Black hole entropy calculation from near horizon symmetries

U ovom radu pokazali smo jedan način za računanje entropije (2+1) stacionarne crne rupe. Pri tome smo koristili dimenzionalnu redukciju na dvije dimenzije što je rezultiralo dilatonskim modelom te simetrije na horizontu crne rupe. Za generatore tih simetrija je pokazano da zadovoljavaju Virasoro algebru što nam je omogućilo korištenje Cardyjeve formule za entropiju. Rezultat koji smo dobili slaže se s Bekenstein-Hawkingovom formulom za entropiju.In this paper we showed one way to compute the entropy of (2+1) stationary black hole. We did so by using dimensional reduction on two dimensions, which resulted in dilaton model, and symmetries on the black hole horizon. It has been shown that generators of those symmetries satisfy Virasoro algebra which allowed us to use Cardy formula for entropy. The result is consistent with Bekenstein-Hawking formula

Konvergencija cikličke Jacobijeve metode za hermitsku matricu reda 4

U ovom radu prikazali smo Jacobijevu metodu za hermitske matrice reda 4 definiranu općom cikličkom pivotnom strategijom. Uveli smo relacije ekvivalencije \sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p} na skupu svih cikličkih strategija te pokazali da konvergenost metode pod nekom strategijom povlači konvergentnost metode pod njoj ekvivalentnom strategijom. Zatim smo pokazali globalnu konvergenciju metode pod strategijama iz specijalne familije $C_1$ te pod jednom paralelnom strategijom. Pomoću računalnog programa podijelili smo 720 cikličkih strategija u 5 klasa ekvivalencije, te u svakoj klasi pronašli strategiju za koju smo pokazali globalnu konvergenciju. To je bilo dovoljno da se pokaže globalna konvergencija metode pod svih 720 cikličkih strategija.In this work we have presented the Jacobi method for Hermitian matrices of order 4 defined by a general cyclic pivot strategy. We have introduced equivalence relations \sim, \underaccent{\tilde}{s}, \underaccent{\tilde}{w}, \underaccent{\tilde}{p} on the set of cyclic strategies and shown that convergence of the method under some strategy implies convergence of the method under an equivalent strategy. Then we have shown the global convergence of the method under the strategies from the special family $C_1$ and under one parallel strategy. Using a computer program, we have partitioned the set of 720 cyclic strategies in 5 equivalence classes. For each class we have found a strategy for which the method is convergent. That is enough to show the global convergence of the method under all 720 cyclic strategies

Sinteza i koroziono ponašanje polianilina na mekom čeliku, bakru i aluminijumu iz benzoatnih rastvora

The electrochemical synthesis of polyaniline (PANI) on mild steel, aluminum and copper from the sodium benzoate solutions has been investigated. It has been shown that thin, highly adherent, polyaniline films on the investigated metals could be obtained by anodic oxidation with current densities in the range of 0.5 and 1.5 mA cm-2. The corrosion behavior of mild steel, aluminum and copper with polyaniline coating in 0.5 mol dm3 NaCl (pH 3) solutions, has been investigated by polarization technique. The corrosion current densities, porosity and protection efficiency was determined. It has been shown that polyaniline coating provided corrosion protection of all mentioned metals.U radu je ispitivana elektrohemijska sinteza polianilina (PANI) na mekom čeliku, aluminijumu i bakru iz rastvora natrijum-benzoata i monomera anilina. Ustanovljeno je da se tanki, dobro adherentni, filmovi polianilina mogu formirati na svim ispitivanim metalima pri anodnim gustinama struja od 0,5-1,5 mA cm-2. Ispitivano je koroziono ponašanje metala sa prevlakom polianilina u rastvoru 0,5 mol dm-3 NaCl (3%). Ustanovljeno je da ove prevlake pružaju korozionu zaštitu svim ispitivanim metalima u datoj korozionoj sredini

Electrochemically deposited nano fibrous polyanilne for amperometric determination of glucose

Electrochemical deposition of polyaniline (PANI) on graphite electrode was performed galvanostaticaly at constant current density in the range of 1.0 – 5.0 mA cm-2 from aqueous acidic electrolyte containing aniline monomer. Based on ratio of doping/dedoping\ud charge capacities, it was estimated that current density of 2.0 mA cm-2 was optimal. The structure of the electrochemically synthesized PANI was fibrous, uniform and three dimensional with highly developed surface. Immobilization of glucose oxidise (GOx) was achieved by cross linking via glutaraldehyde and the efficiency of the immobilization was determined spectrophotometrically. Chronoamperometric curves were recorded at different glucose concentrations and used to estimate the apparent Michaelis constant, which was shown to be 0.27 mM. The storage stability of the PANI enzyme electrode was also estimated

The Membrane Receptor Complex Regulating Induction and Clonal Expansion of Normal Murine B Lymphocytes

Induction of resting B lymphocytes results from the interaction of competent ligands or helper cells with "triggering receptors.” Subsequent clonal expansion and performance are thought to be regulated by the interaction of selective growth or maturation factors with specific receptors on induced B cells. A set of membrane molecules of B lymphocytes, including IgM, IgD, lA, IE, lipopolysaccharide receptors, receptors for Fe and C3b, and other non-immunoglobulin structures recognized by some antiidiotypic antibodies, display ligand-induced relationships. Functional studies also indicate that this group of molecules functions as a complex that regulates delivery of inductive signals, the expression of growth and maturation receptors, and/or the outcome of the interactions of these receptors with the corresponding factor

Comment on “Towards exact solutions for the superconducting T c induced by electron-phonon interaction”

In a series of recent papers starting with Phys. Rev. B 103, 094501 (2021), Liu, Yang, Pan et al. claim to have determined the exact dressed electron-boson vertex for a number of very general interacting many-body problems by inverting certain Ward-Takahashi identities. Here, we point out that their Ward-Takahashi identities are missing terms which make the inversion of the identities impossible. One therefore cannot formulate exact self-contained integral equations for the dressed electron propagator. In addition, the proposed vertex expressions do not reproduce well-established results for the leading perturbative corrections

Dirac sigma models from gauging the nonlinear sigma models and its BV action

We present the construction of the Dirac sigma models by gauging the 2-dimensional nonlinear sigma models, but also including the possibility of nonminimal coupling to the metric sector. We show that for a large variety of possible cases, the minimal coupling to the metric sector is the only nontrivial possibility. In addition, we present the construction of the classical Batalin-Vilkovisky action for the Dirac sigma models. We follow a direct approach in its construction, by requiring it to be a solution of the classical master equation.Comment: Written for Proceeding in Science, 18 page

Exactly solvable spin- 1/2 XYZ models with highly degenerate partially ordered ground states

Exactly solvable models play a special role in condensed matter physics, serving as secure theoretical starting points for investigation of new phenomena. Changlani et al. [Phys. Rev. Lett. 120, 117202 (2018)] have discovered a limit of the XXZ model for S=1/2 spins on the kagome lattice, which is not only exactly solvable, but features a huge degeneracy of exact ground states corresponding to solutions of a three-coloring problem. This special point of the model was proposed as a parent for multiple phases in the wider phase diagram, including quantum spin liquids. Here, we show that the construction of Changlani et al. can be extended to more general forms of anisotropic exchange interaction, finding a line of parameter space in an XYZ model which maintains both the macroscopic degeneracy and the three-coloring structure of solutions. We show that the ground states along this line are partially ordered, in the sense that infinite-range correlations of some spin components coexist with a macroscopic number of undetermined degrees of freedom. We therefore propose the exactly solvable limit of the XYZ model on corner-sharing triangle-based lattices as a tractable starting point for discovery of quantum spin systems which mix ordered and spin-liquid-like properties