SICs and Algebraic Number Theory

We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.     

Models of spherical shells as sources of Majumdar–Papapetrou type spacetimes

By starting with a seed Newtonian potential–density pair we construct relativistic thick spherical shell models for a Majumdar–Papapetrou type conformastatic spacetime. As a simple example, we considerer a family of Plummer–Hernquist type relativistic spherical shells. As a second application, these structures are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around such configurations. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions.     

Gravitational and electromagnetic signatures of accretion into a charged black hole

We present the derivation and the solutions to the coupled electromagnetic and gravitational perturbations with sources in a charged black hole background. We work in the so called ghost gauge and consider as source of the perturbations the infall of radial currents. In this way, we study a system in which it is provoked a response involving both, gravitational and electromagnetic waves, which allows us to analyze the dependence between them. We solve numerically the wave equations that describe both signals, characterize the waveforms and study the relation between the input parameters of the infalling matter with those of the gravitational and electromagnetic responses.     

Synthesis,Optical Investigation and Biological Properties of Europium(III) Complexes with 2-(4-Chlorophenyl)-1-(2-Hydroxy-4-Methoxyphenyl)Ethan-1-one and Ancillary Ligands

Synthesis and photoluminescence behaviour of six novel europium complexes with novel β-hydroxyketone ligand, 2-(4-chlorophenyl)-1-(2-hydroxy-4-methoxyphenyl)ethan-1-one (CHME) and 2,2′-bipyridine (bipy) or neocuproine (neo) or 1,10-phenanthroline (phen) or 5,6-dimethyl-1,10-phenanthroline (dmphen) or bathophenanthroline (bathophen) were reported in solid state. The free ligand CHME and europium complexes, Eu(CHME)₃.2H₂O [1] Eu(CHME)₃.bipy [2], Eu(CHME)₃.neo [3], Eu(CHME)₃.phen [4], Eu(CHME)₃.dmphen [5] and Eu(CHME)₃.bathophen [6]were characterized by elemental analysis, FT-IR and ¹H-NMR. The photoluminescence emission spectra exhibited four characteristic peaks arising from the ⁵D₀ → ⁷F_J (J = 1–4) transitions of the europium ion in the solid state on monitoring excitation at λ_ex = 395 nm. The luminescence decay curves of these europium complexes possess single exponential behaviour indicating the presence of a single luminescent species and having only one site symmetry in the complexes. The luminescence quantum efficiency (η) and the experimental intensity parameters, Ω ₂ and Ω ₄ of europium complexes have also been calculated on the basis of emission spectra and luminescence decay curves. In addition, the antimicrobial and antioxidant activities were also studied of the investigated complexes.     

Substituent Effect on Absorption and Fluorescence Properties of Thieno[3, 2-<Emphasis Type="Italic">c</Emphasis>]Pyridine Derivatives

New substituted thieno[3,2-c]pyridine derivatives 5 were synthesized by the reaction of 3-bromo-4-chlorothieno[3,2-c]pyridine 1 with cyclic amine 2, which further on Suzuki reaction with boronic acids 4 converted to corresponding 3-arylthieno[3,2-c]pyridine 5. Substituent R³ has predominant effect on fluorescence properties of thienopyridines. However, the electron donor amine at C₄ has no effect on fluorescence properties of thienopyridines.

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Graphical Abstract New thieno[3,2-c]pyridine derivatives were synthesized from 3-bromo-4-chlorothieno[3,2-c]pyridine and cyclic amines, which by on Suzuki reaction with boronic acids converted to corresponding 3-arylthieno[3,2-c]pyridine. Substituent R3 has predominant effect on fluorescence properties of thienopyridines. However, the electron donor amine at C4 has no effect on fluorescence properties of thienopyridines

     

Theoretical and Experimental Study of the Diffraction Intensity of Gradient Refractive-Index Lenses

We develop the wave-optics approach for calculating the diffraction distribution of gradient refractiveindex lenses and observing the diffraction pattern of gradient refractive-index lenses in the experiments. The results of our calculation are in good agreement with the experimental results obtained. We show that the diffraction can be regarded as a method to check the quality of the refractive-index distributions of gradient refractive-index lenses.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

A remark on analytic Fredholm alternative

We apply a recent result of Borichev–Golinskii–Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the Fredholm-type analytic operator-valued functions.     

Synthesis,characterization and molecular docking studies of thiouracil derivatives as potent thymidylate synthase inhibitors and potential anticancer agents

Thymidylate synthase (TS), one of folate-dependent enzymes, is a key and well-recognized target for anticancer agents. In this study, a series of 6-aryl-5-cyano thiouracil derivatives were designed and synthesized in accordance with essential pharmacophoric features of known TS inhibitors. Nineteen compounds were screened in vitro for their anti-proliferative activities toward HePG-2, MCF-7, HCT-116, and PC-3 cell lines. Compounds \(\mathbf{21}_{\mathbf{c}}\), \(\mathbf{21}_{\mathbf{d}}\), and 24 exhibited high anti-proliferative activity, comparable to that of 5-fluorouracil. Additionally, ten compounds with potent anti-proliferative activities were further evaluated for their ability to inhibit TS enzyme. Six compounds (\(\mathbf{21}_{\mathbf{b}}\), \(\mathbf{21}_{\mathbf{c}}\), \(\mathbf{21}_{\mathbf{d}}\), 22, 23 and 24) demonstrated potent dose-related TS inhibition with \(\hbox {IC}_{50}\) values ranging from 1.57 to \(3.89\,\upmu \hbox {M}\). The in vitro TS activity results were consistent with those of the cytotoxicity assay where the most potent anti-proliferative compounds of the series showed good TS inhibitory activity comparable to that of 5-fluorouracil. Furthermore, molecular docking studies were carried out to investigate the binding pattern of the designed compounds with the prospective target, TS (PDB-code: 1JU6).     

Generation of an arbitrary chirped microwave waveform with high time-bandwidth product for increasing range resolution of RADAR by using photonic technique

An approach for photonic generation of an arbitrary chirped microwave waveform with an increased time-bandwidth product (TBWP) is proposed and experimentally demonstrated. In the proposed model, light from the mode locked laser is splitted into two parts by using 1 × 2 power splitter: one is sent to linearly chirped fiber Bragg grating (LCFBG) through circulator and the other is time delayed by fiber delay line. The optical pulse in upper arm is time stretched by the LCFBG. Meanwhile, the optical pulse in lower arm experiences a time delay and then stretched by the dispersive single mode fiber. Temporal interference pattern is generated with an increasing or decreasing free spectral range by combination of two time-stretched optical pulses. Finally, the temporal interference pattern which is obtained at the output of optical coupler is transformed into an arbitrary chirped microwave waveform by using a photo-detector. The main advantage of this proposed model is high TBWP in the range of 750–1000 which ultimately results in an increased range resolution of radio detection and ranging.