Geometries, Electronic Structures, and Electron Detachment Energies of Small Boron Sulfide Anions: A Density Functional Theory Investigation

A density functional theory investigation on the geometries, electronic structures, and electron detachment energies of BS, BS2, B（BS）2 and B（BS）3 has been performed in this work. The linear ground-state structures of BS （C∞v, ^1∑^＋） and BS2^- （O∞h, ^1∑g^＋） prove to be similar to the previously reported BO and BO2 with systematically lower electron detachment energies. Small boron sulfide clusters are found to favor the formation of -B=S groups which function basically as a-radicals and dominate the ground-state structures of the systems. The perfect linear B（BS）2^-（D∞h, ^3∑g） and beautiful equilateral triangle B（BS）3^- （D3h,^2A1”） turn out to be analogous to the well-known C2v BH2 and O3h BH3, respectively. The electron affinities of BS, BS2, B（BS）2 and B（BS）3 are predicted to be 2.3, 3.69, 3.00 and 3.45 eV, respectively. The electron detachment energies calculated for BS^-, BS2^-, B（BS）2^-, and B（BS）3^- may facilitate future photoelectron spectroscopy measurements to characterize the geometrical and electronic structures of these anions.

Evaluaton model for the geometry complexity of casting based on fuzzy theory

The parameters that describe the complex degree of a certain casting are of some uncertainty. Therefore, a new method based on the fuzzy theory to classify the complex degree of castings has been presented in this paper. The feasibility of fuzzy theory in describing the complex degree of castings has been discussed and the procedure of this method has been specified by analyzing the complex degrees of some typical castings. The element factors that influence the casting complexity, have been summarized, which include the wall-thickness and the number of transition surface, etc. The results show that it is reasonable and practicable to classify the complex degree of castings with the fuzzy theory.

Influence of Wires Properties on Warp-Knitted Loop Geometry in Plane Based on Theory of Elastic Rod

Based on classic theory of elastic rod,the warp-knitted loop geometry in plane is independent of yarn properties,while there is a certain gap between the geometrical model and the actual fabrics.According to this problem,further analysis of loop geometry is done based on the theory of elastic rod with theoretical calculation and experiments.The theoretical analysis found that the distance between the contacted points at the loop root affected the loop geometry,and the distance was affected by the ratio of bending rigidity and the friction between yarns.The experiments,forming simple loop by taking the yarn as an elastic rod,found that the bending rigidity affected the loop geometry.Then the relationships between warp-knitted loop geometry in plane of metallic fabrics and wires properties were studied.The results show that metallic fabrics are more suitable for the theory of elastic rod;the friction and bending rigidity of wire yarns affect the loop geometry in plane.Also,the elongation of yarn affects the loop geometry in the actual warp-knitted fabric.

Gravitational constant in f(R) theories of gravity with non-minimal coupling between matter and geometry

We study the effect of the non-minimal coupling between matter and geometry on the gravitational constant in the context of f(R) theories of gravity on cosmic scales. For a class of f(R) models,the result shows that the value of the gravitational constant not only changes over time but also has the dampened oscillation behavior.Compared with the result of the standard ACDM model, the consequence suggests that the coupling between matter and geometry should be weak.

Modeling and Performance Analysis of UAV-Aided Millimeter Wave Cellular Networks with Stochastic Geometry

UAV-aided cellular networks,millimeter wave(mm-wave) communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G) and even 6G communications.By leveraging the power of stochastic geometry,this paper aims at providing an effective framework for modeling and analyzing a UAV-aided heterogeneous cellular network,where the terrestrial base stations(TBSs) and the UAV base stations(UBSs) coexist,and the UBSs are provided with mm-wave and multi-antenna techniques.By modeling the TBSs as a PPP and the UBSs as a Matern hard-core point process of type Ⅱ(MPH-Ⅱ),approximated but accurate analytical results for the average rate of the typical user of both tiers are derived through an approximation method based on the mean interference-to-signal ratio(MISR) gain.The influence of some relevant parameters is discussed in detail,and some insights into the network deployment and optimization are revealed.Numerical results show that some trade-offs are worthy of being considered,such as the antenna array size,the altitude of the UAVs and the power control factor of the UBSs.

Reciprocal Screw Theory Based Singularity Analysis of a Novel 3-DOF Parallel Manipulator

Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

Density Functional Theory Study of Selectivity of Crown Ethers to Li^+ in Spent Lithium-Ion Batteries Leaching Solutions

It is a challenge to recover lithium from the leaching solution of spent lithium-ion batteries,and crown ethers are potential extractants due to their selectivity to alkali metal ions.The theoretical calculations for the selectivity of crown ethers with different structures to Li ions in aqueous solutions were carried out based on the density functional theory.The calculated results of geometries,binding energies,and thermodynamic parameters show that 15C5 has the strongest selectivity to Li ions in the three crown ethers of 12C4,15C5,and 18C6.B15C5 has a smaller binding energy but more negative free energy than 15C5 when combined with Li^+,leading to that the lithium ions in aqueous solutions will combine with B15C5 rather than 15C5.The exchange reactions between B15C5 and hydrated Li^+,Co^2+,and Ni^2+were analyzed and the results show that B15C5 is more likely to capture Li^+from the hydrated ions in an aqueous solution containing Li^+,Co^2+,and Ni^2+.This study indicates that it is feasible to extract Li ions selectively using B15C5 as an extractant from the leaching solution of spent lithium-ion batteries.

On a Fractal Version of Witten’s M-Theory

Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos

The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.

One-loop renormalizability of noncommutative U(1) gauge theory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propa- gators in noncommutative U（1） gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to 02-order, but for a massive scalar field they are renormalizable only to O-order.

Density functional theory calculations of tetracene on low index surfaces of copper crystal

This paper carries out the density functional theory calculations to study the adsorbate-substrate interaction between tetracene and Cu substrates （Cu （110） and Cu （100） surface）. On each of the surfaces, two kinds of geometry are calculated, namely ＇flat-lying＇ mode and ＇upright standing＇ mode. For ＇flat-lying＇ geometry, the molecule is found to be aligned with its longer molecular axis along close-packed direction of the substrate surfaces. For ＇upright standing＇ geometry, the long axis of tetracene is found to be parallel to the surface normal of the substrate on Cu （110） surface. However, tetracene appears as ＇tilted＇ mode on Cu （100） surface. Structures with ＇flat-lying＇ mode have much larger adsorption energy and charge transfer upon adsorption than that with ＇upright standing＇ mode, indicating the preference of ＇flat-lying＇ geometry on both Cu （110） and Cu （100） surface.

Theoretical Analysis on Geometry Structure and Electronic Structure of LaNi_4Co

The theoretical calculation of LaNi4Co, in which Co substituted for Ni at various sites, was performed by adopting the method of total energy based on the Density Functional Theory. The augmented plane wave function was selected as a basis set in combination with Ultra-soft Pseudopotential technology. The geometry of LaNi5 was optimized and the parameters and properties of the structure were given. The theoretical results accord well with experiments. This method provides a theoretical approach for the structure prediction of such alloy. The calculations of total energy, electronic density of states and Mulliken population of LaNi4Co were carried out. The electronic structure of LaNi4Co and the change of the electronic structure due to the Co-substitution in LaNi5 alloy were analyzed from the calculated results. The stability of the alloy in which Ni was partially substituted by Co at various sites was compared and the factors controlling stability were discussed. The theoretical value of formation heat was calculated.

A note on teleparallel Killing vector fields in Bianchi type Ⅷ and Ⅸ space-times in teleparallel theory of gravitation

In this paper we classify Bianchi type Ⅷ and IX space-times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique. It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5. From the above study we have shown that the Killing vector fields for Bianchi type Ⅷ and Ⅸ space-times in the context of teleparallel theory are different from that in general relativity.

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS (Ⅱ)——PLANE STRESS PROBLEM

Fundamental theory presented in Part (I)[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.

The geometry structures and electronic properties of Li_mB_n(m+n=12) clusters

The geometric structures, electronic properties, total and binding energies, harmonic frequencies, the highest occupied molecular orbital to the lowest unoccupied molecular orbital energy gaps, and the vertical ionization potential energies of small LimBn （m＋ n = 12） clusters were investigated by the density functional theory B3LYP with a 6-31 I＋G （2d, 2p） basis set. All the calculations were performed using the Gaussian09 program. For the study of the LimBn clusters, the global minimum of the B 12 cluster was chosen as the starting point and the boron atoms were gradually replaced by Li atoms. The results showed that as the number of Li atoms increased, the stability of the LimBn cluster decreased and the physical and chemical properties became more active. In addition, on average there was a large charge transfer from the Li atoms to the B atoms.

Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory

The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.

A Novel Design Method for Protein-Like Molecules from the Perspective of Sheaf Theory

Proteins perform a variety of functions in living organisms and their functions are largely determined by their shape. In this paper, we propose a novel mathematical method for designing protein-like molecules of a given shape. In the mathematical model, molecules are represented as loops of n-simplices (2-simplices are triangles and 3-simplices are tetrahedra). We design a new molecule of a given shape by patching together a set of smaller molecules that cover the shape. The covering set of small molecules is defined using a binary relation between sets of molecules. A new molecule is then obtained as a sum of the smaller molecules, where addition of molecules is defined using transformations acting on a set of (n + 1)-dimensional cones. Due to page limitations, only the two-dimensional case (i.e., loops of triangles) is considered. No prior knowledge of Sheaf Theory, Category Theory, or Protein Science is required. The author hopes that this paper will encourage further collaboration between Mathematics and Protein Science.

Unified Field Theory in a Nutshell—Elicit Dreams of a Final Theory Series

The present reading is part of our on-going attempt at the foremost endeavour of physics since man began to comprehend the heavens and the earth. We present a much more improved Unified Field Theory of all the forces of Nature i.e. the gravitational, the electromagnetic, the weak and the strong nuclear forces. The proposed theory is a radical improvement of Professor Hermann Weyl’s supposedly failed attempt at a unified theory of gravitation and electromagnetism. As is the case with Professor Weyl’s theory, unit vectors in the proposed theory vary from one point to the next, albeit, in a manner such that they are—for better or for worse;compelled to yield tensorial affinities. In a separate reading, the Dirac equation is shown to emerge as part of the description of the these variable unit vectors. The nuclear force fields—i.e., electromagnetic, weak and the strong— together with the gravitational force field are seen to be described by a four-vector field Aμ, which forms part of the body of the variable unit vectors and hence the metric of spacetime. The resulting theory very strongly appears to be a logically consistent and coherent unification of classical and quantum physics and at the same time a grand unity of all the forces of Nature. Unlike most unification theories, the present proposal is unique in that it achieves unification on a fourdimensional continuum of spacetime without the need for extra-dimensions.

Complex Riemannian Geometry—Bianchi Identities and Einstein Tensor

Riemannian geometry has proved itself to be a useful model of the gravitational phenomena in the universe, but generalizations of it to include other forces have so far not been successful. Here we explore an extension of Riemannian geometry using a complex Hermitian metric tensor. We find that the standard electromagnetic field naturally appears along with two additional fields, which act as mass and charge sources. A first paper set up the basic geometry and derived the Christoffel symbols plus the E&M field equation. This paper continues development with the generalized Riemann curvature tensor, Bianchi identities and the Einstein tensor, laying the basis for field equations. A final paper will then present the field equations.