Complicated Local Structure Research Articles

Extreme values of the Fiedler vector on trees

Let G be a tree on n vertices and let L=D−A denote the Laplacian matrix on G. The second-smallest eigenvalue λ2(G)>0, also known as the algebraic connectivity, as well as the associated eigenvector have been of substantial interest. We investigate the question of when the maxima and minima of an associated eigenvector are assumed at the endpoints of the longest path in G. Our results also apply to more general graphs that ‘behave globally’ like a tree but can exhibit more complicated local structure. The crucial new ingredient is a reproducing formula for eigenvectors of graphs.

Boron structure evolution in magnetic Cr2O3 thin films

B substituting O in antiferromagnetic Cr2O3 is known to increase the Néel temperature, whereas the actual B dopant site and the corresponding functionality remains unclear due to the complicated local structure. Herein, A combination of electron energy loss spectroscopy and first-principles calculations were used to unveil B local structures in B doped Cr2O3 thin films. B was found to form either magnetic active BCr4 tetrahedra or various inactive BO3 triangles in the Cr2O3 lattice, with σ∗ and π∗ bonds exhibiting unique spectral features. Identification of BO3 triangles was achieved by changing the electron momentum transfer to manipulate the differential cross section for the 1s-π* and 1s-σ* transitions. Modeling the experimental spectra as a linear combination of simulated B K edges reproduces the experimental π* / σ* ratios for 15–42% of the B occupying the active BCr4 structure. This result is further supported by first-principles based thermodynamic calculations.

Raman spectra of MCl-Ga2S3-GeS2(M = Na, K, Rb) glasses

AbstractRaman spectra of (MY)x(Ga2S3)0.2−0.2x(GeS2)0.8−0.8xpseudo-ternary glassy systems (M = Na, K, Rb; Y = Cl, Br, I) were investigated systematically as a function of MY nature and alkali content. Raman spectroscopy of the Ga3S3-GeS2glassy matrix shows a complicated local structure: corner-sharing CS- and edge-sharing ES-GeS4/2tetrahedra, Ga-S triclusters and ETH-Ga2S6/2ethane-like units. The Ga2S6/2population decreases with increasingxrelated to a substitution of some bridging sulfur atoms around central Ga by terminal Y species with a respective decrease of the network rigidity. The formation of mixed Ga-(S,Y) environment is affected by the M+ion size and the MY concentration.

Topology Optimization Design of a 914 Mechanical Tee Based on SIMP

A topology optimization design was created forthe key parts of the mechanical tee to find a solution to the challenge posed by its substantial weight and complicated local structure. In this paper, a SIMP algorithm is used as the theoretical basis for the topology optimization, and the numerical simulation was performed by Matlab. Furthermore, it was concluded that the filter radius and density penalty factor were the crucial criteria that affected the optimization result, allowing the relevant parameters of the optimization software to be adjusted. The topological optimization software was used to optimize the upper and lower shells of the mechanical tee, while the weight of the tee was reduced by about 20% without reduce in strength.

On One Application of Infinite Systems of Functional Equations in Function Theory

Abstract The paper presents the investigation of applications of infinite systems of functional equations for modeling functions with complicated local structure that are defined in terms of the nega-˜Q-representation. The infinite systems of functional equations f ( φ ˆ k ( x ) ) = β ˜ i k + 1 , k + 1 + p ˜ i k + 1 , k + 1 f ( φ ˆ k + 1 ( x ) ) , f\left( {{{\hat \varphi }^k}(x)} \right) = \tilde \beta {i_{k + 1}},k + 1 + \tilde p{i_{k + 1}},k + 1f\left( {{{\hat \varphi }^{k + 1}}(x)} \right), where x = Δ i 1 ( x ) i 2 ( x ) … i n ( x ) … - Q ˜ x = \Delta _{{i_1}(x){i_2}(x) \ldots {i_n}(x) \ldots }^{ - \tilde Q} , and φ ̑ is the shift operator of the Q̃-expansion, are investigated. It is proved that the system has a unique solution in the class of determined and bounded on [0, 1] functions. Its analytical presentation is founded. The continuity of the solution is studied. Conditions of its monotonicity and nonmonotonicity, differential, and integral properties are studied. Conditions under which the solution of the system of functional equations is a distribution function of the random variable η = Δ ξ 1 ξ 2 … ξ n … Q ˜ \eta = \Delta _{{\xi _1}\,\xi 2 \ldots {\xi _n} \ldots }^{\tilde Q} with independent Q̃-symbols are founded.

Continuous Functions with Complicated Local Structure Defined in Terms of Alternating Cantor Series Representation of Numbers

Continuous Functions with Complicated Local Structure Defined in Terms of Alternating Cantor Series Representation of Numbers

Crystalline Grain Interior Configuration and Lithium Migration Kinetics in Li-Rich Layered Oxide

The lithium-rich layered oxide materials xLi2MnO3·(1-x)LiTMO2 (LLOs) are considered as the most promising cathode materials for next-generation LIBs and have been developing energetically recently.1-3However, there are many issues still unclear (the structure and reaction mechanism are ambiguous until now), and numerous scientific challenges (low initial coulombic efficiency, poor rate capability and voltage degradation during cycling) of these materials that must be overcome to realize their utilization in commercial lithium-ion batteries. The electrochemical performance of electrode materials is largely controlled by the pathways of charge carriers in and out of a crystal and their kinetic barriers, which are determined by their crystal/electronic structures in their pristine states and the structure evolution that accompanies variation of the lithium concentration. Multiple studies of LLOs have been performed, especially to clarify the kinetics-controlled reaction processes associated with Li+ extraction/insertion behavior from/into the crystalline grains under different voltage ranges. Both electrochemical and kinetics studies have revealed that the Li+ diffusion behavior in LLOs is clearly divided into several processes, thereby indicating possible inhomogeneous crystalline structures4-6. Further studies that used in-situ X-ray absorption spectroscopy (XAS) have indicated that an Li2MnO3-like structure distributed in LLOs is a key factor that affects the rate capability5. However, researchers do not yet understand the cause of the poor electrode kinetics of LLOs, which is challenging primarily because of their pristine structural complexities. Several studies that have investigated the structure of LLOs have been conducted7 , 8. Delmas and Tarascon have revealed that the complicated local structure of LLOs can be attributed to rotation of the LiMn2-like layer in the Li2MnO3-like structure 9 , 10, which has also been demonstrated in our work8. Furthermore, we have identified the coexistence of two structures (rhombohedral LiTMO2 structure with space group and monoclinic Li2MnO3–like structure with C2/m space group) on the grain edge using advanced microscopy technology 8, which has been well validated by refining the synchrotron X-ray diffraction (SXRD) patterns 3. However, the interior configuration of LLO materials, including direct observation of the Li2MnO3-like structure distribution in crystalline grain, structure- or composition-coordination environments, and the relationship with the Li+ migration behavior are still unclear, thus preventing further in-depth understanding of their electrode kinetics, structure evolution, cycle stability and reaction mechanisms. Undoubtedly, it is imperative to gain a clear understanding of the Li2MnO3-like structure of a crystalline grain because it is the basis for understanding these compounds and improving their electrochemical performance. In this conference, based on cross-sectional thin transmission-electron-microscopy (TEM) specimens (CSTTs) ‘anatomized’ from Li1.2Mn0.567Ni0.166Co0.067O2 powders, the atomic-scale Li2MnO3-like structure distribution within multiple monocrystal-like domains and domain boundaries (DBs) in a single crystalline grain was revealed using a variety of microscopy techniques and computer simulations. The Li+ migration in the Li2MnO3-like structure along different directions with or without DBs and the effect of implantation of element segregation were thoroughly investigated using density functional theory (DFT).

Effect of wet jet milling of carbon nanotube on electrical properties of polymer nanocomposites

Wet-type jet milling (WJM) was used as a pre-treatment procedure for carbon nanotube (CNT) which was utilized as electrical conductive filler for polymer nanocomposites. Nanocomposites were prepared by dispersing WJM treated CNT (WJM-CNT) or as-received CNT (AR-CNT) in isotactic polypropylene matrix, and the effect of WJM pre-treatment on nanocomposite properties was investigated. Dispersion structure of CNT was observed by SEM and electrical property was studied by impedance spectroscopy. DC conductivities (σDC) showed different CNT concentration dependences, which were characterized by the percolation critical exponents. At 0.5 wt% of CNT, σDC increased two-fold by using WJM-CNT. Analysis of imaginary part of impedance spectra and complex dielectric permittivity suggested the WJM-CNT nanocomposites had much complicated local structure as compared to the AR-CNT counterparts. These electrical properties were discussed in relation to the dispersion structure of CNT.

Rosenthal operator spaces

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an Lp-space, then it is either an Lp-space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non- Hilbertian complemented operator subspaces of non-commutative Lp-spaces and show that this class is much richer than in the commutative case. We investigate the local properties of some new classes of operator spaces for every 2 < p < 1 which can be considered as operator space analogues of the Rosenthal sequence spaces from Banach space theory, constructed in 1970. Under the usual conditions on the defining sequence we prove that most of these spaces are operator Lp-spaces, not completely isomorphic to previously known such spaces. However, it turns out that some column and row versions of our spaces are not operator Lp-spaces and have a rather complicated local structure which implies that the Lindenstrauss-Rosenthal alternative does not carry over to the non-commutative case.

Discrete quasiperiodic sets with predefined covering cluster

Some of the most remarkable tilings and discrete quasiperiodic sets used in quasicrystal physics can be obtained by using strip projection method in a superspace of dimension four, five or six, and the projection of a unit hypercube as a window of selection. We present some mathematical results which allow one to use this very elegant method in superspaces of dimension much higher, and to generate discrete quasiperiodic sets with a more complicated local structure by starting from the corresponding covering cluster. Hundreds of points of these sets can be obtained in only a few minutes by using our computer programs.

Fractal probability distributions and transformations preserving the HausdorffBesicovitch dimension

This article is devoted to the development of a general theory of transformations of and [0, 1]. A class of distribution functions of random variables with independent s-adic digits is studied in detail. It is proved that any absolutely continuous function from the previously mentioned class is a DP function, despite the fact that it may have a very complicated local structure. Necessary, respectively, sufficient conditions for dimension preservation are also given for singular functions. Relations between the entropy of transformations and their DP properties are investigated.Examples and counterexamples are provided,and some applications are discussed.

Radio Measurements of Coronal Magnetic Fields

AbstractA review of methods of measuring magnetic fields in the solar corona using spectral-polarization observations at microwaves with high spatial resolution is presented. The methods are based on the theory of thermal bremsstrahlung, thermal cyclotron emission, propagation of radio waves in quasi-transverse magnetic field and Faraday rotation of the plane of polarization. The most explicit program of measurements of magnetic fields in the atmosphere of solar active regions has been carried out using radio observations performed on the large reflector radio telescope of the Russian Academy of Sciences — RATAN-600. This proved possible due to good wavelength coverage, multichannel spectrographs observations and high sensitivity to polarization of the instrument. Besides direct measurements of the strength of the magnetic fields in some cases the peculiar parameters of radio sources, such as very steep spectra and high brightness temperatures provide some information on a very complicated local structure of the coronal magnetic field. Of special interest are the results found from combined RATAN-600 and large antennas of aperture synthesis (VLA and WSRT), the latter giving more detailed information on twodimensional structure of radio sources. The bulk of the data obtained allows us to investigate themagnetospheresof the solar active regions as the space in the solar corona where the structures and physical processes are controlled both by the photospheric/underphotospheric currents and surrounding “quiet” corona.