Light from Reissner–Nordstrom–de Sitter black holes

We derive for the first time the form of the spiral null geodesics around the photon sphere of the Reissner–Nordstrom black hole in the de Sitter expanding universe. Moreover, we obtain the principal parameter we need for deriving, according to our method [I. I. Cotăescu, Eur. Phys. J. C 81, 32 (2021)], the black hole shadow and the related redshift as measured by a remote observer situated in the asymptotic zone. We obtain thus a criterion of detecting charged black holes without peculiar velocities when one knows the mass, redshift and the black hole shadow.

Interfacial Concentrations of Hydroxytyrosol Derivatives in Fish Oil-in-Water Emulsions and Nanoemulsions and Its Influence on Their Lipid Oxidation: Droplet Size Effects

Reports on the effect of droplet size on the oxidative stability of emulsions and nanoemulsions are scarce in the literature and frequently contradictory. Here, we have employed a set of hydroxytyrosol (HT) esters of different hydrophobicity and fish oil-in-water emulsified systems containing droplets of different sizes to evaluate the effect of the droplet size, surfactant, (ΦI) and oil (ΦO) volume fractions on their oxidative stability. To quantitatively unravel the observed findings, we employed a well-established pseudophase kinetic model to determine the distribution and interfacial concentrations of the antioxidants (AOs) in the intact emulsions and nanoemulsions. Results show that there is a direct correlation between antioxidant efficiency and the concentration of the AOs in the interfacial region, which is much higher (20–200 fold) than the stoichiometric one. In both emulsified systems, the highest interfacial concentration and the highest antioxidant efficiency was found for hydroxytyrosol octanoate. Results clearly show that the principal parameter controlling the partitioning of antioxidants is the surfactant volume fraction, ΦI, followed by the O/W ratio; meanwhile, the droplet size has no influence on their interfacial concentrations and, therefore, on their antioxidant efficiency. Moreover, no correlation was seen between droplet size and oxidative stability of both emulsions and nanoemulsions.

DAMAGE CRITERIA IN ROUNDHEADS ARMOURED WITH A SINGLE LAYER OF CUBIPOD ARMOR UNITS

The present paper covers the analysis of damage in a single-layer roundhead armored with Cubipods. This study was carried through physical model tests. Firstly, the analysis of the damage in these structures has not been an intensive studied topic. It is normally defined when a piece doesn’t contribute in the stability on the single layer armor and, due to, a new damage criteria was proposed. In addition, vertical and sectorial size of active zone was defined. It could be possible defined three different phases in the evolution of damage due to the homogenous behavior for the roundhead. The most damage sector is 90-135º, and the neighbors, 45-90º and 135-180º, but damage in 45-90º is greater in frequency and value. Also, the dimensionless parameters of roundhead size (Rn, R/H and R/L) are involved in this phenomenon. Besides, the vertical size of active zone is defined in ±1.5Hs since sea water level (SWL), being the wave steepness is the principal parameter involved. It was proposed two level of damage: start of damage (D [%] =0.4) and failure (D [%] =11). Finally, it has been measure the reserve of stability. It is defined like the percentage of wave that the roundhead is able to resists between 2 levels of damage. This parameter allows analyzes the rigid behavior of the roundhead single layer armor. The value of this parameter, except one case, is RE [%] =9. It was conclude that wave steepness is a relevant parameter, when it increased the reserve is reduces.

Pemodelan Nilai Keseimbangan antara Compound Value dan Future Value Menggunakan Aplikasi Geogebra

This study discussed how to utilize Geogebra in the modeling of financial mathematics problem. The balance between compound value and future value will be determined by geometric and algebraic approach. Specific problems are presented in this article. By using slider in Geoegebra, and in same interest (i), n period when balance happened can be determined. On the applet that had been made, n period where happened balance between S and FV could automatically determined by moving principal parameter (P) and annuity (A). Keywords: compound value, future value, balance, geogebra AbstrakArtikel ini membahas bagaimana menggunakan aplikasi Geogebra untuk membuat pemodelan matematika keuangan. Akan dihitung nilai kesetimbangan antara nilai majemuk (Compound Value) dan nilai yang akan datang (Future Value) baik dengan pendekatan aljabar maupun Geometri. Contoh yang spesifik dibahas di artikel ini. Dengan fasilitas slider yang ada pada Geogebra, pada parameter bunga (i) yang sama, didapat nilai n periode dimana terjadi kesetimbangan antara Compound Value dan Future Value. Sekaligus juga di peroleh nilai-nilai kesetimbangan pada periode tertentu. Pada applet yang telah dibuat, periode dimana terjadi kesetimbangan antara S dan FV dapat secara otomatis ditentukan dengan pergerakan parameter pokok hutang (P) dan nilai parameter cicilan anuitas (A). Kata kunci: nilai majemuk, nilai yang akan datang, kesetimbangan, geogebra