Obstructions to the existence of compact Clifford–Klein forms for tangential symmetric spaces

For a homogeneous space [Formula: see text] of reductive type, we consider the tangential homogeneous space [Formula: see text]. In this paper, we give obstructions to the existence of compact Clifford–Klein forms for such tangential symmetric spaces and obtain new tangential symmetric spaces which do not admit compact Clifford–Klein forms. As a result, in the class of irreducible classical semisimple symmetric spaces, we have only two types of symmetric spaces which are not proved not to admit compact Clifford–Klein forms. The existence problem of compact Clifford–Klein forms for homogeneous spaces of reductive type, which was initiated by Kobayashi in 1980s, has been studied by various methods but is not completely solved yet. On the other hand, the one for tangential homogeneous spaces has been studied since 2000s and an analogous criterion was proved by Kobayashi and Yoshino. In concrete examples, further works are needed to verify Kobayashi–Yoshino’s condition by direct calculations. In this paper, some easy-to-check necessary conditions ([Formula: see text][Formula: see text]obstructions) for the existence of compact quotients in the tangential setting are given, and they are applied to the case of symmetric spaces. The conditions are related to various fields of mathematics such as associated pair of symmetric space, Calabi–Markus phenomenon, trivializability of vector bundle (parallelizability, Pontrjagin class), Hurwitz–Radon number and Pfister’s theorem (the existence problem of common zero points of polynomials of odd degree).

Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases

We study spin- and mass-imbalanced mixtures of spin-1/2 fermions interacting via an attractive contact potential in one spatial dimension. Specifically, we address the influence of unequal particle masses on the pair formation by means of the complex Langevin method. By computing the pair-correlation function and the associated pair-momentum distribution we find that inhomogeneous pairing is present for all studied spin polarizations and mass imbalances. To further characterize the pairing behavior, we analyze the density-density correlations in momentum space, the so-called shot noise, which is experimentally accessible through time-of-flight imaging. At finite spin polarization, the latter is known to show distinct maxima at momentum configurations associated with the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) instability. Besides those maxima, we find that additional features emerge in the noise correlations when mass imbalance is increased, revealing the stability of FFLO-type correlations against mass imbalance and furnishing an experimentally accessible signature to probe this type of pairing.

Evolution of the Piscine orthoreovirus Genome Linked to Emergence of Heart and Skeletal Muscle Inflammation in Farmed Atlantic Salmon (Salmo salar)

Heart and skeletal muscle inflammation (HSMI) in farmed Atlantic salmon (Salmo salar) was first diagnosed in Norway in 1999. The disease is caused by Piscine orthoreovirus-1 (PRV-1). The virus is prevalent in farmed Atlantic salmon, but not always associated with disease. Phylogeny and sequence analyses of 31 PRV-1 genomes collected over a 30-year period from fish with or without HSMI, grouped the viral sequences into two main monophylogenetic clusters, one associated with HSMI and the other with low virulent PRV-1 isolates. A PRV-1 strain from Norway sampled in 1988, a decade before the emergence of HSMI, grouped with the low virulent HSMI cluster. The two distinct monophylogenetic clusters were particularly evident for segments S1 and M2. Only a limited number of amino acids were unique to the association with HSMI, and they all located to S1 and M2 encoded proteins. The observed co-evolution of the S1-M2 pair coincided in time with the emergence of HSMI in Norway, and may have evolved through accumulation of mutations and/or segment reassortment. Sequences of S1-M2 suggest selection of the HSMI associated pair, and that this segment pair has remained almost unchanged in Norwegian salmon aquaculture since 1997. PRV-1 strains from the North American Pacific Coast and Faroe Islands have not undergone this evolution, and are more closely related to the PRV-1 precursor strains not associated with clinical HSMI.

Gas and galaxies in filaments between clusters of galaxies

We have performed a multi-wavelength analysis of two galaxy cluster systems selected with the thermal Sunyaev-Zel’dovich (tSZ) effect and composed of cluster pairs and an inter-cluster filament. We have focused on one pair of particular interest: A399-A401 at redshiftz~ 0.073 seperated by 3 Mpc. We have also performed the first analysis of one lower-significance newly associated pair: A21-PSZ2 G114.09-34.34 atz~ 0.094, separated by 4.2 Mpc. We have characterised the intra-cluster gas using the tSZ signal fromPlanckand, when possible, the galaxy optical and infrared (IR) properties based on two photometric redshift catalogues: 2MPZ and WISExSCOS. From the tSZ data, we measured the gas pressure in the clusters and in the inter-cluster filaments. In the case of A399-A401, the results are in perfect agreement with previous studies and, using the temperature measured from the X-rays, we further estimate the gas density in the filament and findn0= (4.3 ± 0.7) × 10-4cm-3. The optical and IR colour–colour and colour–magnitude analyses of the galaxies selected in the cluster system, together with their star formation rate, show no segregation between galaxy populations, both in the clusters and in the filament of A399-A401. Galaxies are all passive, early type, and red and dead. The gas and galaxy properties of this system suggest that the whole system formed at the same time and corresponds to a pre-merger, with a cosmic filament gas heated by the collapse. For the other cluster system, the tSZ analysis was performed and the pressure in the clusters and in the inter-cluster filament was constrained. However, the limited or nonexistent optical and IR data prevent us from concluding on the presence of an actual cosmic filament or from proposing a scenario.

On the Ornstein–Zernike equation for stationary cluster processes and the random connection model

In the first part of this paper we consider a general stationary subcritical cluster model in ℝd. The associated pair-connectedness function can be defined in terms of two-point Palm probabilities of the underlying point process. Using Palm calculus and Fourier theory we solve the Ornstein–Zernike equation (OZE) under quite general distributional assumptions. In the second part of the paper we discuss the analytic and combinatorial properties of the OZE solution in the special case of a Poisson-driven random connection model.

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This study examines, analyzes dna discusses Simultaneous elections Politics and Law: controversy Central Government Policies Related Legal Decisions Election District, North Sumatra Simalungun Where the Year 2015. On December 9, 2015 ago in elections Simalungun which is one of five areas was postponed due Regent Amran deputy candidate Sinaga experienced legal permaslahan. This study uses the theory of Elections, the concept of democracy and the electoral law. This study used qualitative methods with qualitative descriptive analysis techniques. The results of this study are Chronologically elections Simalungun, Inconsistency Regulations, Budget Swelling elections, Process Inaugural JR Saragih. Where the conclusions of this research local elections December 9, 2015 simultaneously experiencing the same problem as well as a substantial permasalahn. Registration problems associated pair of candidates is the responsibility of political parties to avoid any single candidate. On the issue of the availability of budget, the government and local governments need to give a strong political will to urgently solve the problem.

Associated symmetric pair and multiplicities of admissible restriction of discrete series

Let [Formula: see text] be a symmetric pair for a real semisimple Lie group [Formula: see text] and [Formula: see text] its associated pair. For each irreducible square integrable representation [Formula: see text] of [Formula: see text] so that its restriction to [Formula: see text] is admissible, we find an irreducible square integrable representation [Formula: see text] of [Formula: see text] which allows us to compute the Harish-Chandra parameter of each irreducible [Formula: see text]-subrepresentation of [Formula: see text] as well as its multiplicity. The computation is based on the spectral analysis of the restriction of [Formula: see text] to a maximal compact subgroup of [Formula: see text]

Dynamics of Gamma Bursts in Local Field Potentials

In this letter, we provide a stochastic analysis of, and supporting simulation data for, a stochastic model of the generation of gamma bursts in local field potential (LFP) recordings by interacting populations of excitatory and inhibitory neurons. Our interest is in behavior near a fixed point of the stochastic dynamics of the model. We apply a recent limit theorem of stochastic dynamics to probe into details of this local behavior, obtaining several new results. We show that the stochastic model can be written in terms of a rotation multiplied by a two-dimensional standard Ornstein-Uhlenbeck (OU) process. Viewing the rewritten process in terms of phase and amplitude processes, we are able to proceed further in analysis. We demonstrate that gamma bursts arise in the model as excursions of the modulus of the OU process. The associated pair of stochastic phase and amplitude processes satisfies their own pair of stochastic differential equations, which indicates that large phase slips occur between gamma bursts. This behavior is mirrored in LFP data simulated from the original model. These results suggest that the rewritten model is a valid representation of the behavior near the fixed point for a wide class of models of oscillatory neural processes.

Graphic representation of a triaxial ellipsoid by means of a sphere in general collinear spaces

For graphic representation of the projective creations, such as the quadrics (II degree surfaces) in projective, general collinear spaces, it is necessary to firstly determine the characteristic parameters, such as: vanishing planes, axes and centers of space. An absolute conic of a space is an imaginary conic, residing in the infinitely distant plane of that space. The common elements of the absolute conic and infinitely distant conic of a quadric in the infinitely distant plane of that space are the autopolar triangle and two double straight lines which are always real and it is necessary to use the common elements of their associated pair of conics in the vanishing plane of the associated space. The quadric axes are passing through the apices of the autopolar triangle, and they are important for graphic representation of the quadrics. In order to map a sphere in the first space into the triaxial ellipsoid in the second space, it is necessary to select a sphere so that its center is not on the axis of that space and that it intersects the vanishing plane of the second space along the imaginary circumference, which is in general position with the figure of the absolute conic of the second space (the associated pair of conics in the vanishing plane).

Analysis of mapping of general II degree surfaces in collinear spaces

Mapping of projective creations which includes the II degree surfaces in the projective, general collinear spaces is complex. In order to simplify it, firstly the characteristic parameters must be constructively determined: vanishing planes, axes and centers of spaces. All II degree surfaces are mapped using the common elements of absolute conic and infinitely distant conic of quadrics in the infinitely distant plane of space, which provide the determination of parameters of any surface of II degree. The common elements of their associated pair of conics in vanishing plane of space are used. The paper analyzed the conditions of choice of general surface of II degree in the first space to be mapped into the respective general surface of II degree in the second collinear space. The mapping is biunivocal. A sphere is chosen in the first space, and it was analyzed how it should be placed in respect to the characteristic parameters of the space, so that it would be mapped in rotating or triaxial general surfaces of II degree in the second space.