Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular among approaches manipulating constructible sets. In this paper, an arbitrary finite set F ⊂ [y1,...,yn] we apply comprehensive in order to obtain F-invariant cylindrical n-dimensional complex space, from which extract real space. We report on implementation new approach constructing decompositions.

The structures and properties of rhenium nitrides are studied with density function based first principle method. New candidate ground states or high-pressure phases at Re:N ratios 3:2, 1:3 1:4 identified via a series evolutionary structure searches. We find that the 3D polyhedral stacking strong covalent N-N Re-N bonding could stabilize Re to form nitrogen rich phases, meanwhile, remarkably improve mechanical performance than sub-nitrides, as Re3N, Re2N Re3N2. By evaluating trends crystal...

To investigate the impact of maternal microbiota during lactation in different beef cattle breeds on their own immune levels, milk quality, and growth development offspring, this study measured parameters, intestinal diversity, quality Pingliang red Simmental cattle, performed a correlation analysis with offspring. Our showed that lactation, had significantly higher IL-6 levels than while latter exhibited factors such as IgG, IgA, IgM, IL-1β, TNFα. The lactating cows found were rich...

In this paper we introduce the two compounds $\ensuremath{\alpha}{\text{-C}}_{3}{\text{N}}_{2}$ and $\ensuremath{\beta}{\text{-C}}_{3}{\text{N}}_{2}$ with cubic symmetry, which are derived from a simple carbon $({\text{C}}_{20})$ reported recently. Our first-principles calculations show that both solids highly incompressible high bulk modulus (380 343 GPa), large shear $G$ (365 368 great elastic constant ${C}_{44}$ (327 329 Vickers hardness ${H}_{V}$ (both 86 respectively. Accordingly come...

In this paper, we suggest a novel potential superhard material, new carbon nitride phase consisted of sp3 hybridized bonds, possessing cubic P213 symmetry (8 atoms/cell, labeled by cg-CN) which is similar to gauche nitrogen (cg-N) first-principles calculations. It metallic compound, while most other materials are insulators or semiconductors. The Vickers hardness cg-CN 82.56 GPa, and if considered the negative effect component on hardness, it 54.7 much harder than any materials. found that...

Ab initio calculations are performed to probe the hydrogen bonding, structural, and superconducting behaviors of HBr HCl under high pressure. The calculated results show that bond symmetrization (Cmc21→Cmcm transition) occurs at 25 40 GPa, respectively, which can be attributed symmetry stretching A1 mode softening. After symmetrization, a pressure-induced soft transverse acoustic phonon Cmcm phase is identified unique metallic with monoclinic structure P21/m (4 molecules/cell) for both...

Abstract Recently quantum nonlocality has been classified into three distinct types: entanglement, Einstein-Podolsky-Rosen steering, and Bell’s nonlocality. Among which, is the strongest type. for states usually detected by violation of some inequalities, such as Clause-Horne-Shimony-Holt inequality two qubits. Steering a manifestation intermediate between entanglement This peculiar feature led to curious phenomenon, one-way steering. The steering was an important open question presented in...

Quantum steering is an important nonclassical resource for quantum information processing. However, even though lots of criteria exist, it still very difficult to efficiently determine whether arbitrary two-qubit state shared by Alice and Bob steerable or not, because the optimal measurement directions are unknown. In this work, we provide efficient detection scheme with help machine learning, where only need measure in a few fixed directions. order prove validity method, first realize...

Regular chains and triangular decompositions are fundamental well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations these focusing on real analogue: semi-algebraic

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a weakened notion GCD modulo regular chain, which permits greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also key feature algorithms. In experimental results implementation algorithms, realized with RegularChains library in MAPLE, outperforms solvers specifications...

The MgxZn(1-x)O alloy system may provide an optically tunable family of wide band gap materials that can be used in various UV luminescences, absorption, lighting, and display applications. A systematic investigation the MgO-ZnO using ab initio evolutionary simulations shows alloys exist ordered ground-state structures at pressures above about 6.5 GPa. Detailed enthalpy calculations for most stable allowed us to construct pressure-composition phase diagram. In entire composition, no...

Entanglement, quantum steering and nonlocality are distinct correlations which the resources behind various of information computation applications. However, a central question determining precise quantitative relation among them is still unresolved. Here, we present mapping criterion between Bell in bipartite qudit-qubit system, as well entanglement qubit-qudit starting from fundamental concepts correlations. Precise criteria derived analytically. Such independent form state. In particular,...

A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular chains is presented. The main idea to refine a complex tree until the signs of polynomials appearing in are sufficient distinguish true and false cells. We report an implementation our RegularChains library Maple illustrate its effectiveness examples.

In this paper, the theory of regular chains and a triangular decomposition method relying on modular computations are presented in order to symbolically solve multivariate polynomial systems. Based focus values for dynamic systems obtained by using normal form theory, is applied compute limit cycles bifurcating from Hopf critical points. particular, quadratic planar system used demonstrate solving process show how obtain center conditions. The based cubic computation efficiency method, all...

This article is a continuation of our earlier work [3], which introduced triangular decompositions semi-algebraic systems and algorithms for computing them. Our new contributions include theoretical results based on we obtain practical improvements these decomposition algorithms.

High-pressure structures of MH2 (M = V, Nb) are explored through ab initio evolutionary methodology. As the same main group metal hydrides, VH2 and NbH2 adopt tetragonal structure with space Fm-3m at low pressures. However, high pressures possess Pnma P63mc phases differently. The two phase transitions both first order transition identified by volume collapses. Our calculations suggest that high-pressure have dynamical mechanical stability up to 100 GPa. metallic demonstrated band density...

The novel superconducting C2/m phases of HCl and HBr were predicted using the developed particle swarm optimization algorithm for crystal structure prediction. calculated results showed that phase transition from P-1 to occurred at 250 120 GPa HBr, respectively. Hydrogen bond symmetrization was observed in newly phase. No imaginary phonon frequencies whole Brillouin zone indicated dynamically stable. In addition, most stable structure, which rejected earlier hypotheses elemental...