Effect of dimensional expansion on carrier transport behaviors of the hexagonal Bi-based perovskite crystals

All-inorganic Cs_(3)Bi_(2)I_(9)(CBI)halide perovskites are sought to be candidate for photoelectrical materials because of their low toxicity and satisfactory stability.Unfortunately,the discrete molecular[Bi2I9]3−clusters limit the charge-transport behaviors.Herein,the defect halide perovskite based on trivalent Bi^(3+)is expanded to Cs_(3)Bi_(2)I_(6)Br_(3)(CBIB).Centimeter-size CBIB single crystal(Φ15×70 mm^(3))was grown by the vertical Bridgeman method.The powder X-ray diffraction analysis shows that CBIB has structure with lattice parameters of a=b=8.223Å,c=10.024Å,α=β=90°andγ=120°.The density functional theory(DFT)calculations demonstrate that the charge density distribution was enhanced after the dimensional expansion.The enhancement of carrier transport ability of(00l)in-plane is characterized before and after dimensional improvement.The obtained CBIB(001)exhibited an electron mobility up to 40.03 cm^(2)V^(−1)s^(−1)by time-of-flight(TOF)technique,higher than 26.46 cm^(2)V^(−1)s^(−1)of CBI(001).Furthermore,the X-ray sensitivity increases from 707.81μC Gy^(−1)cm^(−2)for CBI(001)to 3194.59μC Gy−1 cm^(−2)for CBIB(001).This research will deepen our understanding of Bi-based perovskite materials and afford more promising strategies for lead-free perovskite optoelectronic devices modification.

Thermal expansion and dimensional stability of unidirectional and orthogonal fabric M40/AZ91D composites

Unidirectional (60%, volume fraction) and orthogonal (50%, volume fraction) M40 graphite fibre reinforced AZ91D magnesium alloy matrix composites were fabricated by pressure infiltration method. The coefficients of thermal expansion (in the temperature range of 20-350 ℃) and dimensional stability (in the temperature range of 20-150 ℃) of the composites and the corresponding AZ91D magnesium alloy matrix were measured. The results show that coefficients of thermal expansion of the composites in longitudinal direction decrease with elevating temperature. The coefficients of thermal expansion (CTE) for unidirectional M40/AZ91D composites and orthogonal M40/AZ91D composites are 1.24×10-6 ℃-1 and 5.71×10-6 ℃-1 at 20 ℃, and 0.85×10-6 ℃-1 and 2.75×10-6 ℃-1 at 350 ℃, respectively, much lower than those of the AZ91D alloy matrix. Thermal cycling testing demonstrates that the thermal stress plays an important role on residual deformation. Thus, a better dimensional stability is obtained for the AZ91D magnesium alloy matrix composites. More extreme strain hysteresis and residual plastic deformation are observed in orthogonally fabric M40 reinforced AZ91D composite, but its net residual strain after each cycle is similar to that of the unidirectional M40/AZ91D composite.

Nonlocal symmetries,consistent Riccati expansion integrability,and their applications of the (2+1)-dimensional Broer–Kaup–Kupershmidt system

For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion

An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.

Analytical Treatment of the Evolutionary (1 + 1)-Dimensional Combined KdV-mKdV Equation via the Novel (G'/G)-Expansion Method

The novel (G'/G)-expansion method is a powerful and simple technique for finding exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we study explicit exact traveling wave solutions for the (1 + 1)-dimensional combined KdV-mKdV equation by using the novel (G'/G)-expansion method. Consequently, various traveling wave solutions patterns including solitary wave solutions, periodic solutions, and kinks are detected and exhibited.

Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation

This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

Exact Traveling Wave Solutions for the (1 + 1)-Dimensional Compound KdVB Equation via the Novel (G'/G)-Expansion Method

In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are derived, in terms of hyperbolic, trigonometric and rational functions, involving various parameters. When the parameters are tuned to special values, both solitary, and periodic wave models are distinguished. State of the art symbolic algebra graphical representations and dynamical interpretations of the obtained solutions physics are provided and discussed. This in turn ends up revealing salient solutions features and demonstrating the used method efficiency.

Design new chaotic maps based on dimension expansion

Based on the high-dimensional(HD) chaotic maps and the sine function, a new methodology of designing new chaotic maps using dimension expansion is proposed. This method accepts N dimensions of any existing HD chaotic map as inputs to generate new dimensions based on the combined results of those inputs. The main principle of the proposed method is to combine the results of the input dimensions, and then performs a sine-transformation on them to generate new dimensions.The characteristics of the generated dimensions are totally different compared to the input dimensions. Thus, both of the generated dimensions and the input dimensions are used to create a new HD chaotic map. An example is illustrated using one of the existing HD chaotic maps. Results show that the generated dimensions have better chaotic performance and higher complexity compared to the input dimensions. Results also show that, in the most cases, the generated dimensions can obtain robust chaos which makes them attractive to usage in a different practical application.

HAUSDORFF DIMENSION OF SOME KIND OF ALTERNATING OPPENHEIM SERIES EXPANSION

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.

Four-Dimensional Mathematics Creates the Super Universe

In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π3R3 in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π3R4. The volume of the Universe has been calculated π3R3 = 62 × 1030 ly3. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study.

The symplectic eigenfunction expansion theorem and its application to the plate bending equation

This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner.

Urban Spatial Expansion Characteristics in China’s Rapid Urbanization Region—A Case Study of SXC Region

Urban spatial expansion characteristics are the responses of urbanization acts on the geographical space. Analyzing the characteristics can reveal the process of urban expansion and mechanism which is one of useful methods to find out the sustainable land use strategy balancing development and protection. In this paper, two main methods have been deployed in analyzing the spatial expansion characteristics of rapid urbanization region. One is the expansion index method and the other is fractal dimension method. And the results show that town-level urban sprawl has increased in a non-linear way since 1985, and even the increments of the urban expansion intensity are fluctuated. Morphology transformation from scatter to concentration is common phenomenon in the process of urbanization in the towns. From the morphology point of view, downtowns are more homogenous than towns with less variation. The concentration is the leading development trend in downtowns. And the more distance from the downtown is, the more spatial pattern morphology will be observed. These characteristics indicate that macro-scale policies of economic development and land use management have great impacts on the formation and characteristics of spatial patterns of urban dynamic patterns.

ON POINTS CONTAIN ARITHMETIC PROGRESSIONS IN THEIR LROTH EXPANSION

For any x ∈ （0, 1] （except at most countably many points）, there exists a unique sequence {dn（x）}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1（x）（d1（x）-1）……dj-1（x）（dj-1（x）-1）dj（x）. The dexter infinite series expansion is called the Liiroth expansion of x. This paper is con- cerned with the size of the set of points x whose digit sequence in its Liiroth expansion is strictly increasing and contains arbitrarily long arithmetic progressions with arbitrary com- mon difference. More precisely, we determine the Hausdorff dimension of the above set.

ON AN EXTENSION OF ABEL-GONTSCHAROFF'S EXPANSION FORMULA

We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.

Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity

We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The first theory used is based on G ‘t Hooft’s remarkably simple renormalization procedure in which a neat mathematical maneuver is introduced via the dimensionality of our four dimensional spacetime. Thus, ‘t Hooft used instead of D = 4 and then took at the end of an intricate and subtle computation the limit to obtain the result while avoiding various problems including the pole singularity at D = 4. Here and in contradistinction to the classical form of dimensional and renormalization we set and do not take the limit where and is the theoretically and experimentally well established Hardy’s generic quantum entanglement. At the end we see that the dark energy density is simply the ratio of and the smooth disentangled D = 4, i.e. (dark) = (4 -k)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure details by rounding 21 + k to 21 and 22 + k to 22 in a manner not that much different from of the original form of dimensional regularization theory. The result is subsequently validated by another equally ingenious approach due mainly to E. Witten and his school of topological quantum field theory. We notice that in that theory the local degrees of freedom are zero. Therefore, we are dealing essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.

Spatial Characteristics Analysis of Urban Expansion in Luoyang, China

The characteristics of urban space expansion reflect the changes of urban spatial layout and structure, as well as the orientation of urban development in the future. This paper uses the regional sector division method to divide the urban land into 8 orientations, based on the urban land space compaction index, and designs a sector partition compaction index. Based on the remote sensing image data of 1990, 2000, 2010, and 2020, the spatial characteristics of urban land expansion of Luoyang are analyzed by using the partition compaction index, expansion intensity index, fractal dimension, and standard deviation ellipse. The results show that: from 1990 to 2020, the urban overall planning of Luoyang has effectively guided the urban development, the urban land expands rapidly, the urban land compaction has been maintained at a low level, and the urban form has been tending to be reasonable;the urban land centroid gradually shifts to the southwest, and the distribution axis rotates clockwise from southwest-northeast to northwest-southeast, and the directionality of distribution gradually disappears;the urban land has gone through the development process of land filling-enlarging-refilling. The urban land expansion is relatively active in the region with an azimuth of 90°- 225°, and the urban expansion in the north of Luo River is relatively stable and is always filling mode.

THE CONSTITUTIVE RELATION OF CRACK-WEAKENED ROCK MASSES UNDER AXIAL-DIMENSIONAL UNLOADING

An accurate and efficient numerical method for solving the crack-crack interaction problem is presented. The method is mainly by means of the dislocation model, stress superposition principle and Chebyshev polynomial expansion of the pseudo-traction. This method can be applied to compute the stress intensity factors of multiple kinked cracks and multiple rows of periodic cracks as well as the overall strains of rock masses containing multiple kinked cracks under complex loads. Many complex computational examples are given. The dependence of the crack-crack interaction on the crack configuration, the geometrical and physical parameters, and loads pattern, is investigated. By comparison with numerical results under confining pressure unloading, it is shown that the crack-crack interaction under axial-dimensional unloading is weaker than those under confining pressure unloading. Numerical results for single faults and crossed faults show that the single faults are more unstable than the crossed faults. It is found from numerical results for different crack lengths and different crack spacing that the interaction among kinked cracks decreases with an increase in length of the kinked cracks and the crack spacing under axial-dimensional unloading.

Nonlocal symmetry and exact solutions of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation

In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the（2＋1）-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the（2＋1）-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion（CRE） solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions.

The exact solutions to (2+1)-dimensional nonlinear Schrdinger equation

By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.