Універсал Директорії Української Народної Республіки про злуку з Західно-Українською Народною Республікою

Публікується документ: Акт про злуку – проведення державного об’єднання Української Народної Республіки з Західно-Українською Народною Республікою. Подається короткий опис подій та характеристика унікальності історичного документа.Публикуется документ: Акт о воссоединении – создании государственного объединения Украинской Народной Республики с Западно-Украинской Народной Республикой. приводится краткое описание событий и характеристика уникальности исторического документа.The publication of the document: “Act zluky” (“The Reunion Act”) – the agreement by which Ukrainian People’s Republic and West Ukrainian People’s Republic are reunited into one state. A short historical passage and specification of the document is given

Reconstructing the Equation of State for Dark Energy In the Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory (DCSGT). The universe we live in is taken as the real part of the whole spacetime ${\cal M}^4_C(J)$ which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann Equations but also the two constraint conditions $p_J=0$ and $J^2=1$ are obtained. Furthermore, using parametric $D_L(z)$ ansatz, we reconstruct the $\omega^{'}(z)$ and $V(\phi)$ for dark energy from real observational data. We find that in the two cases of $J=i,p_J=0$ and $J=\epsilon,p_J\neq 0$, the corresponding equations of state $\omega^{'}(z)$ remain close to -1 at present ($z=0$) and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime ${\cal M}^4_C(J)$, may be either ordinary complex ($J=i,p_J=0$) or hyperbolic complex ($J=\epsilon,p_J\neq 0$). And the fate of the universe would be Big Rip in the future.Comment: 5 pages, 5 figures, accepted by Commun. Theor. Phy

Triply Threaded [4]Rotaxanes

[4]Rotaxanes featuring three axles threaded through a single ring have been prepared through active metal template synthesis. Nickel-catalyzed sp3-sp3 homocouplings of alkyl bromide ‘half threads’ through 37- and 38-membered 2,2':6',2"-terpyridyl macrocycles generates triply-threaded [4]rotaxanes in up to 11 % yield. An analogous 39-membered macrocycle produced no rotaxane products under similar conditions. The constitutions of the [4]rotaxanes were determined by NMR spectroscopy and mass spectrometry. Doubly-threaded [3]rotaxanes were also obtained from the reactions but no [2]rotaxanes were isolated, suggesting that upon demetallation the axle of a singly-threaded rotaxane can slip through a macrocycle that is sufficiently large to accommodate three threads

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Observational Constraints on the Modified Gravity Model (MOG) Proposed by Moffat: Using the Magellanic System

A simple model for the dynamics of the Magellanic Stream (MS), in the framework of modified gravity models is investigated. We assume that the galaxy is made up of baryonic matter out of context of dark matter scenario. The model we used here is named Modified Gravity (MOG) proposed by Moffat (2005). In order to examine the compatibility of the overall properties of the MS under the MOG theory, the observational radial velocity profile of the MS is compared with the numerical results using the $\chi^2$ fit method. In order to obtain the best model parameters, a maximum likelihood analysis is performed. We also compare the results of this model with the Cold Dark Matter (CDM) halo model and the other alternative gravity model that proposed by Bekenstein (2004), so called TeVeS. We show that by selecting the appropriate values for the free parameters, the MOG theory seems to be plausible to explain the dynamics of the MS as well as the CDM and the TeVeS models.Comment: 14 pages, 3 Figures, accepted in Int. J. Theor. Phy

BES3 time of flight monitoring system

A Time of Flight monitoring system has been developed for BES3. The light source is a 442-443 nm laser diode, which is stable and provides a pulse width as narrow as 50 ps and a peak power as large as 2.6 W. Two optical-fiber bundles with a total of 512 optical fibers, including spares, are used to distribute the light pulses to the Time of Flight counters. The design, operation, and performance of the system are described.Comment: 8 pages 16 figures, submitted to NI

Thermodynamic properties of the d-density wave order in cuprates

We solve a popular effective Hamiltonian of competing $d$-density wave and d-wave superconductivity orders self-consistently at the mean-field level for a wide range of doping and temperature. The theory predicts a temperature dependence of the $d$-density wave order parameter seemingly inconsistent with the neutron scattering and $\mu$SR experiments of the cuprates. We further calculate thermodynamic quantities, such as chemical potential, entropy and specific heat. Their distinct features can be used to test the existence of the $d$-density wave order in cuprates.Comment: changed to 4 pages and 4 figures. More reference added. Accepted by Phys. Rev.

Molecular dynamics and energy landscape of decanethiolates in self-assembled monolayers on Au(111) studied by scanning tunneling microscopy

The energetics and dynamics of the various phases of decanethiolate self-assembled monolayers on Au(111) surfaces were studied with scanning tunneling microscopy. We have observed five different phases of the decanethiolate monolayer on Au(111): four ordered phases (β, δ, χ*, and φ) and one disordered phase (ε). We have determined the boundary free energies between the disordered and order phases by analyzing the thermally induced meandering of the domain boundaries. On the basis of these results, we are able to accurately predict the two-dimensional phase diagram of the decanethiolate/Au(111) system. The order-disorder phase transition of the χ* phase occurs at 295 K, followed by the order-disorder phase transition of the β phase at 325 K. Above temperatures of 325 K, only the densely packed φ and disordered ε phases remain. Our findings are in good agreement with the phase diagram of the decanethiolate/Au(111) system that was put forward by Poirier et al. [ Langmuir 2001, 17 (4), 1176-1183 ]

Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers

We demonstrate numerically the diffraction-free propagation of sub-wavelength sized optical beams through simple elements built of metal-dielectric multilayers. The proposed metamaterial consists of silver and a high refractive index dielectric, and is designed using the effective medium theory as strongly anisotropic and impedance matched to air. Further it is characterised with the transfer matrix method, and investigated with FDTD. The diffraction-free behaviour is verified by the analysis of FWHM of PSF in the function of the number of periods. Small reflections, small attenuation, and reduced Fabry Perot resonances make it a flexible diffraction-free material for arbitrarily shaped optical planar elements with sizes of the order of one wavelength.Comment: 5 pages, 4 figure

Action of Singular Instantons of Hawking-Turok Type

Using Kaluza-Klein technique we show that the singularity of Hawking-Turok type has a fixed point (bolt) contribution to the action in addition to the usual boundary contribution. Interestingly by adding this contribution we can obtain a simple expression for the total action which is feasible for both regular and singular instantons. Our result casts doubt on the constraint proposed by Turok in the recent calculation in which Vilenkin's instantons are regarded as a limit of certain constrained instantons.Comment: 14 pages, LaTe