Properties Of Cones Research Articles

Kriteria Buku Referensi Media Pembelajaran Matematika Yang Diperlukan Bagi Guru-Guru SMP Di Mataram

The purpose of this study was to determine the criteria for a mathematics learning media reference book that is needed for junior high school mathematics teachers in the city of Mataram. The research begins with a survey on whether learning mathematics requires media, then identifies the frequency with which teachers use media in learning mathematics, as well as the reasons teachers never or rarely use media in learning mathematics. Based on the survey, it was found that teachers need reference books to develop mathematics learning media, so it is necessary to develop the criteria for the required reference books. Furthermore, a literature review was conducted to compare the needs (ideal conditions) for Learning Media reference books with the current state (real conditions). Conclusion The results of the study show that the materials that require media are: arithmetic operations Integers and fractions, Linear Equations, Sets and Venn Diagrams, geometry, Function values, function graph sketches, slopes of lines, Pythagoras, circles, tangents, inner circles and the outer circle of a triangle, the properties of geometric figures, similarity, congruence, cylinders, cones, and spheres. In addition, the media needed are Concept Maps, Informative Power Points, Interactive Power Points, Student Worksheets, Learning Videos, Teaching Aids, and GeoGebra. Furthermore, the criteria for a valid book were developed based on the results of the study which included 4 aspects, namely material aspects, language, presentation of material, and graphics

Artificial intelligence in periodontics: A dip in the future

BACKGROUND: Artificial intelligence is a relatively newer technology in the field of medical world. This science uses the machine – learning algorithm and computer software to aid in the diagnostics in medical and dental fields. It is a huge talking point in the field of technology which is spreading it’s wings in all possible sectors at a great speed. This field covers solutions from coaching solutions to diagnostics in medical field covering under the umbrella of all what can be achieved by machine and deep learning. CONTENT: In dentistry, artificial intelligence is creating a revolution in all sections from collection of data, creating algorithms for orthodontic procedures, diagnostic records in the aspect of radiographic data, three dimensional scans and cone beam computed tomography, CAD CAM systems for restorative and prosthetic purposes. Similarly continuous research is being done in the field of periodontics in terms of measuring bone loss, amount of plaque present and much more. CONCLUSION: The field of artificial technology with its varied applications will change the face of dentistry in the upcoming times. Artificial intelligence with its application of machine learning will change the face of dentistry in future.

Acoustic Tunneling Study for Hexachiral Phononic Crystals Based on Dirac-Cone Dispersion Properties

Acoustic tunneling is an essential property for phononic crystals in a Dirac-cone state. By analyzing the linear dispersion relations for the accidental degeneracy of Bloch eigenstates, the influence of geometric parameters on opening the Dirac-cone state and the directional band gaps’ widths are investigated. For two-dimensional hexachiral phononic crystals, for example, the four-fold accidental degenerate Dirac point emerges at the center of the irreducible Brillouin zone (IBZ). The Dirac cone properties and the band structure inversion problem are discussed. Finally, to verify acoustic transmission properties near the double-Dirac-cone frequency region, the numerical calculation of the finite-width phononic crystal structure is carried out, and the acoustic transmission tunneling effect is proved. The results enrich and expand the manipulating method in the topological insulator problem for hexachiral phononic crystals.

On the Aromaticity and 13C-NMR Pattern of Pentagonal-Pyramidal Hexamethylbenzene Dication [C6(CH3)6]2+: A {C5(CH3)5}−–{CCH3}3+ Aggregate

The experimentally characterized hexamethylbenzene dication C6(CH3)62+ shows a pentagonal-pyramidal structure involving a carbon-capped five-membered ring. The structural characterization of this hypercoordination (or hypervalency) gives rise if the aromatic behavior remains in the resulting pentagon ring. Here, we investigated the induced magnetic field of C6(CH3)62+ to gain a deeper understanding of the resulting non-classical structural situation in a representative pentagonal-pyramidal structure. Our results support the view of a C5(CH3)5−/CCH33+ structure, depicting a π-aromatic pentamethylcyclopentadienyl anion with a 6π-electron kernel, with a capped carbon which does not decrease the characteristic shielding cone property of the aromatic ring. Hence, carbon-capped rings are suggested to retain the aromatic behavior from the former aromatic ring. We expect that the analysis of both the overall magnetic response and NMR chemical shifts may be informative to unravel the characteristic patterns in the formation of hypervalent carbon atoms involving non-classical chemical environments.

Minimizing Curves in Prox-regular Subsets of Riemannian Manifolds

We obtain a characterization of the proximal normal cone to a prox-regular subset of a Riemannian manifold and some properties of Bouligand tangent cones to these sets are presented. Moreover, we show that on an open neighborhood of a prox-regular set, the metric projection is locally Lipschitz and it is directionally differentiable at the boundary points of the set. Finally, a necessary condition for a curve to be a minimizing curve in a prox-regular set is derived.

Fuzzy Cone Normed Linear Space and Some Fixed Point Results for Weakly Compatible Mappings

In this paper, an idea of fuzzy cone normed linear space is introduced with underlying space is Felbin’s type fuzzy Banach space. Some basic results as well as results in finite dimensional fuzzy cone normed linear space are studied. Lastly, some fixed point theorems for weakly compatible mappings are established in such spaces.

Numerical simulation of particles flow in Laser Metal Deposition technology comparing Eulerian-Eulerian and Lagrangian-Eulerian approaches

The present work deals with the numerical prediction of the particle flow within a three-way nozzle in Laser Metal Deposition (LMD) technology adopted during additive manufacturing processes. In particular, the paper focuses on CFD (Computational Fluid Dynamics) simulations of the particle flow problem, regarding the coupling between a fluid phase, i . e ., the carrier gas, and a solid phase, i . e ., a metallic material powder that is delivered through the nozzle of the LMD machine. Two different numerical approaches are investigated, both implemented in a in-house code using OpenFOAM open source C++ toolbox. The former is based on a mixed formulation, combining an Eulerian description of the carrier gas flow with a Lagrangian description of the particle flow. The latter on a pure Eulerian formulation of both carrier gas and particles. In agreement with the experimental evidences, the present work compares the two approaches in terms of capability of simulating some key physical features of the LMD process, i . e ., the geometrical properties of the powder cone formed out from the nozzle.

Denting points of convex sets and weak property ($$\pi $$) of cones in locally convex spaces

Denting points of convex sets and weak property ($$\pi $$) of cones in locally convex spaces

Controllability of a Linear System With Nonnegative Sparse Controls

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system is unidirectional, and activating each input node adds to the cost of control. We derive the necessary and sufficient conditions for controllability of the system, without imposing any constraints on the system matrices. Unlike the well-known Kalman rank based controllability criteria, the conditions presented in this paper can be verified in polynomial time, and the verification complexity is independent of the sparsity level. The proof of the result is based on the analytical tools concerning the properties of a convex cone. Our results also provide a closed-form expression for the minimum number of control nodes to be activated at every time instant to ensure controllability of the system using positive controls.

Fermionic Condensate on Finite Radius Cones

The fermionic condensate is investigated for a field localized on a finite radius 2- dimensional cone in the presence of a magnetic flux threading the cone apex. On the edge of the cone a boundary condition is imposed that differs from the MIT bag boundary condition, most frequently used for the confinement of fermions. The fermionic condensate is decomposed into the boundary-free and edge-induced contributions. Both these parts are periodic functions of the magnetic flux with the period equal to the flux quantum.

Schauder estimates on products of cones

We prove an interior Schauder estimate for the Laplacian on metric products of two dimensional cones with a Euclidean factor, generalizing the work of Donaldson and reproving the Schauder estimate of Guo–Song. We characterize the space of homogeneous subquadratic harmonic functions on products of cones, and identify scales at which geodesic balls can be well approximated by balls centered at the apex of an appropriate model cone. We then locally approximate solutions by subquadratic harmonic functions at these scales to measure the Hölder continuity of second derivatives.

Sets with constant normal in Carnot groups: properties and examples

We analyze subsets of Carnot groups that have intrinsic constant normal, as they appear in the blowup study of sets that have finite subRiemannian perimeter. The purpose of this paper is threefold. First, we prove some mild regularity and structural results in arbitrary Carnot groups. Namely, we show that for every constant-normal set in a Carnot group its subRiemannian-Lebesgue representative is regularly open, contractible, and its topological boundary coincides with the reduced boundary and with the measure-theoretic boundary. We infer these properties from a metric cone property. Such a cone will be a semisubgroup with nonempty interior that is canonically associated with the normal direction. We characterize the constant-normal sets exactly as those that are arbitrary unions of translations of such semisubgroups. Second, making use of such a characterization, we provide some pathological examples in the specific case of the free-Carnot group of step 3 and rank 2. Namely, we construct a constant normal set that, with respect to any Riemannian metric, is not of locally finite perimeter; we also construct an example with non-unique intrinsic blowup at some point, showing that it has different upper and lower subRiemannian density at the origin. Third, we show that in Carnot groups of step 4 or less, every constant-normal set is intrinsically rectifiable, in the sense of Franchi, Serapioni, and Serra Cassano.

On the assignability of LTI systems with arbitrary control structures

ABSTRACT In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure known as fixed-mode radius is developed. However, its evaluation is confronted with a highly non-convex optimization problem combined with the need for a combinatorial search. This study utilises properties of positive-definite cones and duality theory to formulate the assignability assessment as an optimization problem with linear matrix inequality (LMI) constraints. Based on the suggested formulation, three alternative methods are proposed to evaluate the distance to unassignability. The first two methods offer alternative non-iterative and convex programs. The third method proposes an iterative convex optimization while updating the binary variables based on the dual variables. All the proposed methods rely on convex optimization, do not involve gridding over the complex plane and circumvent the combinatorial nature of the problem by using properties of positive definite cones. Simulation results confirm the effectiveness of the proposed methods in the assessment of fixed-mode radius with respect to arbitrary control structures.

Observing movement of Dirac cones from single-photon dynamics

Graphene with honeycomb structure, being critically important in understanding physics of matter, exhibits exceptionally unusual half-integer quantum Hall effect and unconventional electronic spectrum with quantum relativistic phenomena. Particularly, graphene-like structure can be used for realizing topological insulator which inspires an intrinsic topological protection mechanism with strong immunity for maintaining coherence of quantum information. These various peculiar physics arise from the unique properties of Dirac cones which show high hole degeneracy, massless charge carriers and linear intersection of bands. Experimental observation of Dirac cones conventionally focuses on the energy-momentum space with bulk measurement. Recently, the wave function and band structure have been mapped into the real-space in photonic system, and made flexible control possible. Here, we demonstrate a direct observation of the movement of Dirac cones from single-photon dynamics in photonic graphene under different biaxial strains. Sharing the same spirit of wave-particle nature in quantum mechanics, we identify the movement of Dirac cones by dynamically detecting the edge modes and extracting the diffusing distance of the packets with accumulation and statistics on individual single-particle registrations. Our results of observing movement of Dirac cones from single-photon dynamics, together with the method of direct observation in real space by mapping the band structure defined in momentum space, pave the way to understand a variety of artificial structures in quantum regime.

CuP: A new type of anisotropic and very stable Dirac cone material

Abstract The anisotropic Dirac cone has the advantage of anisotropic carrier mobility, which is different from other Dirac materials and can be applied to direction-dependent quantum devices. By first-principle calculation, we systematically research the Dirac cone and quantum properties of CuP. The calculation results show that CuP monolayer is a new type of anisotropic Dirac material. In addition, there is no virtual frequency in the phonon spectrum of this structure. At 300 K, the CuP monolayer can be remained well and there is no loose fracture of the structure. Based on grounds of Born criteria, CuP monolayer has good mechanical stability. Interestingly, considering the effect of spin-orbit coupling (SOC), the Dirac cone does not open the band gap. Moreover, the addition of stress does not destroy the Dirac cone. The material is mechanically and thermally stable. The results of Poisson's ratio and Young's modulus show that the structure has obvious anisotropy. It is worth noting that, the Fermi velocity to the right is 2.3 × 105 m/s and the left is 4.5 × 105 m/s, which is in the same order of magnitude as the Fermi velocity of graphene (8.0 × 105 m/s). The calculation results provide an ideal basis for the design of directional electron transport devices in spintronics.

Hyperelastic Curves in 3-dimensional Lightlike Cone

We study hyperelastic curves known as a generalization of elastic curves in $3-$dimensional lightlike cone which is a degenerate hypersurface in Minkowski $4-$space as critical points of the cone curvature energy functional constructed with the $r-$th power of the cone curvature depending on the given boundary conditions for the natural number $r \geq 2$. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according to the selected cylindrical coordinate systems in $3-$dimensional lightlike cone using these Killing vector fields.

Set-valued variational inclusion problem with fuzzy mappings involving XOR-operation

In this paper, we introduce a set-valued variational inclusion problem with fuzzy mappings involving XOR-operation. We define a resolvent operator involving a bi-mapping and prove resolvent operator is single-valued, comparison and Lipschitz-type continuous. Based on resolvent operator we proposed an iterative algorithm to find the approximate solution of our problem. An existence and convergence result is proved for set-valued variational inclusion problem with fuzzy mappings involving XOR-operation without using the properties of a normal cone. Examples are constructed for illustration.

LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD

The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of com­plex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of opti­mization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

Changes in the Composition and Surface Properties of Torrefied Conifer Cones.

The paper investigated the torrefaction of cones from three tree species: Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies L.), and European larch (Larix decidua Mill.). The objective was to determine the effects of torrefaction temperature on the properties of cones with a view to their further use as a renewable energy source. Torrefaction was conducted at 200, 235, 275, and 320 °C for 60 min under an inert gas atmosphere. Elemental composition, ash content, and lower heating value (LHV) were measured for the original and torrefied samples. Torrefaction performance was evaluated using formulas for solid yield, higher heating value (HHV), HHV enhancement factor, as well as energy yield. Scanning electron microscopy (SEM) was used to assess elemental composition and structural changes at the surface of the torrefied material. For all the studied conifer species, the higher the torrefaction temperature, the greater the carbon and ash content and the higher the LHV (a maximum of 27.6 MJ·kg−1 was recorded for spruce and larch cones torrefied at 320 °C). SEM images showed that an increase in process temperature from 200 to 320 °C led to partial decomposition of the scale surface as a result of lignin degradation. Cone scales from all tree species revealed C, O, N, Mg, K, and Si at the surface (except for pine scales, which did not contain Si). Furthermore, the higher the temperature, the higher the enhancement factor and the lower the energy yield of the torrefied biomass. Under the experimental conditions, spruce cones were characterized by the lowest weight loss, the highest HHV, and the highest energy yield, and so they are deemed the best raw material for torrefaction among the studied species.

Existence of solutions and solving method of lexicographic problem of convex optimization with the linear criteria functions

Among vector problems, the lexicographic ones constitute a broad significant class of problems of optimization. Lexicographic ordering is applied to establish rules of subordination and priority. Hence, a lot of problems including the ones of complex system optimization, of stochastic programming under a risk, of the dynamic character, etc. may be presented in the form of lexicographic problems of optimization. We have revealed the conditions of existence of solutions of multicriteria of lexicographic optimization problems with an unbounded set of feasible solutions on the basis of applying the properties of a recession cone of a con vex feasible set, the cone which puts it in order lexicographically with respect to optimization criteria. The obtained conditions may be successfully used while developing algorithms for finding the optimal solutions of the mentioned problems of lexicographic optimization. A method of finding the optimal solutions of convex lexico graphic problems with the linear functions of criteria is built and grounded on the basis of ideas of the method of linearization and the Kelley cutting plane method.