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121.
S is a local maximum stable set of a graph G, and we write S∈Ψ(G), if the set S is a maximum stable set of the subgraph induced by S∪N(S), where N(S) is the neighborhood of S. In Levit and Mandrescu (2002) [5] we have proved that Ψ(G) is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in Levit and Mandrescu (2003) [6] and Levit and Mandrescu (2007) [7] respectively.In this paper we give necessary and sufficient conditions for Ψ(G) to form a greedoid, where G is:
- (a)
- the disjoint union of a family of graphs;
- (b)
- the Zykov sum of a family of graphs;
- (c)
- the corona X°{H1,H2,…,Hn} obtained by joining each vertex x of a graph X to all the vertices of a graph Hx.
122.
Vadim Azhmyakov Vladimir Boltyanski 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):1110-1119
The aim of this paper is to extend the dynamic programming (DP) approach to multi-model optimal control problems (OCPs). We deal with robust optimization of multi-model control systems and are particularly interested in the Hamilton-Jacobi-Bellman (HJB) equation for the above class of problems. In this paper, we study a variant of the HJB for multi-model OCPs and examine the natural relationship between the Bellman DP techniques and the Robust Maximum Principle (MP). Moreover, we describe how to carry out the practical calculations in the context of multi-model LQ-problems and derive the associated Riccati-type equation. 相似文献
123.
124.
125.
Dmitry Zhdanov Alexey Garbul Vadim Mayorov Vadim Sokolov Igor Potemin Takashi Hyodo Alexey Voloboy Vladimir Galaktionov 《Optical Review》2013,20(2):155-159
The approach for autodesign of optical characteristics of different illumination units such as backlight systems, led arrays and light boxes is considered. Suggested software solution allows finding optimal configuration of lighting scheme for providing necessary distribution of output light. Additional preprocessing phase is introduced in design process, which provides reduction of design iterations and better convergence compared to conventional design methods, utilizing random fluctuations of design parameter between iterations. The results of several designs of different kinds of illumination systems are presented. 相似文献
126.
Oleg P. Korobeinichev Alexander A. Paletsky Tatyana A. Bolshova Vadim D. Knyazev 《Combustion Theory and Modelling》2013,17(5):927-939
The phenomenon of superadiabatic flame temperature (SAFT) was discovered and investigated in a low-pressure HN3/N2 flame using numerical modelling. A previously developed mechanism of chemical reactions in the HN3/N2 flame at the pressure 50 Torr and the initial temperature T0 = 296 K was revised. Rate constants of several important reactions involving HN3 (HN3 (+N2) = N2 + NH (+N2), R1; HN3 (+HN3) = N2 + NH (+HN3), R2; HN3 + H = N2 + NH2, R4; HN3 + N = N2 + NNH, R5; and HN3 + NH2 = NH3 + N3, R7) were calculated using quantum chemistry and reaction rate theories. Modified Arrhenius expressions for these reactions are provided for the 300–3500 K temperature range. Modelling of the flame structure and flame propagation velocity of the HN3/N2 flame at p = 50 Torr and T0 = 296 K was performed using the revised mechanism. The results demonstrate the presence of the SAFT phenomenon in the HN3/N2 flame. Analysis of the flame structure and the kinetic mechanism indicates that the cause of SAFT is in the kinetic mechanism: exothermic reactions of radicals with hydrogen atoms occur in the post flame zone, which results in the formation of super equilibrium H2 concentrations. The flame propagation velocity is largely determined by the second-order HN3 decomposition reaction and not by the reaction of HN3 with H, as was previously assumed. Calculation of the flame propagation velocity according to the Zeldovich-Frank-Kamenetsky theory with the decomposition reaction as a limiting stage yielded a value that agrees with that obtained in numerical modelling using the complete reaction mechanism. 相似文献
127.
Seppo Hassi Mark Malamud Vadim Mogilevskii 《Integral Equations and Operator Theory》2013,77(4):449-487
Let A be a densely defined simple symmetric operator in ${\mathfrak{H}}$ , let ${\Pi=\{\mathcal{H},\Gamma_0, \Gamma_1}\}$ be a boundary triplet for A * and let M(·) be the corresponding Weyl function. It is known that the Weyl function M(·) determines the boundary triplet Π, in particular, the pair {A, A 0}, uniquely up to the unitary similarity. Here ${A_0 := A^* \upharpoonright \text{ker}\, \Gamma_0 ( = A^*_0)}$ . At the same time the Weyl function corresponding to a boundary triplet for a dual pair of operators defines it uniquely only up to the weak similarity. We consider a symmetric dual pair {A, A} with symmetric ${A \subset A^*}$ and a special boundary triplet ${\widetilde{\Pi}}$ for{A, A} such that the corresponding Weyl function is ${\widetilde{M}(z) = K^*(B-M(z))^{-1} K}$ , where B is a non-self-adjoint bounded operator in ${\mathcal{H}}$ . We are interested in the problem whether the result on the unitary similarity remains valid for ${\widetilde{M}(\cdot)}$ in place of M(·). We indicate some sufficient conditions in terms of the operators A 0 and ${A_B= A^* \upharpoonright \text{ker}\, (\Gamma_1-B \Gamma_0)}$ , which guaranty an affirmative answer to this problem. Applying the abstract results to the minimal symmetric 2nth order ordinary differential operator A in ${L^2(\mathbb{R}_+)}$ , we show that ${\widetilde{M}(\cdot)}$ defined in ${\Omega_+ \subset \mathbb{C}_+}$ determines the Dirichlet and Neumann realizations uniquely up to the unitary equivalence. At the same time similar result for realizations of Dirac operator fails. We obtain also some negative abstract results demonstrating that in general the Weyl function ${\widetilde{M}(\cdot)}$ does not determine A B even up to the similarity. 相似文献
128.
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller Markov process. The dynamical correlation functions of the limit process are determinantal with an explicit correlation kernel. The key idea is to identify random point processes on ${\mathbb Z}$ with q-Gibbs measures on Gelfand–Tsetlin schemes and construct Markov processes on the latter space. Independently, we analyze the large time behavior of PushASEP with finitely many particles and particle-dependent jump rates (it arises as a marginal of our dynamics on Gelfand–Tsetlin schemes). The asymptotics is given by a product of a marginal of the GUE-minor process and geometric distributions. 相似文献
129.
Parallel MRI at microtesla fields 总被引:2,自引:2,他引:0
Zotev VS Volegov PL Matlashov AN Espy MA Mosher JC Kraus RH 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2008,192(2):197-208
Parallel imaging techniques have been widely used in high-field magnetic resonance imaging (MRI). Multiple receiver coils have been shown to improve image quality and allow accelerated image acquisition. Magnetic resonance imaging at ultra-low fields (ULF MRI) is a new imaging approach that uses SQUID (superconducting quantum interference device) sensors to measure the spatially encoded precession of pre-polarized nuclear spin populations at microtesla-range measurement fields. In this work, parallel imaging at microtesla fields is systematically studied for the first time. A seven-channel SQUID system, designed for both ULF MRI and magnetoencephalography (MEG), is used to acquire 3D images of a human hand, as well as 2D images of a large water phantom. The imaging is performed at 46 mu T measurement field with pre-polarization at 40 mT. It is shown how the use of seven channels increases imaging field of view and improves signal-to-noise ratio for the hand images. A simple procedure for approximate correction of concomitant gradient artifacts is described. Noise propagation is analyzed experimentally, and the main source of correlated noise is identified. Accelerated imaging based on one-dimensional undersampling and 1D SENSE (sensitivity encoding) image reconstruction is studied in the case of the 2D phantom. Actual threefold imaging acceleration in comparison to single-average fully encoded Fourier imaging is demonstrated. These results show that parallel imaging methods are efficient in ULF MRI, and that imaging performance of SQUID-based instruments improves substantially as the number of channels is increased. 相似文献
130.
Zotev VS Matlashov AN Volegov PL Savukov IM Espy MA Mosher JC Gomez JJ Kraus RH 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2008,194(1):115-120
One of the challenges in functional brain imaging is integration of complementary imaging modalities, such as magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI). MEG, which uses highly sensitive superconducting quantum interference devices (SQUIDs) to directly measure magnetic fields of neuronal currents, cannot be combined with conventional high-field MRI in a single instrument. Indirect matching of MEG and MRI data leads to significant co-registration errors. A recently proposed imaging method--SQUID-based microtesla MRI--can be naturally combined with MEG in the same system to directly provide structural maps for MEG-localized sources. It enables easy and accurate integration of MEG and MRI/fMRI, because microtesla MR images can be precisely matched to structural images provided by high-field MRI and other techniques. Here we report the first images of the human brain by microtesla MRI, together with auditory MEG (functional) data, recorded using the same seven-channel SQUID system during the same imaging session. The images were acquired at 46 microT measurement field with pre-polarization at 30 mT. We also estimated transverse relaxation times for different tissues at microtesla fields. Our results demonstrate feasibility and potential of human brain imaging by microtesla MRI. They also show that two new types of imaging equipment--low-cost systems for anatomical MRI of the human brain at microtesla fields, and more advanced instruments for combined functional (MEG) and structural (microtesla MRI) brain imaging--are practical. 相似文献