Narrow Results

Using the modern equations of state derived from microscopic calculations, we have calculated the neutron star structure. For the neutron star, we have obtained a minimum mass about 0.1 M_⊙ which is nearly independent of the equation of state, and a maximum mass between 1.47 M_⊙ and 1.98 M_⊙ which is strongly dependent on the equation of state. It is shown that among the equations of state of neutron star matter which we have used, the stiffest one leads to higher maximum mass and radius and lower central density. It is seen that the given maximum mass for the Reid-93 equation of state shows a good consistency with the accurate observations of radio pulsars. We have indicated that the thickness of neutron star crust is very small compared to the predicted neutron star radius.

The equation of state of deconfined quark matter within the MIT bag model is calculated. This equation of state is used to compute the structure of a neutron star with quark core. It is found that the limiting mass of the neutron star is affected considerably by this modification of the equation of state. Calculations are carried out for different choices of the bag constant.

We present an exact solution that could describe compact star composed of color-flavor locked (CFL) phase. Einstein’s field equations were solved through CFL equation of state (EoS) along with a specific form of $g_{rr}$ metric potential. Further, to explore a generalized solution we have also included pressure anisotropy. The solution is then analyzed by varying the color superconducting gap $\delta$ and its effects on the physical parameters. The stability of the solution through various criteria is also analyzed. To show the physical validity of the obtained solution we have generated the $M-R$ curve and fitted three well-known compact stars. This work shows that the anisotropy of the pressure at the interior increases with the color superconducting gap leading to decrease in adiabatic index closer to the critical limit. Further, the fluctuating range of mass due to the density perturbation is larger for lower color superconducting gap leading to more stable configuration.

A finitely generated ℤ[t, t^-1]-module without ℤ-torsion and having nonzero order Δ(M) of degree d is determined by a pair of sub-lattices of ℤ^d. Their indices are the absolute values of the leading and trailing coefficients of Δ(M). This description has applications in knot theory.

We introduce a new class of semigroups called strict abundant semigroups, which are concordant semigroups and subdirect products of completely ${\mathcal{J}}^{\ast }$-simple abundant semigroups and completely 0-${\mathcal{J}}^{\ast }$-simple primitive abundant semigroups. A general construction and a tree structure of such semigroups are established. Consequently, the corresponding structure theorems for strict regular semigroups given by Auinger in 1992 and by Grillet in 1995 are generalized and extended. Finally, an example of strict abundant semigroups is also given.

Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.

We say that a set of the form $[a,b]:=\{c\in \mathbb{Z}:a\le c\le b\}$ for some $a,b\in \mathbb{Z}$ is an interval. For a nonempty finite subset $A$ of $\mathbb{Z}$ and $n\in \mathbb{N}$, Vsevolod Lev proved in [Optimal representations by sumsets and subset sums, J. Number Theory62(1) (1997) 127–143] some results about the existence of long intervals contained in the $n$-fold iterated sumset of $A$. Furthermore, in the same paper, he proposed a conjecture [Optimal representations by sumsets and subset sums, J. Number Theory62(1) (1997) 127–143, Conjecture 1], see also [V. Lev, Consecutive integers in high-multiplicity sumsets, Acta Math. Hungar.129(3) (2010) 245–253, Conjecture 1]. Lev proved some particular cases of his conjecture, and he showed that these few cases have important applications. In this paper, we prove his conjecture.

A knowledge graph is a visual method that can display the information contained in the knowledge points, core structure, and comprehensive knowledge structure technology. In recent years, with the innovation of science and technology, the business field became keen on knowledge graphs and the graphical display method. However, the application of knowledge graphs in the business field is mainly limited to search engines, question, and answer systems because of the technical difficulties of knowledge extraction and knowledge graph drawing of unstructured text, especially the knowledge extraction of amorphous culture. It can provide knowledgeable service to users by analyzing the knowledge entity contained in encyclopedia knowledge or knowledge base. This paper will focus on the critical link of knowledge extraction of the knowledge graph, adopt a depth learning algorithm to solve this urgent problem and combine with the application of knowledge graph in substation fault to analyze the construction process of substation fault knowledge map based on AI.

The paper studies the effect of temperature ($T$), ($T=300$, 3200, 4000, 5000, 6000, 7000K) at pressure $P=0$GPa; pressure ($P$), ($P=0$, 100, 200, 300, 350, 400GPa) at $T=7000$K and thermal annealing time ($t$), $t=47.8$ps (after 10⁵ steps) at $T=7000$K, $P=400$Gpa) on the structure of MgSiO₃ bulk 3000 atoms by Molecular Dynamics (MD) simulation using Born–Mayer (BM) pair interaction potential and periodic boundary conditions. The structural results are analyzed through the Radial Distribution Function (RDF), the Coordination Number (CN), the angle distribution, size ($l$), total energy of the system ($E_{\mathrm{\text{tot}}}$) and the bonding lengths. The results show that the temperature and pressure had influenced the structural properties of MgSiO₃ bulk and formation process geology of the Earth. In addition, the center of the Earth with $T=7000$K and $P=350$GPa has appearance and disappearance of the Si–Si, Si–O, O–O, Si–Mg, O–Mg, Mg–Mg bonds and SiO₄, SiO₅, SiO₆, MgO₃, MgO₄, MgO₅, MgO₆, MgO₇, MgO₈, MgO₉, MgO${}_{10}$, MgO${}_{11}$, MgO${}_{12}$ angle distributions. When increasing the depth of the Earth’s surface $(h)$ lead to size $(l)$ of MgSiO₃ decreases, total energy of the system ($E_{\mathrm{\text{tot}}}$) increases, position of first peak of Radial Distribution Function (RDF) is $(r)$, height of RDF is $g(r)$ varies greatly with $h$ from $h=0$km to $h=1820$km, gradually decreasing with $h$ from $h=2000$km to $h=3200$km and the smallest structural change with $h>3200$km that shows has influence affects on the geological formation of the Earth.

This paper studies the effect of atoms number $(N)$ of bulk Ag: $N=2916$ atoms (Ag${}_{2916}$), 4000 atoms (Ag${}_{4000}$), 5324 atoms (Ag${}_{5324})$, 6912 atoms (Ag${}_{6912})$ at temperature $T=300$K, 400K, 500K, 600K, 700K, 800K, 900K, 1000K on bulk Ag${}_{5324}$ and annealing time $t$ = 200 ps on the structure and phase transition of Ag bulk by Molecular Dynamics (MD) method with Sutton–Chen (SC) pair interaction potential, periodic boundary conditions. The structural results are analyzed through the Radial Distribution Function (RDF), the total energy of the system ($E_{tot})$, the size $(l)$, the phase transition (determined by the relationship between $E_{tot}$ and $T$), and combined with the Common Neighbors Analysis (CNA) method. The obtained results show that the first peak’s position ($r)$ of the RDF has negligible change value, $r=2.78$Å, which is completely consistent with the experimental results. For bulk Ag, there are always four types of structure: FCC, HCP, BCC, Amor and glass transition temperature $T_g=500$K. When decreasing the temperature, bulk Ag changes from liquid state to crystalline state, when increasing the annealing time at $T_g=500$K, bulk Ag changes from amorphous phase to crystalline phase state, leading to the increase of FCC, HCP, BCC structures and the decrease of Amor structure. The obtained results will be used as guide for future experiments.

We first discuss the concept of structure to differentiate between structural and systemic properties. Within this framework we discuss processes of establishing structures, such as phase transitions, organization and self-organization. The paper introduces concepts and insights about the process of Acquiring Properties (AP) in systems, not just possessing properties. The last point relates to establishing, sustaining and managing new properties in emergent and organizational systems. In the Appendix we briefly discuss this approach for the concept of mind possessed by living matter.

When we do usual Computation in Science, especially in Metrology, we assume that we do Mathematics. This is only partly true in spite of the fact that database handling and data processing are most important indeed. The field of Measurement plus Observation is much more entangled with Mathematics. The following survey “Metrology and Mathematics” will focus on selected ideas, concepts, rules, models, and structures, each of which is of a basic mathematical nature. When doing this, it is not surprising at all that most theoretical and applicational requirements in the field can be reduced to just a few basic logical and mathematical structures. This is also true for complex processes in fields like humanity and society. Signal and System Theory (SST) supports this claim. However, such an endeavour asks for an orderly and consistent definition of quantities and processes and of their mathematical models, called signals and systems. These models represent all kinds of issues, items, and phenomena in the real world. The term model indicates the superordinate means of mathematical description, observation, and representation in Science and Technology. The question arises, what the role of Logic and Mathematics looks like in detail. The term structure will be consistently pivotal. And, as is generally known, structures are best visualised by graphical means, here called Signal Relation Graphs (SRG).