On Existence of Primitive Normal Elements of Cubic Form over Finite Fields

For a prime [Formula: see text]and a positive integer[Formula: see text], let [Formula: see text] and [Formula: see text] be the extension field of [Formula: see text]. We derive a sufficient condition for the existence of a primitive element [Formula: see text] in[Formula: see text] such that [Formula: see text] is also a primitive element of [Formula: see text], a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is a primitive element of [Formula: see text], and a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is also a primitive normal element of [Formula: see text] over [Formula: see text].

BPS black hole entropy and attractors in very special geometry. Cubic forms, gradient maps and their inversion

We consider Bekenstein-Hawking entropy and attractors in extremal BPS black holes of $$ \mathcal{N} $$ N = 2, D = 4 ungauged supergravity obtained as reduction of minimal, matter-coupled D = 5 supergravity. They are generally expressed in terms of solutions to an inhomogeneous system of coupled quadratic equations, named BPS system, depending on the cubic prepotential as well as on the electric-magnetic fluxes in the extremal black hole background. Focussing on homogeneous non-symmetric scalar manifolds (whose classification is known in terms of L(q, P, Ṗ) models), under certain assumptions on the Clifford matrices pertaining to the related cubic prepotential, we formulate and prove an invertibility condition for the gradient map of the corresponding cubic form (to have a birational inverse map which is given by homogeneous polynomials of degree four), and therefore for the solutions to the BPS system to be explicitly determined, in turn providing novel, explicit expressions for the BPS black hole entropy and the related attractors as solution of the BPS attractor equations. After a general treatment, we present a number of explicit examples with Ṗ = 0, such as L(q, P), 1 ⩽ q ⩽ 3 and P ⩾ 1, or L(q, 1), 4 ⩽ q ⩽ 9, and one model with Ṗ = 1, namely L(4, 1, 1). We also briefly comment on Kleinian signatures and split algebras. In particular, we provide, for the first time, the explicit form of the BPS black hole entropy and of the related BPS attractors for the infinite class of L(1, P) P ⩾ 2 non-symmetric models of $$ \mathcal{N} $$ N = 2, D = 4 supergravity.

Cubic Octa-Carbon: Quantum-Chemical Design of Molecular Structure and Potential Way of Its Synthesis from Cubane

Quantum-chemical calculation of most important parameters of molecular and electronic structures of octa-carbon C8 having cubic form (bond lengths, bond and torsion angles) using CCSD(T)/QZVP and DFT B3PW91/QZVP methods, has been carried out. NBO analysis data and HOMO/LUMO images for this compound are presented, too. Good agreement was found between the structural data obtained using the above two quantum-chemical methods and, also, with corresponding experimental data. Also, the standard thermodynamic parameters of formation of cubic C8 considered here, and namely standard enthalpy ΔfH0(298K), entropy Sf0(298K) and Gibbs’ energy ΔfG0(298K) of formation for this compound were calculated. By using this data, a theoretically possible variant of the synthesis of this compound by dehydrogenation of cubane C8H8 is considered, and the thermodynamic characteristics of each of the four stages of this process have been calculated. It is noted that each of the four stages of this process is characterized by a very high (about 500 kJ/mol) enthalpy of activation, as a result of that, for their realization within a sufficiently short time, the use of appropriate catalysts is necessary.

Basic properties of the mangrove tree branches as a raw material of wood pellets and briquettes

In order to sustain mangrove forests, only branches part of the mangrove trees have been utilized. In this context, these parts have been used as the raw material of wood pellets and briquettes. These solid biofuels are produced by compressing pulverized woody biomass with or without additives in cubic-form or cylindrical units. In this study, five predominant mangrove trees, namely Avicennia marina, Bruguiera sexangula, Excoecaria agallocha, Rhizopora apiculata, and R. mucronata, have been harvested their branches. Wood with and without bark derived from branches has been investigated for their fundamental properties, namely percentage of bark, ash-content, and physical properties (moisture content, density, and specific gravity). These properties will determine the quality class of the resulted wood pellets and briquettes considering pre-treatment or the nature of the branches’ wood.

Representing squares by cubic forms

Let [Formula: see text] be an arbitrary cubic form. In this paper, we show that for non-homogeneous cubic equations like [Formula: see text], there exists a non-trivial solution when [Formula: see text].

Numerical modeling on dynamics of droplet in aircraft wing structure at different velocities

Purpose The purpose of this paper is to find the droplets impact on the airplane wing structure. Two kinds of characteristics of the droplet at different velocity and viscosity are assumed. The droplet is assumed to be spherical cubic form and it is injected from the convergent divergent nozzle with a passive control. Design/methodology/approach This paper presents the results of a numerical simulation of droplet impact on the horizontal surface. The effects of impact parameters are studied. The splash effect of the droplet also visualized. The results are presented in form of stress, strain, displacement magnitude of the droplet. Findings Crosswire is used as passive control. The behavior of the droplet impact is observed based on the kinetic energy and the gravitational forces. Originality/value The results predict that smooth particle hydrodynamic designed droplet not only depend on the equation of state of the droplet but also the injection velocity from the nozzle. It also determined that droplet velocity is depending on the viscosity of the fluid.

CFD Numerical Investigation of a New Solar Flat Air-Collector Having Different Obstacles with Various Configurations and Arrangements

This work deals with a numerical parametric optimization study of a new Solar Flat Air Collector (SFAC) configuration. The CFD numerical parametric study investigates various SFAC structures inside the air cavity without obstacles and with spherical, cubic, cylindrical, and pyramidal obstacles. The study optimizes the most convenient configuration and arrangement that allow for the increase of the heat-transfer surface and to make the flow homogeneous in order to generate turbulence zones inside the SFAC air cavity. The result shows that the thermal performances of the cubic form are close to those of the spherical obstacles. Another set of simulations was performed to evaluate the performances of the cubic shape baffles for three orientation angles equal to 0°, 22.5°, and 45°, respectively. Each configuration has three forms of arrangement with a relative roughness pitch (b/a) varying between 2, 4, and 6. The results of the simulation study showed that the relative roughness pitch, the Reynolds number, as well as the angle of orientation influence the performance and the operation of the SFAC. The results of the simulations showed that the combination of an orientation of 45° with a roughness pitch of b/a = 2 increases the SFAC thermal performances, which can reach 85%.

Reinforcing Glaze Layer of Restorative Dental Zirconia by Adding Nano Alumina Ceramics

The objective of this work is to study the effect of adding varying ratios of Nano Alumina to the glazing powder on glazing layer of restorative dental ceramic. The effect of addition is examined by applying Vickers hardness and surface roughness tests on the glazing layer. The specimens have been cut in a cubic form. The specimens were placed in the furnace for sintering up to temperature of 1450 oC. One specimen is glazed with glazing materials and the remaining three specimens are glazed with glazing materials but supported with varying ratios of Nano Alumina (10, 15 and 25 wt%) and all these specimens sintered at 850 oC. It was found that Vickers hardness is increased with increasing the ratios of Nano Alumina but the surface roughness decreased with increasing the ratios of Nano Alumina. Weibull modulus increased with Alumina additive increases for glass coating layer.

Multiple Spectral Resolution 3D Convolutional Neural Network for Hyperspectral Image Classification

In recent years, benefiting from the rapid development of deep learning technology in the field of computer vision, the study of hyperspectral image (HSI) classification has also made great progress. However, compared with ordinary RGB images, HSIs are more like 3D cubes; therefore, it is necessary and beneficial to explore classification methods suitable for the very special data structure of HSIs. In this paper, we propose Multiple Spectral Resolution 3D Convolutional Neural Network (MSR-3DCNN) for HSI classification tasks. In MSR-3DCNN, we expand the idea of multi-scale feature fusion and dilated convolution from the spatial dimension to the spectral dimension, and combine 3D convolution and residual connection; therefore, it can better adapt to the 3D cubic form of hyperspectral data and make efficient use of spectral information in different bands. Experimental results on four benchmark datasets show the effectiveness of the proposed approach and its superiority as compared with some state-of-the-art (SOTA) HSI classification methods.

Synthesis and structural characterization of orthorhombic Cu3–δ Sb (δ ≈ 0.1) and hexagonal Cu3Sb1–xInx (x ≈ 0.2) phases

Cu3Sb is a known copper-rich phase in the Cu–Sb binary phase diagram. It is reported to be dimorphic, with a low-temperature form adopting the orthorhombic Cu3Ti structure type (space group Pmmn, No. 59). The high-temperature form crystallizes in the cubic space group F m 3 ‾ m $Fm‾{3}m$ (No. 225), and is isostructural with BiF3. Neither polymorph has been carefully characterized to date, with both structures being assigned to the respective structure type, but never refined. With this study, we provide structural evidence, based on single-crystal and powder X-ray diffraction data that the low-temperature orthorhombic phase exists with a significant amount of defects on one of the Cu-sites. As a result, its composition is not Cu3Sb, but rather Cu3–δ Sb (δ = 0.13(1)). The cubic form could not be accessed as a part of this study, but another Cu-rich phase, Cu3Sb≈0.8In≈0.2, was also identified. It adopts the hexagonal Ni3Sn structure type (space group P63/mmc, No. 194) and represents an In-substituted variant of a hitherto unknown structural modification of Cu3Sb. Whether the latter can exist as a binary phase, or what is the minimum amount of In inclusions needed to stabilize it remains to be determined. Measurements of the thermopower of Cu3–δ Sb (δ = 0.13(1)) were conducted in the range of 300–600 K and demonstrated a maximum value of ca. 50 μV/K at 600 K, indicative of a p-type transport mechanism. Electrical resistivity measurements for the same sample confirmed that it exhibits metallic-like behavior, with a room temperature value of 0.43 mΩ cm. Electronic structure calculations show the absence of a band gap. Thermal analysis was utilized to ascertain the congruent melting of both phases.