On the ambiguity in the notion of transverse traceless modes of gravitational waves

Somewhat surprisingly, in many of the widely used monographs and review articles the term Transverse-Traceless modes of linearized gravitational waves is used to denote two entirely different notions. These treatments generally begin with a decomposition of the metric perturbation that is local in the momentum space (and hence non-local in physical space), and denote the resulting transverse traceless modes by \(h_{ab}^{\mathrm{TT}}\). However, while discussing gravitational waves emitted by an isolated system—typically in a later section—the relevant modes are extracted using a ‘projection operator’ that is local in physical space. These modes are also called transverse-traceless and again labeled \(h_{ab}^{\mathrm{TT}}\), implying that this is just a reformulation of the previous notion. But the two notions are conceptually distinct and the difference persists even in the asymptotic region. We show that this confusion arises already in Maxwell theory that is often discussed as a prelude to the gravitational case. Finally, we discuss why the distinction has nonetheless remained largely unnoticed, and also point out that there are some important physical effects where only one of the notions gives the correct answer.     

An Novel Protocol for the Quantum Secure Multi-Party Summation Based on Two-Particle Bell States

A protocol for the quantum secure multi-party summation based on two-particle Bell states is proposed. In this protocol, two-particle Bell states are used as private information carriers. Without using the entangled character of Bell states, we also use Pauli matrices operations to encode information and Hadamard matrix to extract information. The proposed protocol can also resist various attacks and overcomes the problem of information leakage with acceptable efficiency. In theory, our protocol can be used to build complex secure protocols for other multiparty computations and also lots of other important applications in distributed networks.     

A highly Selective Fluorescent Sensor for Monitoring Cu<Superscript>2+</Superscript> Ion: Synthesis,Characterization and Photophysical Properties

A new fluorescent sensor, 4-allylamine-N-(N-salicylidene)-1,8-naphthalimide (1), anchoring a naphthalimide moiety as fluorophore and a Schiff base group as receptor, was synthesized and characterized. The photophysical properties of sensor 1 were conducted in organic solvents of different polarities. Our study revealed that, depending on the solvent polarity, the fluorescence quantum yields varied from 0.59 to 0.89. The fluorescent activity of the sensor was monitored and the sensor was consequently applied for the detection of Cu²⁺ with high selectivity over various metal ions by fluorescence quenching in Tris-HCl (pH = 7.2) buffer/DMF (1:1, v/v) solution. From the binding stoichiometry, it was indicated that a 1:1 complex was formed between Cu²⁺ and the sensor 1. The fluorescence intensity was linear with Cu²⁺ in the concentration range 0.5–5 μM. Moreso, the detection limit was calculated to be 0.32 μM, which is sufficiently low for good sensitivity of Cu²⁺ ion. The binding mode was due to the intramolecular charge transfer (ICT) and the coordination of Cu²⁺ with C = N and hydroxyl oxygen groups of the sensor 1. The sensor proved effective for Cu²⁺ monitoring in real water samples with recovery rates of 95–112.6 % obtained.     

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.

Open image in new window

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

     

Synthesis of Naked-eye Detectable Fluorescent 2<Emphasis Type="Italic">H-</Emphasis>chromen-2-One 2, 6-Dicyanoanilines: Effect of Substituents and pH on Its Luminous Behavior

A variety of new coumarin derivatives containing C-4 bridged 2,6-dicyanoanilines (4a-4d) were synthesized via multicomponent one pot approach. These novel sensors were characterized by spectral analysis and a series of pH sensing fluorescence studies were performed, the results indicating that the sensors are highly selective and more effective at various pH. The fluorescence colour changes at different pH could be directly detected by naked eyes.     

A Ratiometric and near-Infrared Fluorescent Probe for Imaging Cu<Superscript>2+</Superscript> in Living Cells and Animals

We have rationally constructed a novel ratiometric and near-infrared Cu²⁺ fluorescent probe based on a tricarbocyanine chromophore. The new probe NIR-Cu showed a ratiometric fluorescent response to Cu²⁺ with a large emission wavelength shift (up to 142 nm) in the far-red to near-infrared region. The probe also displayed a large variation in the fluorescence ratio (I₆₃₆/I₇₇₈) to Cu²⁺ species with high sensitivity and selectivity. Additionally, the developed probe NIR-Cu was suitable for fluorescence imaging of Cu²⁺ in living cells and mice.     

Novel Fluorometric Turn On Detection of Aluminum by Chalcone-Based Chemosensor in Aqueous Phase

A novel, 100% water-soluble chalcone based chemosensing receptor {1-[3-(2-Hydroxy-phenyl)-3-oxo-propenyl]-naphthalen-2-yloxy}-acetic acid, L was synthesized and characterized. The receptor L is designed based on the chelation enhanced fluorescence (CHEF) mechanism. The chemosensing properties of L were evaluated by UV–vis and fluorescence spectrometric methods. It exhibits highly selective recognition ability towards aluminum ions in water over other metal ions. The binding stoichiometry of L? Al³⁺ complex is 2:1 by means of Job’s plot and the detection limit is 5.66?×?10^??8 M.     

Study on the Interaction of the CpG Alternating DNA with CdTe Quantum Dots

A novel sensitive method for detection of DNA methylation was developed with thioglycollic acid (TGA)-capped CdTe quantum dots (QDs) as fluorescence probes. Recognition of methylated DNA sites would be useful strategy due to the important roles of methylation in disease occurrence and developmental processes. DNA methylation occurs most often at cytosine-guanine sites (CpG dinucleotides) of gene promoters. The QDs significantly interacted with hybridized unmethylated and methylated DNA. The interaction of CpG rich methylated and unmethylated DNA hybrid with quantum dots as an optical probe has been investigated by fluorescence spectroscopy and electrophoresis assay. The fluorescence intensity of QDs was highly dependent to unmethylated and methylated DNA. Specific site of CpG islands of Adenomatous polyposis coli (APC), a well-studied tumor suppressor gene, was used as the detection target. Under optimum conditions, upon the addition of unmethylated dsDNA, the fluorescence intensity increased in linear range from 1.0?×?10^??10 to 1.0?×?10^??6M with detection limit of 6.2?×?10^??11 M and on the other hand, the intensity of QDs showed no changes with addition of methylated dsDNA. We also demonstrated that the unmethylated and methylated DNA and QDs complexes showed different mobility in electrophoresis assay. This easy and reliable method could distinguish between methylated and unmethylated DNA sequences.     

Triangle Geometry of the Qubit State in the Probability Representation Expressed in Terms of the Triada of Malevich’s Squares

We map the density matrix of the qubit (spin-1/2) state associated with the Bloch sphere and given in the tomographic probability representation onto vertices of a triangle determining Triada of Malevich’s squares. The three triangle vertices are located on three sides of another equilateral triangle with the sides equal to\( \sqrt{2} \). We demonstrate that the triangle vertices are in one-to-one correspondence with the points inside the Bloch sphere and show that the uncertainty relation for the three probabilities of spin projections +1/2 onto three orthogonal directions has the bound determined by the triangle area introduced. This bound is related to the sum of three Malevich’s square areas where the squares have sides coinciding with the sides of the triangle. We express any evolution of the qubit state as the motion of the three vertices of the triangle introduced and interpret the gates of qubit states as the semigroup symmetry of the Triada of Malevich’s squares. In view of the dynamical semigroup of the qubit-state evolution, we constructed nonlinear representation of the group U(2).     

High-Power Diode-End-Pumped Slab Composite Tm:YLF Compact Laser

We design a continuous-wave Tm:YLF laser with a composite slab crystal end-pumped by two fiber-coupled laser diodes at room temperature. We achieve a maximum continuous wave output power of 105 W for the bonded slab Tm:YLF laser; the corresponding slope efficiency is 47.7% and the optical-to-optical conversion efficiency is 42.0% with respect to the incident pump power. The laser operated at 1,907.5 nm with a beam quality factor of M² ～3.2 at the highest output power.