Political theory and theoretical physics

This paper argues, somewhat along a Simmelian line, that political theory may produce practical and universal theories like those developed in theoretical physics. The reasoning behind this paper is to show that the theory of ‘basic democracy’ may be true by way of comparing it to Einstein’s Special Relativity – specifically concerning the parameters of symmetry, unification, simplicity, and utility. These parameters are what make a theory in physics as meeting them not only fits with current knowledge, but also produces paths towards testing (application). As the theory of ‘basic democracy’ may meet these same parameters, it could settle the debate concerning the definition of democracy. This will be argued firstly by discussing what the theory of ‘basic democracy’ is and why it differs from previous work; secondly by explaining the parameters chosen (as in why these and not others confirm or scuttle theories); and thirdly by comparing how Special Relativity and the theory of ‘basic democracy’ may match the parameters.

Ions in motor vehicle exhaust and their dispersion near busy roads

Measurements in the exhaust plume of a petrol-driven motor car showed that molecular cluster ions of both signs were present in approximately equal amounts. The emission rate increased sharply with engine speed while the charge symmetry remained unchanged. Measurements at the kerbside of nine motorways and five city roads showed that the mean total cluster ion concentration near city roads (603 cm-3) was about one-half of that near motorways (1211 cm-3) and about twice as high as that in the urban background (269 cm-3). Both positive and negative ion concentrations near a motorway showed a significant linear increase with traffic density (R2=0.3 at p<0.05) and correlated well with each other in real time (R2=0.87 at p<0.01). Heavy duty diesel vehicles comprised the main source of ions near busy roads. Measurements were conducted as a function of downwind distance from two motorways carrying around 120-150 vehicles per minute. Total traffic-related cluster ion concentrations decreased rapidly with distance, falling by one-half from the closest approach of 2m to 5m of the kerb. Measured concentrations decreased to background at about 15m from the kerb when the wind speed was 1.3 m s-1, this distance being greater at higher wind speed. The number and net charge concentrations of aerosol particles were also measured. Unlike particles that were carried downwind to distances of a few hundred metres, cluster ions emitted by motor vehicles were not present at more than a few tens of metres from the road.

Three-dimensional hydrogen-bonded structures in the guanidinium salts of the monocyclic dicarboxylic acids rac-trans-cyclohexane-1,2-dicarboxylic acid (2:1, anhydrous), isophthalic acid (1:1, monohydrate) and terephthalic acid (2:1, trihydrate).

The structures of bis(guanidinium)rac-trans-cyclohexane-1,2-dicarboxylate, 2(CH6N3+) C8H10O4- (I), guanidinium 3-carboxybenzoate monohydrate CH6N3+ C8H5O4- . H2O (II) and bis(guanidinium) benzene-1,4-dicarboxylate trihydrate, 2(CH6N3+) C8H4O4^2- . 3H2O (III) have been determined and the hydrogen bonding in each examined. All three compounds form three-dimensional hydrogen-bonded framework structures. In anhydrous (I), both guanidinium cations give classic cyclic R2/2(8) N--H...O,O'(carboxyl) and asymmetric cyclic R1/2(6) hydrogen-bonding interactions while one cation gives an unusual enlarged cyclic interaction with O acceptors of separate ortho-related carboxyl groups [graph set R2/2(11)]. Cations and anions also associate across inversion centres giving cyclic R2/4(8) motifs. In the 1:1 guanidinium salt (II), the cation gives two separate cyclic R1/2(6) interactions, one with a carboxyl O-acceptor, the other with the water molecule of solvation. The structure is unusual in that both carboxyl groups give short inter-anion O...H...O contacts, one across a crystallographic inversion centre [2.483(2)\%A], the other about a two-fold axis of rotation [2.462(2)\%A] with a half-occupancy hydrogen delocalized on the symmetry element in each. The water molecule links the cation--anion ribbon structures into a three-dimensional framework. In (III), the repeating molecular unit comprises a benzene-1,4-dicarboxylate dianion which lies across a crystallographic inversion centre, two guanidinium cations and two water molecules of solvation (each set related by two-fold rotational symmetry), and a single water molecule which lies on a two-fold axis. Each guanidinium cation gives three types of cyclic interactions with the dianions: one R^1^~2~(6), the others R2/3(8) and R3/3(10) (both of these involving the water molecules), giving a three-dimensional structure through bridges down the b cell direction. The water molecule at the general site also forms an unusual cyclic R2/2(4) homodimeric association across an inversion centre [O--H...O, 2.875(2)\%A]. The work described here provides further examples of the common cyclic guanidinium cation...carboxylate anion hydrogen-bonding associations as well as featuring other less common cyclic motifs.

catena-Poly[[[diaquacobalt(II)]-mu-(3,5-dinitro-2-oxidobenzoato)-kappa3O1,O2:O1'-[tetraaquacobalt(II)]-mu-(3,5-dinitro-2-oxidobenzoato)-kappa3-O1:O1',O2] dihydrate]

In the structure of polymeric title compound, {[Co2(C7H2N2O7)2(H2O)6] . 2H2O}n from the reaction of 3,5-dinitrosalicylic acid with cobalt(II) acetate, both slightly distorted octahedral Co(II) centres have crystallographic inversion symmetry. The coordination sphere about one Co centre comprises four O donors from two bidentate chelate O(phenolate), O(carboxyl) and bridging dianionic ligands and two water molecules [Co-O range, 2.0249(11)-2.1386(14)A] while that about the second Co centre has four water molecules and two bridging carboxyl O donor atoms [Co-O range, 2.0690(14)-2.1364(11)A]. The coordinated water molecules as well as the water molecules of solvation give water-water and water-carboxyl hydrogen-bonding interactions in the three-dimensional framework structure.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Pseudo-merohedral twinning in the structure of the hydrated 1:1 proton-transfer compound of 5-sulfosalicylic acid with 4-aminopyridine

The structure of the pseudo-merohedrally twinned crystal of the 1:1 proton-transfer compound of 5-sulfosalicylic acid (3-carboxy-4-hydroxybenzenesulfonic acid) with 4-aminopyridine: 4-aminopyridinium 3-carboxy-4-hydroxybenzenesulfonate sesquihydrate has been determined at 180 K and the hydrogen-bonding pattern is described. Crystals of the compound are monoclinic with space group P21/c, with unit cell dimensions a = 35.2589(8), b = 7.1948(1), c = 24.5851(5) Å, β = 110.373(2)o, and Z = 16. The monoclinic asymmetric unit comprises four cation-anion pairs and six water molecules of solvation with only the pyridinium cations having pseudo-symmetry as a result of inter-cation aromatic ring π-π stacking effects. Extensive hydrogen bonding gives a three-dimensional framework structure.

Patterns

In recent years there has been widespread interest in patterns, perhaps provoked by a realisation that they constitute a fundamental brain activity and underpin many artificial intelligence systems. Theorised concepts of spatial patterns including scale, proportion, and symmetry, as well as social and psychological understandings are being revived through digital/parametric means of visualisation and production. The effect of pattern as an ornamental device has also changed from applied styling to mediated dynamic effect. The interior has also seen patterned motifs applied to wall coverings, linen, furniture and artefacts with the effect of enhancing aesthetic appreciation, or in some cases causing psychological and/or perceptual distress (Rodemann 1999). ----- ----- While much of this work concerns a repeating array of surface treatment, Philip Ball’s The Self- Made Tapestry: Pattern Formation in Nature (1999) suggests a number of ways that patterns are present at the macro and micro level, both in their formation and disposition. Unlike the conventional notion of a pattern being the regular repetition of a motif (geometrical or pictorial) he suggests that in nature they are not necessarily restricted to a repeating array of identical units, but also include those that are similar rather than identical (Ball 1999, 9). From his observations Ball argues that they need not necessarily all be the same size, but do share similar features that we recognise as typical. Examples include self-organized patterns on a grand scale such as sand dunes, or fractal networks caused by rivers on hills and mountains, through to patterns of flow observed in both scientific experiments and the drawings of Leonardo da Vinci.

Multiple human single-stranded DNA binding proteins function in genome maintenance : structural, biochemical and functional analysis

DNA exists predominantly in a duplex form that is preserved via specific base pairing. This base pairing affords a considerable degree of protection against chemical or physical damage and preserves coding potential. However, there are many situations, e.g. during DNA damage and programmed cellular processes such as DNA replication and transcription, in which the DNA duplex is separated into two singlestranded DNA (ssDNA) strands. This ssDNA is vulnerable to attack by nucleases, binding by inappropriate proteins and chemical attack. It is very important to control the generation of ssDNA and protect it when it forms, and for this reason all cellular organisms and many viruses encode a ssDNA binding protein (SSB). All known SSBs use an oligosaccharide/oligonucleotide binding (OB)-fold domain for DNA binding. SSBs have multiple roles in binding and sequestering ssDNA, detecting DNA damage, stimulating strand-exchange proteins and helicases, and mediation of protein–protein interactions. Recently two additional human SSBs have been identified that are more closely related to bacterial and archaeal SSBs. Prior to this it was believed that replication protein A, RPA, was the only human equivalent of bacterial SSB. RPA is thought to be required for most aspects of DNA metabolism including DNA replication, recombination and repair. This review will discuss in further detail the biological pathways in which human SSBs function.

meso-Porphyrinylphosphine Oxides: Mono- and Bidentate Ligands for Supramolecular Chemistry and the Crystal Structures of Monomeric [10,20-Diphenylporphyrinatonickel(II)-5,15-diyl]-bis-[P(O)Ph2] and Polymeric Self-Coordinated ([10,20-Diphenylporphyrinatozinc(II)-5,15-diyl]-bis-[P(O)Ph2])

A series of porphyrins substituted in one or two meso-positions by diphenylphosphine oxide groups has been prepared by the palladium catalysed reaction of diphenylphosphine or its oxide with the corresponding bromoporphyrins. Compounds {MDPP-[P(O)Ph2]n} (M = H2, Ni, Zn; H2DPP = 5,15-diphenylporphyrin; n = 1, 2) were isolated in yields of 60-95%. The reaction is believed to proceed via the conventional oxidative addition, phosphination and reductive elimination steps, as the stoichiometric reaction of η1-palladio(II) porphyrin [PdBr(H2DPP)(dppe)] (H2DPP = 5,15-diphenylporphyrin; dppe = 1,2-bis(diphenylphosphino)ethane) with diphenylphosphine oxide also results in the desired mono-porphyrinylphosphine oxide [H2DPP-P(O)Ph2]. Attempts to isolate the tertiary phosphines failed due to their extreme air-sensitivity. Variable temperature 1H NMR studies of [H2DPP-P(O)Ph2] revealed an intrinsic lack of symmetry, while fluorescence spectroscopy showed that the phosphine oxide group does not behave as a "heavy atom" quencher. The electron withdrawing effect of the phosphine oxide group was confirmed by voltammetry. The ligands were characterised by multinuclear NMR and UV-visible spectroscopy as well as mass spectrometry. Single crystal X-ray crystallography showed that the bis(phosphine oxide) nickel(II) complex {[NiDPP-[P(O)Ph2]2} is monomeric in the solid state, with a ruffled porphyrin core and the two P=O fragments on the same side of the average plane of the molecule. On the other hand, the corresponding zinc(II) complex formed infinite chains through coordination of one Ph2PO substituent to the neighbouring zinc porphyrin through an almost linear P=O---Zn unit, leaving the other Ph2PO group facing into a parallel channel filled with disordered water molecules. These new phosphine oxides are attractive ligands for supramolecular porphyrin chemistry.

Raman spectroscopy of selected borate minerals of the pinakiolite group

The Raman spectra of a series of related minerals of the pinakiolite group of minerals have been collected and the spectra related to the mineral structure. These minerals are based upon an isolated BO33- ion. The site symmetry is reduced from D3h to C1. Intense Raman bands are observed for the minerals takeuchiite, pinakiolite, fredrikssonite and azoproite at 1084, 1086, 1086 and 1086 cm-1. These bands are assigned to the ν1 BO33- symmetric stretching mode. Low intensity Raman bands are observed for the minerals at 1345, 1748; 1435, 1748; 1435, 1750; 1436, 1749 cm-1. One probable assignment is to ν3 BO33- antisymmetric stretching mode. Intense Raman bands of takeuchiite, pinakiolite, fredrikssonite and azoproite at 712 cm-1 attributed to the ν2 out-of-plane bending mode. Importantly, through the comparison of the Raman spectra, the molecular structure of borate minerals with ill-defined structures can be obtained.

A Raman spectroscopic study of M2+M3+ sulfate minerals, römerite Fe2+Fe23+ (SO4)4· 14H2O and botryogen Mg2+Fe3+ (SO4)2(OH)·7H2O

The mixed valency (M2+M3+) sulphate minerals, römerite Fe2+Fe23+(SO4)4•14H2O and botryogen Mg2+Fe3+(SO4)2(OH).7H2O have been studied by Raman spectroscopy. The Raman spectra of the two types of crystals proved very similar but not identical. The observation of two symmetric stretching modes confirmed the presence of the two non-equivalent sulphate units in the römerite structure. The observation of multiple bands in the antisymmetric stretching region and in the bending regions proves the symmetry of the sulphate anion is significantly reduced in the römerite structure. The number of Raman bands related to the (SO4)2- symmetric and antisymmetric vibrations support the X-ray single crystal structure conclusion that two symmetrically distinct S6+ are present in the structure of botryogen. Römerite is a mineral of environmental significance as it is commonly found in tailings and dumps.

Similarity metrics within a point of view

In vector space based approaches to natural language processing, similarity is commonly measured by taking the angle between two vectors representing words or documents in a semantic space. This is natural from a mathematical point of view, as the angle between unit vectors is, up to constant scaling, the only unitarily invariant metric on the unit sphere. However, similarity judgement tasks reveal that human subjects fail to produce data which satisfies the symmetry and triangle inequality requirements for a metric space. A possible conclusion, reached in particular by Tversky et al., is that some of the most basic assumptions of geometric models are unwarranted in the case of psychological similarity, a result which would impose strong limits on the validity and applicability vector space based (and hence also quantum inspired) approaches to the modelling of cognitive processes. This paper proposes a resolution to this fundamental criticism of of the applicability of vector space models of cognition. We argue that pairs of words imply a context which in turn induces a point of view, allowing a subject to estimate semantic similarity. Context is here introduced as a point of view vector (POVV) and the expected similarity is derived as a measure over the POVV's. Different pairs of words will invoke different contexts and different POVV's. Hence the triangle inequality ceases to be a valid constraint on the angles. We test the proposal on a few triples of words and outline further research.

A Raman spectroscopic study of copiapites Fe2+Fe3+(SO4)6(OH)2 · 20H2O: environmental implications

Raman spectroscopy has been used to study selected mineral samples of the copiapite group. Copiapite (Fe2+Fe3+(SO4)6(OH)2 · 20H2O) is a secondary mineral formed through the oxidn. of pyrite. Minerals of the copiapite group have the general formula AFe4(SO4)6(OH)2 · 20H2O, where A has a + 2 charge and can be either magnesium, iron, copper, calcium and/or zinc. The formula can also be B2/3Fe4(SO4)6(OH)2 · 20H2O, where B has a + 3 charge and may be either aluminum or iron. For each mineral, two Raman bands are obsd. at around 992 and 1029 cm-1, assigned to the (SO4)2-ν1 sym. stretching mode. The observation of two bands provides evidence for the existence of two non-equiv. sulfate anions in the mineral structure. Three Raman bands at 1112, 1142 and 1161 cm-1 are obsd. in the Raman spectrum of copiapites, indicating a redn. of symmetry of the sulfate anion in the copiapite structure. This redn. in symmetry is supported by multiple bands in the ν2 and ν4(SO4)2- spectral regions.

Single crystal Raman spectroscopy of brandholzite Mg[Sb(OH)6]2•6H2O and bottinoite Ni[Sb(OH)6]2•6H2O and the polycrystalline Raman spectrum of mopungite Na[Sb(OH)6]

The single crystal Raman spectra of minerals brandholzite and bottinoite, formula M[Sb(OH)6]2•6H2O, where M is Mg+2 and Ni+2 respectively, and the non-aligned Raman spectrum of mopungite, formula Na[Sb(OH)6], are presented for the first time. The mixed metal minerals comprise of alternating layers of [Sb(OH)6]-1 octahedra and mixed [M(H2O)6]+2 / [Sb(OH)6]-1 octahedra. Mopungite comprises hydrogen bonded layers of [Sb(OH)6]-1 octahedra linked within the layer by Na+ ions. The spectra of the three minerals were dominated by the Sb-O symmetric stretch of the [Sb(OH)6]-1 octahedron, which occurs at approximately 620 cm-1. The Raman spectrum of mopungite showed many similarities to spectra of the di-octahedral minerals informing the view that the Sb octahedra gave rise to most of the Raman bands observed, particularly below 1200 cm-1. Assignments have been proposed based on the spectral comparison between the minerals, prior literature and density field theory calculations of the vibrational spectra of the free [Sb(OH)6]-1 and [M(H2O)6]+2 octahedra by a model chemistry of B3LYP/6-31G(d) and lanl2dz for the Sb atom. The single crystal data spectra showed good mode separation, allowing the majority of the bands to be assigned a symmetry species of A or E.

Single-crystal Raman spectroscopy of natural schafarzikite FeSb2O4 from Pernek, Slovak Republic

The single crystal Raman spectra of natural mineral schafarzikite FeSb2O4 from the Pernek locality of the Slovak Republic are presented for the first time. Raman spectra of natural mineral apuanite Fe2+Fe43+Sb4O12S, originating from the Apuan Alps in Italy, as well as spectra of synthetic ZnSb2O4 and arsenite mineral trippkeite CuAs2O4 are also presented for the first time. The spectra of the antimonite minerals are characterized by a strong band in the region 660 – 680 cm-1 with shoulders on either side, and a band of medium intensity near 300 cm-1. The spectrum of the arsenite mineral is characterized by a medium band near 780 cm-1 with a shoulder on the high wavenumber side and a strong band at 370 cm-1. Assignments are proposed based on the spectral comparison between the compounds, symmetry modes of the bands and prior literature. The single crystal spectra of schafarzikite showed good mode separation, allowing bands to be assigned a symmetry species of A1g, B1g, B2g or Eg.