Narrow Results

In this paper, we generalize virtual knot theory to multi-virtual knot theory where there are a multiplicity of virtual crossings. Each virtual crossing type can detour over the other virtual crossing types, and over classical or immersed crossings. New invariants of multi-virtual knots and links are introduced and new problems that arise are described. We show how the extensions of the Penrose coloring evaluation for trivalent plane graphs and our generalizations of this to non-planar graphs and arbitrary numbers of colors acts as a motivation for the construction of the multi-virtual theory.

In the Cold Dark Matter (hereafter CDM) scenario even isolated density peaks contain a high fraction of small scale clumps having velocities larger than the average escape velocity from the structure. These clumps populate protoclusters, especially in the peripheral regions, r≥R_f (where R_f is the filtering scale). During the cluster collapse and the subsequent secondary infall, collapsing or infalling clumps (having v<v_esc) interact with the quoted unboundclumps (or high speed clumps, as we also call them) having v>v_esc. We study the interaction between these two kinds of clumps by means of the impulse approximation¹ and we find that the collapse of bound clumps is accelerated with respect to the homogeneous case (Gunn and Gott's model, Ref. 2). The acceleration of the collapse increases with decreasing height of the peak, ν. We finally compare the acceleration produced by this effect to the slowing down effect produced by the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-clusters studied by Del Popolo and Gambera.³ We find that the magnitude of the slowing down effect is larger than the acceleration produced by the effect studied in this paper, only in the outskirts of the cluster. We want to stress that the one which we study in this paper is also present in an isolated protocluster, being produced by the interaction of the collapsing clumps with the unbound substructure internal to the collapsing clumps itself while that studied in Ref. 3 is produced by substructure external to the density peak.

Single-crystalline SnO₂ zigzag nanobelts and straight nanobelts with triangular tip were synthesized by a simple Tin–water reaction method. The product was characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, Raman scattering and micro-photoluminescence spectroscopy to obtain the structural and optical information. Why zigzag nanobelts and straight nanobelts can be formed respectively under the same experimental conditions? On the basis of TEM characterization and thermodynamic analysis, the formation mechanism of zigzag nanobelts and straight nanobelts were proposed respectively.

In this paper, an adaptive attractive/repulsive (A/R) swarming model is proposed to explore the role of self-organized formation in swarming systems. By defining the adjustable A/R range γ_i, which is affected by the localized steady state of agents, the standard collective crystal-like swarming formations are straightforwardly unfolded in different scale. Meanwhile, with numerical simulations and analyses, the results show that the adaptive A/R swarming model provides an effective solution to the current existing dilemma of the collective liquid-like formation with unexpected neighbor distances and the split crystal-like formation. The actual neighbor distance of the adaptive A/R model could converge to the expected neighbor distance as planned, based on the different settings of the expected neighbor distance and the A/R range. Moreover, such adjustable A/R swarming formations may find their potential applications such as the formation of self-organized multi-robots and unmanned aerial vehicles, the automatic networking of sensors, etc.

Molecular dynamics simulation was adopted to investigate the nanoscale titanium nitride formation at the early formation stage in high-strength low-alloy steel. During the cluster formation process, the nitride clusters were formed through the atom aggregation. The atomic interactions of titanium and nitride atoms were revealed and the cluster property was discussed. The nanoscale titanium nitride clusters own a wide composition, and the cluster formation mechanism was concluded.

This paper presents the results of a study on the production of nanofiber anisotropic nanoporous materials based on silk fibroin and cotton cellulose by electrospinning using a rotating screen-receiver of nanofibers in the form of a thin material. The difference in the anisotropic properties of the nanofiber material is shown by the method of birefringence, sorption of water vapor and filtration of a liquid-phase mixture. The possibility of using nanofiber nanoporous fibroin and cotton cellulose materials as a nanofilter of gaseous and liquid-phase mixtures has been shown.

The effects of parameters on nanoscale titanium nitride during the formation process in ferrite were studied via the molecular dynamics (MD) simulation. The formation of titanium nitride was executed by employing a dislocation-motivated formation model in which the atomic diffusion has a significant contribution. The roles of N/Ti atom ratio, temperature and matrix defect were identified and the according nitride formation property was analyzed.

In a planetary or satellite system, idealized as n small bodies in an initially coplanar with concentric orbits around a large central body obeying the Newtonian point-particle mechanics, resonant perturbations will cause a dynamical evolution of the orbital radii except for cases with highly specific mutual relationships. In particular, the most stable situation can be achieved only when each planetary orbit is roughly twice as far from the Sun as the preceding one. This has been empirically observed by Titius (1766) and Bode (1778). By reformulating the problem as a hierarchical sequence of (unrestricted) 3-body problems and considering only the gravitational interactions among the central body and the body of interest and the adjacent outer body in the orbits, it is proved that the resonant perturbations from the outer body will destabilize the inner body (and vice versa) unless its mean orbital radius is a unique and specific multiple of β, the distal multiplier, of the inner body. In this way a sequence of concentric orbits can each stabilize the adjacent inner orbit, and since the outermost orbit is already tied to the collection of the inner orbits by conservation of total angular momentum, the entire configuration is stabilized.

We study the redshift and mass dependence of the inner slopes of relaxed ΛCDM dark matter haloes with and without baryons. We find that in the density profiles composed just of dark matter, the mass and redshift dependence of the slope is very slight, while the inner logarithmic density slope of dark matter haloes with baryons has a significant dependence on the halo mass and redshift. Slopes of structures increase with increasing mass and redshift, and this trend reduces from galaxies to clusters. The results of the present paper argue against universality of density profiles composed of dark matter and baryons, and confirm claims of a systematic variation in profile shape with halo mass, for dark matter haloes.

We study how galaxy morphology changes the relation among the inner slope $\alpha$ of galactic density profiles and the stellar mass, and rotation velocity.

We find that the slope $\alpha$ flattens monotonically from $\alpha \simeq -1$ to $\alpha \simeq 0$ going from giant galaxies (ellipticals, spirals) to dwarf galaxies ($\simeq 10^8{M}_{*}$). At masses smaller than $\simeq 10^8{M}_{*}$, in the mass range dominated by nonrotational supported galaxies (e.g. dSphs), the slope steepens due to the offset in angular momentum of rotational dominated, and nonrotational dominated galaxies.

A comparison with SPH simulations finds our result in qualitative agreement with them, but the inner slope $\alpha$ at small stellar masses is flatter than that in their simulations. Density profiles become cuspy for $M_{*}$ in the range $10^4$–$10^5{M}_{\odot }$, similarly to Õnorbe.

In this paper, we have worked on the concept of complexity factor for nonstatic spherically-symmetric self-gravitating source filled with anisotropic fluid distribution in $f(R,T)$ gravity theory. The definition of complexity for dynamical sources, proposed by Herrera, is examined in the framework of $f(R,T)$ gravity. We intended to analyze the behavior of complexity factor in modified theory. For this, we defined the scalar functions through orthogonal splitting of Reimann tensor in $f(R,T)$ gravity and worked out the structure scalars. We considered the structure scalar $Y_{TF}$ as a complexity factor to evaluate the complexity of the structure of dynamical system and also to analyze the complexity of the evolutionary patterns of the system under consideration. We took into account the homologous condition and homogeneous expansion condition in order to present the simplest mode of evolution, and found that homologous evolution is the simplest one. We considered both dissipative and nondissipative cases and found that shearing behavior of the fluid is not the same in both cases, however it remained geodesic in both cases. In the end, we established the results for the vanishing of the complexity factor. It has been found that zero complexity condition is satisfied if the energy density inhomogeneity and pressure anisotropy of the fluid configuration cancel each other.

Titanium alloys are widely used in aerospace and other fields due to their advantages of low density, high specific strength and good corrosion resistance. Laser oscillating welding is an innovative process in the realm of welding technology. In this study, two laser oscillating welding methods (circular and linear) were employed to analyze the influence of different oscillation parameters on the formation of titanium alloy. The results indicate that the oscillation frequency has a significant impact on weld formation. The laser scanning trajectory also affects weld formation, with circular and linear scanning trajectories resulting in better weld quality. Finally, the effects of oscillation modes on the microstructure and properties of laser oscillating welding titanium alloy were investigated based on optimized process parameters. Among them, circular laser oscillating welding of titanium alloy exhibits higher tensile strength, with a maximum tensile strength of up to 1188.3MPa.

In this paper, we prove the p-nilpotency of a finite group G with the assumption that some subgroups of a Sylow subgroup are semi CAP-or c-supplemented subgroups. We get some interesting new results.

A subgroup H of a finite group G is said to be SS-quasinormal in G if there exists a supplement B of H in G such that H is permutable with every Sylow subgroup of B. In this paper, we get some new characterizations of supersolvability and p-nilpotency of G by assuming some subgroups of prime power order of G are SS-quasinormal.

The main aim of this note is to give a criterion for a subgroup-closed formation to be solubly saturated, which we hope may provide a useful proving ground for outstanding questions about this family of formations.

A formation $𝔉$ of finite groups has the generalized Wielandt property for residuals, or $𝔉$ is a GWP-formation, if the $𝔉$-residual of a group generated by two $𝔉$-subnormal subgroups is the subgroup generated by their $𝔉$-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.

Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be a BNA-subgroup of $G$ if either $H^x=H$ or $x\in 〈H,H^x〉$ for all $x\in G$. A subgroup $H$ of $G$ is said to be a weakly BNA-subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H\cap T$ is a BNA-subgroup of $G$. In this paper, we investigate the structure of a finite group $G$ under the assumption that every minimal subgroup of $G$ not having a supersolvable supplement in $G$ is a weakly BNA-subgroup of $G$.

A subgroup $H$ of a group $G$ is called an $\mathcal{\mathscr{H}}C$-subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H^g\cap N_T(H)\le H$ for all $g\in G$. In this paper, we obtain new criteria for a normal subgroup to be contained in the $p𝔉$-hypercenter of a finite group by assuming that some of its subgroups are $\mathcal{\mathscr{H}}C$-subgroups. Our results generalize and uniform many known results.

The mechanics of cerebral aneurysm pathogenesis, evolution and rupture are not yet well understood. This paper presents a numerical analysis of the formation of a saccular cerebral aneurysm in for the first time in a 3D model of the basilar artery bifurcation under normal and hypertensive blood pressure. Due to the excessive endothelium derived nitric oxide produced in high wall shear stress, we assumed that smooth muscle cell relaxation is the origin of the aneurysm formation. Arterial wall remodeling under constant tension was considered to be the other mechanism of disease evolution. The wall was constructed from two elastic and hyperelastic isotropic regions. The flow was considered steady, laminar, Newtonian, and incompressible. The fully coupled fluid and structure models were solved with the finite elements package ADINA 8.5. The wall shear stress, effective stress and deformation distributions under normal and hypertensive blood pressure were compared to a healthy bifurcation. The model shows that although the malfunction of the endothelial cell layer and the corresponding smooth muscle cell-related loss of vascular tone is important to the inception of the disease; A saccular aneurysm may not be formed by this mechanism alone, and also requires the fiber-related arterial wall remodeling for further development.

We introduce a new subgroup embedding property of finite groups called c-normal embedding. By using this embedding property, formation theory and some special techniques, we obtain `iff' versions of theorems of Itô, Buckley, Srinivasan and other related results on p-nilpotence, nilpotence and supersolvability.