Eucalyptus camaldulensis known as the river red gum, is a tree, endemic to Australia. It has smooth white or cream-coloured bark, lance-shaped or curved adult leaves, flower buds in groups of seven or nine, white flowers and hemispherical fruit with the valves extending beyond the rim. A familiar and iconic tree, it is seen along many watercourses across inland Australia, providing shade in the extreme temperatures of central Australia. Eucalyptus camaldulensis is a tree that grows to a height of 20 metres but sometimes to 45 metres and does not develop a lignotuber; the bark is smooth white or cream-coloured with patches of pink or brown. There is loose, rough slabs of rough bark near the base; the juvenile leaves are lance-shaped, 80 -- 13 -- 25 mm wide. Adult leaves are lance-shaped to curved, the same dull green or geyish green colour on both sides, 50–300 mm long and 7–32 mm wide on a petiole 8–33 mm long; the flower buds are arranged in groups of seven, nine or sometimes eleven, in leaf axils on a peduncle 5–28 mm long, the individual flowers on pedicels 2–10 mm long.

Mature buds are oval to more or less spherical, green to creamy yellow, 6–9 mm long and 4–6 mm wide with a prominently beaked operculum 3–7 mm long. Flowering occurs in summer and the flowers are white; the fruit is a woody, hemispherical capsule 2–5 mm long and 4–10 mm wide on a pedicel 3–12 mm long with the valves raised above the rim. The limbs of river red gums, sometimes whole trees fall without warning so that camping or picnicking near them is dangerous if a tree has dead limbs or the tree is under stress. Eucalyptus camaldulensis was first formally described in 1832 by Friedrich Dehnhardt who published the description in Catalogus Plantarum Horti Camaldulensis. Seven subspecies of E. camaldulensis have been described and accepted by the Australian Plant Census. The most variable character is the shape and size of the operculum, followed by the arrangement of the stamens in the mature buds and the density of veins visible in the leaves; the subspecies are: Eucalyptus camaldulensis subsp.

Acuta Ian Brooker & M. W. McDonald has mature flower buds with a pointed operculum 6–9 mm long and erect stamens and broadly lance-shaped or egg-shaped juvenile leaves. Arida Ian Brooker & M. W. McDonald has bluish green adult leaves with only a few veins and mature flowers buds with a curved to rounded operculum 3–7 mm long. Subsp. Camaldulensis has a beaked operculum, incurved or irregularly bent stamens and narrow lance-shaped juvenile leaves. Minima Ian Brooker & M. W. McDonald has mature flower buds that are small with a conical operculum 2–4 mm long and broad juvenile leaves that are covered with a powdery bloom. Obtusa Ian Brooker & M. W. McDonald has white, powdery bark in some months and mature flower buds with a curved, conical operculum 4–7 mm long. Refulgens Ian Brooker & M. W. McDonald has glossy green adult leaves with a dense network of veins. Simulata Ian Brooker & Kleinig. has a horn-shaped operculum 9–16 mm long. The specific epithet is a reference to a private estate garden near the Camaldoli monastery in Naples, where Frederick Dehnhardt was the chief gardener.

The type specimen was grown in the gardens from seed collected in 1817 near Condobolin by Allan Cunningham, was grown there for about one hundred years before being removed in the 1920s. Although Dehnhardt was the first to formally describe E. camaldulensis, his book was unknown to the botanical community. In 1847 Diederich von Schlechtendal gave the species the name Eucalyptus rostrata but the name was illegitimate because it had been applied by Cavanilles to a different species. In the 1850s, Ferdinand von Mueller labelled some specimens of river red gum as Eucalyptus longirostris and in 1856 Friedrich Miquel published a description of von Mueller's specimens, formalising the name E. longirostris. In 1934, William Blakely recognised Dehnhardt's priority and the name E. camaldulensis for river red gum was accepted. Northern Territory aboriginal names for this species are: aper, aper or per, aylpele, ngapiri, yitara apara, piipalya, kunjumarra and ngapiri. Dimilan is the name of this tree in the Miriwoong language of the Kimberley.

Eucalyptus camaldulensis has the widest natural distribution of any eucalyptus species. It is found along waterways and there are only a few locations where the species is found away from a watercourse. Subspecies acuta is common along rivers from south of Cape York Peninsula in Queensland to the north west slopes and plains of New South Wales but is absent from coastal areas and the arid inland. Subspecies arida has the widest distribution of the subspecies and is found in all mainland states except Victoria, it grows in arid regions but only. Subspecies camaldulensis is the dominant eucalypt along the Murray-Darling river system and its tributaries, it occurs on the Eyre and Yorke Peninsulas and Kangaroo Island in South Australia and in some locations along the Hunter River in New South Wales. I

In the field of wireless communication, macrodiversity is a kind of space diversity scheme using several receiver antennas and/or transmitter antennas for transferring the same signal. The distance between the transmitters is much longer than the wavelength, as opposed to microdiversity where the distance is in the order of or shorter than the wavelength. In a cellular network or a wireless LAN, macro-diversity implies that the antennas are situated in different base station sites or access points. Receiver macro-diversity is a form of antenna combining, requires an infrastructure that mediates the signals from the local antennas or receivers to a central receiver or decoder. Transmitter macro-diversity may be a form of simulcasting, where the same signal is sent from several nodes. If the signals are sent over the same physical channel, the transmitters are said to form a single frequency network—a term used in the broadcasting world; the aim is to combat fading and to increase the received signal strength and signal quality in exposed positions in between the base stations or access points.

Macro diversity may facilitate efficient broadcasting and multicasting services, where the same frequency channel can be used for all transmitters sending the same information. The diversity scheme may be based on transmitter macro-diversity and/or receiver macro-diversity. CDMA soft handoff: UMTS softer handover. OFDM and frequency-domain equalization based Single Frequency Networks are a form of transmitter macrodiversity used in broadcasting networks such as DVB-T and DAB Dynamic Single Frequency Networks, where a scheduling scheme adapts the SFN formations dynamically to traffic conditions and/or receiver conditions 802.16e macro diversity handover 3GPP long term evolution multicast-broadcast single frequency network, making it possible to efficiently send the same data to many mobiles in adjacent cells. Cooperative diversity, for example 3GPP long term evolution coordinated multipoint transmission/reception, making it possible to increase the data rate to a mobile situated in the overlap of several base station transmission ranges.

The baseline form of macrodiversity is called single-user macrodiversity. In this form, single user which may have multiple antennas, communicates with several base stations. Therefore, depending on the spatial degree of freedom of the system, user may transmit or receive multiple independent data streams to/from base stations in the same time and frequency resource. Single-user macrodiversity Uplink macrodiversity Downlink macrodiversityIn next more advanced form of macrodiversity, multiple distributed users communicate with multiple distributed base stations in the same time and frequency resource; this form of configuration has been shown to utilize available spatial DoF optimally and thus increasing the cellular system capacity and user capacity considerably. Multi-user macrodiversity Macrodiversity multiple access channel Macrodiversity broadcast channel The macrodiversity multi-user MIMO uplink communication system considered here consists of N distributed single antenna users and n R distributed single antenna base stations.

Following the well established narrow band flat fading MIMO system model, input-output relationship can be given as y = H x + n where y and x are the receive and transmit vectors and H and n are the macrodiversity channel matrix and the spatially uncorrelated AWGN noise vector, respectively. The power spectral density of AWGN noise is assumed to be N 0; the i, j th element of H, h i j represents the fading coefficient of the i, j th constituent link which in this particular case, is the link between j th user and the i th base station. In macrodiversity scenario, E = g i j ∀ i, j,where g i, j is called the average link gain giving average link SNR of g i j N 0; the macrodiversity power profile matrix can thus be defined as G = ( g 11 … g 1 N g 21 … g 2 N … … …

In the mathematical subject of group theory, a co-Hopfian group is a group, not isomorphic to any of its proper subgroups. The notion is dual to that of a Hopfian group, named after Heinz Hopf. A group G is called co-Hopfian if whenever φ: G → G is an injective group homomorphism φ is surjective, φ = G; every finite group G is co-Hopfian. The infinite cyclic group Z is not co-Hopfian since f: Z → Z, f = 2 n is an injective but non-surjective homomorphism; the additive group of real numbers R is not co-Hopfian, since R is an infinite-dimensional vector space over Q and therefore, as a group R ≅ R × R. The additive group of rational numbers Q and the quotient group Q / Z are co-Hopfian; the multiplicative group Q ∗ of nonzero rational numbers is not co-Hopfian, since the map Q ∗ → Q ∗, q ↦ sign ⁡ q 2 is an injective but non-surjective homomorphism. In the same way, the group Q + ∗ of positive rational numbers is not co-Hopfian; the multiplicative group C ∗ of nonzero complex numbers is not co-Hopfian.

For every n ≥ 1 the free abelian group Z n is not co-Hopfian. For every n ≥ 1 the free group F n is not co-Hopfian. There exists a finitely generated non-elementary free group, co-Hopfian, thus a subgroup of finite index in a finitely generated co-Hopfian group need not be co-Hopfian, being co-Hopfian is not a quasi-isometry invariant for finitely generated groups. Baumslag–Solitar groups B S, where m ≥ 1, are not co-Hopfian. If G is the fundamental group of a closed aspherical manifold with nonzero Euler characteristic G is co-Hopfian. If G is the fundamental group of a closed connected oriented irreducible 3-manifold M G is co-Hopfian if and only if no finite cover of M is a torus bundle over the circle or the product of a circle and a closed surface. If G is an irreducible lattice in a real semi-simple Lie group and G is not a free group G is co-Hopfian. E.g. this fact applies to the group S L for n ≥ 3. If G is a one-ended torsion-free word-hyperbolic group G is co-Hopfian, by a result of Sela.

If G is the fundamental group of a complete finite volume smooth Riemannian n-manifold of pinched negative curvature G is co-Hopfian. The mapping class group of a closed hyperbolic surface is co-Hopfian; the group Out is co-Hopfian. Delzant and Polyagailo gave a characterization of co-Hopficity for geometrically finite Kleinian groups of isometries of H n without 2-torsion. A right-angled Artin group A is not co-Hopfian. A finitely generated torsion-free nilpotent group G may be either co-Hopfian or not co-Hopfian, depending on the properties of its associated rational Lie algebra. If G is a hyperbolic group and φ: G → G is an injective but non-surjective endomorphism of G either φ k is parabolic for some k >1 or G splits over a cyclic or a parabolic subgroup. Grigorchuk group G of intermediate growth is not co-Hopfian. Thomposon group F is not co-Hopfian. There exists a finitely generated group G, not co-Hopfian but has Kazhdan's property. If G is Higman's universal finitely presented group G is not co-Hopfian, G cannot be embedded in a finitely generated recursively presented co-Hopfian group.

A group G is called finitely co-Hopfian if