the narrow region called the front, where the concentration gradient is large. For most grain stores the isobars have a negative curvature and in these situations the front moves more slowly than in uniform flow and the width of the front increases more rapidly as it travels through the grain bed. It is shown that sorption has an effect on the CO2 concentration in the air for some grains such as canola but not for others such as wheat. 相似文献
16.
17.
F. Schilling Oskar Rudolf Adler William Küster Kratter Jeserich Popp Piettre J. Ville und E. Derrien 《Fresenius' Journal of Analytical Chemistry》1905,44(8-9):582-585
Ohne Zusammenfassung 相似文献
18.
Esa Järvenpää Maarit Järvenpää Antti Käenmäki Tapio Rajala Sari Rogovin Ville Suomala 《Mathematische Zeitschrift》2010,266(1):83-105
Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dimp(A) £ s-crs{{\rm {dim}_p}(A)\le s-c\varrho^s} where dimp is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the
corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that
dimp(A) £ dimp(X)-c(log\tfrac1r)-1rt{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} . 相似文献
19.
Roberto Di Remigio Arnfinn Hykkerud Steindal Krzysztof Mozgawa Ville Weijo Hui Cao Luca Frediani 《International journal of quantum chemistry》2019,119(1):e25685
PCMSolver is an open-source library for continuum electrostatic solvation. It can be combined with any quantum chemistry code and requires a minimal interface with the host program, greatly reducing programming effort. As input, PCMSolver needs only the molecular geometry to generate the cavity and the expectation value of the molecular electrostatic potential on the cavity surface. It then returns the solvent polarization back to the host program. The design is powerful and versatile: minimal loss of performance is expected, and a standard single point self-consistent field implementation requires no more than 2 days of work. We provide a brief theoretical overview, followed by two tutorials: one aimed at quantum chemistry program developers wanting to interface their code with PCMSolver , the other aimed at contributors to the library. We finally illustrate past and ongoing work, showing the library's features, combined with several quantum chemistry programs. 相似文献
20.
We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula. 相似文献