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21.
Let (P, ≤) be a finite poset (partially ordered set), where P has cardinality n. Consider linear extensions of P as permutations x1x2?xn in one-line notation. For distinct elements x, y ∈ P, we define ?(x ? y) to be the proportion of linear extensions of P in which x comes before y. For \(0\leq \alpha \leq \frac {1}{2}\), we say (x, y) is an α-balanced pair if α ≤ ?(x ? y) ≤?1 ? α. The 1/3–2/3 Conjecture states that every finite partially ordered set which is not a chain has a 1/3-balanced pair. We make progress on this conjecture by showing that it holds for certain families of posets. These include lattices such as the Boolean, set partition, and subspace lattices; partial orders that arise from a Young diagram; and some partial orders of dimension 2. We also consider various posets which satisfy the stronger condition of having a 1/2-balanced pair. For example, this happens when the poset has an automorphism with a cycle of length 2. Various questions for future research are posed. 相似文献
22.
Arkadiusz Lewandowski 《Journal of Geometric Analysis》2018,28(3):2466-2476
We prove that given a family \((G_t)\) of strictly pseudoconvex domains varying in \(\mathcal {C}^2\) topology on domains, there exists a continuously varying family of peak functions \(h_{t,\zeta }\) for all \(G_t\) at every \(\zeta \in \partial G_t\). 相似文献
23.
Anatol Jaworek Tadeusz Czech Arkadiusz T. Sobczyk Andrzej Krupa 《Journal of Electrostatics》2013,71(2):165-175
This paper presents comparative experimental studies of the morphology and elemental composition of fly ash particles from coal- and biomass-fired boilers, deposited in each stage of 3-stage electrostatic precipitators (ESPs). It was shown that fly ash morphology, its physical properties, and the percentage of elements in the fly ash taken from each stage of ESP depend on the kind of fuel. The biomass fly ash contains many irregular large particles, which are pieces of unburned wood. Bulk density of biomass fly ash is on average lower than that of coal fly ash, and drastically decreases in the second and third stages of ESP. The resistivity, measured at electric field of 4 kV/cm, of fly ash from biomass-fired boilers is much lower than that from coal, and can be below 102 Ω m, whereas from coal, except the first stage, varies in the range from 107 to 1010 Ω m. The low resistivity of coal fly ash in the first stage of ESP results from high carbon content, and of biomass is probably an effect of additional high percentage of potassium, calcium and sodium sulfates. The percentage of Si, Al, Na, Fe, and Ti in fly ash from coal-fired boilers is much higher than from biomass, and in the opposite, the percentage of Mg, K, Ca, Mn, Mo, S, Cl, and P in biomass ash exceeds that in coal fly ash. Potential detrimental effects of biomass combustion products (salts, acids, tar) leaving the boiler on the construction elements of the electrostatic precipitator, including electrodes and HV insulators have been discussed in this paper. It was concluded that the long-term effects of biomass co-firing on the electrostatic precipitator performance, including the collection efficiency, have not been sufficiently studied in the literature and these issues require further detailed investigations. 相似文献
24.
Arkadiusz Pawlik Jakub Kozik Tomasz Krawczyk Michał Lasoń Piotr Micek William T. Trotter Bartosz Walczak 《Discrete and Computational Geometry》2013,50(3):714-726
Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the plane. We provide a general construction that for any arc-connected compact set $X$ X in $\mathbb{R }^2$ R 2 that is not an axis-aligned rectangle and for any positive integer $k$ k produces a family $\mathcal{F }$ F of sets, each obtained by an independent horizontal and vertical scaling and translation of $X$ X , such that no three sets in $\mathcal{F }$ F pairwise intersect and $\chi (\mathcal{F })>k$ χ ( F ) > k . This provides a negative answer to a question of Gyárfás and Lehel for L-shapes. With extra conditions we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number. This applies to many common shapes, like circles, square boundaries or equilateral L-shapes. Additionally, we reveal a surprising connection between coloring geometric objects in the plane and on-line coloring of intervals on the line. 相似文献
25.
Applying Mechanochemistry for Bottom‐Up Synthesis and Host–Guest Surface Modification of Semiconducting Nanocrystals: A Case of Water‐Soluble β‐Cyclodextrin‐Coated Zinc Oxide
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Piotr Krupiński Arkadiusz Kornowicz Dr. Kamil Sokołowski Anna M. Cieślak Prof. Janusz Lewiński 《Chemistry (Weinheim an der Bergstrasse, Germany)》2016,22(23):7817-7823
Mechanochemistry has recently emerged as an environmentally friendly solventless synthesis method enabling a variety of transformations including those impracticable in solution. However, its application in the synthesis of well‐defined nanomaterials remains very limited. Here, we report a new bottom‐up mechanochemical strategy to rapid mild‐conditions synthesis of organic ligand‐coated ZnO nanocrystals (NCs) and their further host–guest modification with β‐cyclodextrin (β‐CD) leading to water‐soluble amide‐β‐CD‐coated ZnO NCs. The transformations can be achieved by either one‐pot sequential or one‐step three‐component process. The developed bottom‐up methodology is based on employing oxo‐zinc benzamidate, [Zn4(μ4‐O)(NHOCPh)6], as a predesigned molecular precursor undergoing mild solid‐state transformation to ZnO NCs in the presence of water in a rapid, clean and sustainable process. 相似文献
26.
Arkadiusz Jadczyk 《Advances in Applied Clifford Algebras》2007,17(2):201-240
Using the Clifford algebra formalism we extend the quantum jumps algorithm of the Event Enhanced Quantum Theory (EEQT) to
convex state figures other than those stemming from convex hulls of complex projective spaces that form the basis for the
standard quantum theory. We study quantum jumps on n-dimensional spheres, jumps that are induced by symmetric configurations
of non-commuting state monitoring detectors. The detectors cause quantum jumps via geometrically induced conformal maps (M?bius
transformations) and realize iterated function systems (IFS) with fractal attractors located on n-dimensional spheres. We
also extend the formalism to mixed states, represented by “density matrices” in the standard formalism, (the n-balls), but
such an extension does not lead to new results, as there is a natural mechanism of purification of states. As a numerical
illustration we study quantum fractals on the circle (one-dimensional sphere and pentagon), two–sphere (octahedron), and on
three-dimensional sphere (hypercubetesseract, 24 cell, 600 cell, and 120 cell). The attractor, and the invariant measure on
the attractor, are approximated by the powers of the Markov operator. In the appendices we calculate the Radon-Nikodym derivative
of the SO(n + 1) invariant measure on Sn under SO(1, n + 1) transformations and discuss the Hamilton’s “icossian calculus” as well as its application to quaternionic realization
of the binary icosahedral group that is at the basis of the 600 cell and its dual, the 120 cell.
As a by-product of this work we obtain several Clifford algebraic results, such as a characterization of positive elements
in a Clifford algebra
as generalized Lorentz “spin–boosts”, and their action as M?bius transformation on n-sphere, and a decomposition of any element
of Spin+(1, n + 1) into a spin–boost and a spin–rotation, including the explicit formula for the pullback of the SO(n + 1) invariant Riemannian metric with respect to the associated M?bius transformation. 相似文献
27.
Arkadiusz Józefczak Tomasz Hornowski Miko?aj ?abowski Peter Kop?anský Andrzej Szlaferek 《Journal of magnetism and magnetic materials》2009,321(10):1505-1508
The aim of this study was to investigate the influence of poly(ethylene glycol) surface-active coating on the magnetic and thermal properties of biocompatible magnetic liquids. The data were analyzed using the high-temperature approximation model taking into account polydispersity of a system. Heating ability of the PEG-stabilized magnetic fluids was determined by the calorimetric measurement of specific absorption rate (SAR) at a frequency of 750 kHz and a magnetic field of 0-2 kA/m. MF-Oleate/PEG heating properties were found to be comparable to the ones of MF-Oleate. The PEG shell thus does not seem to effect the thermal characteristics and SAR values and might make the magnetic fluid useful for application in hyperthermia treatment. 相似文献
28.
The article presents the main points of methodology of machine tools subsystem selection for a flexible manufacturing system. In particular, it shows the main algorithm and stages of the methodology which is based on computer database systems, algorithms of elimination and method of multicriteria optimisation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
29.
30.
利用有限单元法,数值分析轴向柱塞泵缝隙高度可变时阀门板上油膜的压力分布.缝隙中油压变化的确定,通常是应用Pasynkow 润滑理论中的Reynolds方程.使用基于有限单元法的自编程序,数值地求解该方程.为了提高结果的精度,基于解的残差估计,应用了加密的自适应网格.给出了依赖于泵的几何条件和工作参数的计算结果. 相似文献