Synthesis and Structural Characterizations of New Coordination Polymers Generated by the Interaction Between the Trinuclear Triangular SBU [Cu 3 (μ 3 -OH)(μ-pz) 3 ] 2+ and 4,4′-Bipyridine. 3°

The reactions of 4,4′-bipyridine with selected trinuclear triangular copper(II) complexes, [Cu3(μ3-OH)(μ-pz)3(RCOO)2Lx], [pz = pyrazolate anion, R = CH3(CH2)n (2 ≤ n ≤ 5); L = H2O, MeOH, EtOH] yielded a series of 1D coordination polymers (CPs) based on the repetition of [Cu3(μ3-OH)(μ-pz)3] secondary building units joined by bipyridine. The CPs were characterized by conventional analytical methods (elemental analyses, ESI-MS, IR spectra) and single crystal XRD determinations. An unprecedented 1D CP, generated through the bipyridine bridging hexanuclear copper clusters moieties, two 1D CPs presenting structural analogies, and two monodimensional tapes having almost exactly superimposable structures, were obtained. In one case, the crystal packing makes evident the presence of small, not-connected pores, accounting for ca. 6% of free cell volume.

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

Multibeam Network Design and Measurement for Triangular Array of Three Radiating Elements

Nowadays, more a more base stations are equipped with active conformal antennas. These antenna designs combine phase shift systems with multibeam networks providing multi-beam ability and interference rejection, which optimize multiple channel systems. GEODA is a conformal adaptive antenna system designed for satellite communications. Operating at 1.7 GHz with circular polarization, it is possible to track and communicate with several satellites at once thanks to its adaptive beam. The antenna is based on a set of similar triangular arrays that are divided in subarrays of three elements called `cells'. Transmission/Receiver (T/R) modules manage beam steering by shifting the phases. A more accurate steering of the antenna GEODA could be achieved by using a multibeam network. Several multibeam network designs based on Butler network will be presented

3x3 Multibeam Network for a Triangular Array of Three Radiating Elements

A multibeam antenna study based on Butler network will be undertaken in this document. These antenna designs combines phase shift systems with multibeam networks to optimize multiple channel systems. The system will work at 1.7 GHz with circular polarization. Specifically, result simulations and measurements of 3 element triangular subarray will be shown. A 45 element triangular array will be formed by the subarrays. Using triangular subarrays, side lobes and crossing points are reduced.

6x3 Microstrip Beam Forming Network for Multibeam Triangular Array

A six inputs and three outputs structure which can be used to obtain six simultaneous beams with a triangular array of 3 elements is presented. The beam forming network is obtained combining balanced and unbalanced hybrid couplers and allows to obtain six main beams with sixty degrees of separation in azimuth direction. Simulations and measurements showing the performance of the array and other detailed results are presented

Non-degenerate developable triangular Bézier patches

In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of non-degenerate developable triangular patches are provided.

Hysteresis phenomena in transverse galloping of triangular cross-section bodies

Transverse galloping is a type of aeroelastic instability characterised by large amplitude, low frequency oscillation of a structure in the direction normal to the mean wind direction. It normally appears in bodies with small stiffness and structural damping, provided the incident flow velocity is high enough. In the simplest approach transverse galloping can be considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which in turn can be described by using a quasi-steady description. In this frame it has been demonstrated that hysteresis phenomena in transverse galloping is related to the existence of inflection points in the curve giving the dependence with the angle of attack of the aerodynamic coefficient normal to the incident flow. Aiming at experimentally checking such a relationship between these inflection points and hysteresis, wind tunnel experiments have been conducted. Experiments have been restricted to isosceles triangular cross-section bodies, whose galloping behaviour is well documented. Experimental results show that, according to theoretical predictions, hysteresis takes place at the angles of attack where there are inflection points in the lift coefficient curve, provided that the body is prone to gallop at these angles of attack.

On the design and measurement of a novel non-orthogonal multi-beam network for triangular arrays of three radiating elements

An innovative dissipative multi-beam network for triangular arrays of three radiating elements is proposed. This novel network provides three orthogonal beams in θ0 elevation angle and a fourth one in the broadside steering direction. The network is composed of 90º hybrid couplers and fixed phase shifters. In this paper, a relation between network components, radiating element distance and beam steering directions will be shown. Application of the proposed dissipative network to the triangular cells of three radiating elements that integrate the intelligent antenna GEODA will be exhibited. This system works at 1.7 GHz, it has a 60º single radiating element beamwidth and a distance between array elements of 0.57 λ. Both beam patterns, theoretical and simulated, obtained with the network will be depicted. Moreover, the whole system, dissipative network built with GEODA cell array, has been measured in the anechoic chamber of the Radiation Group of Technical University of Madrid, demonstrating expected performance.

Study of a new 4×3 beam forming network for triangular arrays of three radiating elements

An innovative dissipative multi-beam network for triangular arrays of three radiating elements is proposed. This novel network provides three orthogonal beams in θ0 elevation angle and a fourth one in the broadside steering direction. The network is composed of 90º hybrid couplers and fixed phase shifters. In this paper, a relation between network components, radiating element distance and beam steering directions will be shown. Application of the proposed dissipative network to the triangular cells of three radiating elements that integrate the intelligent antenna GEODA will be exhibited. This system works at 1.7 GHz, it has a 60º single radiating element beamwidth and a distance between array elements of 0.57λ. Both beam patterns, theoretical and simulated, obtained with the network will be depicted. Moreover, the whole system, dissipative network built with GEODA cell array, has been measured in the anechoic chamber of the Radiation Group of Technical University of Madrid, demonstrating expected performance

Security of plug-and-play QKD arrangements with finite resources

The security of a passive plug-and-play QKD arrangement in the case of finite (resources) key lengths is analysed. It is assumed that the eavesdropper has full access to the channel so an unknown and untrusted source is assumed. To take into account the security of the BB84 protocol under collective attacks within the framework of quantum adversaries, a full treatment provides the well-known equations for the secure key rate. A numerical simulation keeping a minimum number of initial parameters constant as the total error sought and the number of pulses is carried out. The remaining parameters are optimized to produce the maximum secure key rate. Two main strategies are addressed: with and without two-decoy-states including the optimization of signal to decoy relationship.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Molecular origin of the mosaic sequence arrangements of higher primate α-globin duplication units

The human adult α-globin locus consists of three pairs of homology blocks (X, Y, and Z) interspersed with three nonhomology blocks (I, II, and III), and three Alu family repeats, Alu1, Alu2, and Alu3. It has been suggested that an ancient primate α-globin-containing unit was ancestral to the X, Y, and Z and the Alu1/Alu2 repeats. However, the evolutionary origin of the three nonhomologous blocks has remained obscure. We have now analyzed the sequence organization of the entire adult α-globin locus of gibbon (Hylobates lar). DNA segments homologous to human block I occur in both duplication units of the gibbon α-globin locus. Detailed interspecies sequence comparisons suggest that nonhomologous blocks I and II, as well as another sequence, IV, were all part of the ancestral α-globin-containing unit prior to its tandem duplication. However, sometime thereafter, block I was deleted from the human α1-globin-containing unit, and block II was also deleted from the α2-globin-containing unit in both human and gibbon. These were probably independent events both mediated by independent illegitimate recombination processes. Interestingly, the end points of these deletions coincide with potential insertion sites of Alu family repeats. These results suggest that the shaping of DNA segments in eukaryotic genomes involved the retroposition of repetitive DNA elements in conjunction with simple DNA recombination processes.

Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1