scholarly journals Mass functions of a compact manifold

2020 ◽  
Vol 154 ◽  
pp. 103650
Author(s):  
Andreas Hermann ◽  
Emmanuel Humbert
Keyword(s):  
Compact Manifold ◽  
Mass Functions

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

scholarly journals Diffeomorphism cocycles over partially hyperbolic systems

2020 ◽  
pp. 1-24
Author(s):  
VICTORIA SADOVSKAYA
Keyword(s):  
Hyperbolic System ◽  
Compact Manifold ◽  
Hyperbolic Systems ◽  
Riemannian Metrics ◽  
Hölder Continuous ◽  
Group Of Diffeomorphisms ◽  
Small Loss ◽  
Partially Hyperbolic ◽  
Loss Of Regularity

Abstract We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $\mathcal {M}$ . We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma }$ , we show that it has a continuous invariant family of $\gamma $ -Hölder Riemannian metrics on $\mathcal {M}$ . We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.

scholarly journals Cosmological Evolution of Supermassive Black Holes: Mass Functions and Spins

2012 ◽  
Vol 8 (S290) ◽  
pp. 259-260 ◽  
Author(s):  
Yan-Rong Li ◽  
Jian-Min Wang ◽  
Luis C. Ho
Keyword(s):  
Black Holes ◽  
Mass Function ◽  
Supermassive Black Holes ◽  
Cosmological Evolution ◽  
Radiative Efficiency ◽  
Bolometric Luminosity ◽  
History Of ◽  
Minor Mergers ◽  
Mass Dependent ◽  
Mass Functions

AbstractWe derive the mass function of supermassive black holes (SMBHs) over the redshift range 0 > z ≲ 2, using the latest deep luminosity and mass functions of field galaxies. Applying this mass function, combined with the bolometric luminosity function of active galactic nuclei (AGNs), into the the continuity equation of SMBH number density, we explicitly obtain the mass-dependent cosmological evolution of the radiative efficiency for accretion. We suggest that the accretion history of SMBHs and their spins evolve in two distinct regimes: an early phase of prolonged accretion, plausibly driven by major mergers, during which the black hole spins up, then switching to a period of random, episodic accretion, governed by minor mergers and internal secular processes, during which the hole spins down. The transition epoch depends on mass, mirroring other evidence for “cosmic downsizing” in the AGN population.

scholarly journals Stochastic methods defeat regular RSA exponentiation algorithms with combined blinding methods

2021 ◽  
Vol 15 (1) ◽  
pp. 408-433
Author(s):  
Margaux Dugardin ◽  
Werner Schindler ◽  
Sylvain Guilley
Keyword(s):  
State Of The Art ◽  
Stochastic Methods ◽  
Rsa Algorithm ◽  
Montgomery Ladder ◽  
Channel Information ◽  
Probability Mass ◽  
The Cost ◽  
Noisy Measurements ◽  
Mass Functions ◽  
Larger Sample

Abstract Extra-reductions occurring in Montgomery multiplications disclose side-channel information which can be exploited even in stringent contexts. In this article, we derive stochastic attacks to defeat Rivest-Shamir-Adleman (RSA) with Montgomery ladder regular exponentiation coupled with base blinding. Namely, we leverage on precharacterized multivariate probability mass functions of extra-reductions between pairs of (multiplication, square) in one iteration of the RSA algorithm and that of the next one(s) to build a maximum likelihood distinguisher. The efficiency of our attack (in terms of required traces) is more than double compared to the state-of-the-art. In addition to this result, we also apply our method to the case of regular exponentiation, base blinding, and modulus blinding. Quite surprisingly, modulus blinding does not make our attack impossible, and so even for large sizes of the modulus randomizing element. At the cost of larger sample sizes our attacks tolerate noisy measurements. Fortunately, effective countermeasures exist.

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

scholarly journals Galaxy properties as revealed by MaNGA – III. Kinematic profiles and stellar population gradients in S0s

2020 ◽  
Vol 495 (3) ◽  
pp. 2894-2908 ◽  
Author(s):  
H Domínguez Sánchez ◽  
M Bernardi ◽  
F Nikakhtar ◽  
B Margalef-Bentabol ◽  
R K Sheth
Keyword(s):  
Stellar Population ◽  
Velocity Dispersion ◽  
Signal To Noise Ratio ◽  
Elliptical Galaxies ◽  
Element Abundance ◽  
High Signal ◽  
Galactocentric Distance ◽  
Massive Galaxies ◽  
Nearby Galaxies ◽  
Mass Functions

ABSTRACT This is the third paper of a series where we study the stellar population gradients (SP; ages, metallicities, α-element abundance ratios, and stellar initial mass functions) of early-type galaxies (ETGs) at $z$ ≤ 0.08 from the Mapping Nearby Galaxies at APO Data Release 15 (MaNGA-DR15) survey. In this work, we focus on the S0 population and quantify how the SP varies across the population as well as with galactocentric distance. We do this by measuring Lick indices and comparing them to SP synthesis models. This requires spectra with high signal-to-noise ratio which we achieve by stacking in bins of luminosity (Lr) and central velocity dispersion (σ0). We find that: (1) there is a bimodality in the S0 population: S0s more massive than $3\times 10^{10}\, \mathrm{M}_\odot$ show stronger velocity dispersion and age gradients (age and σr decrease outwards) but little or no metallicity gradient, while the less massive ones present relatively flat age and velocity dispersion profiles, but a significant metallicity gradient (i.e. [M/H] decreases outwards). Above $2\times 10^{11}\, \mathrm{M}_\odot$, the number of S0s drops sharply. These two mass scales are also where global scaling relations of ETGs change slope. (2) S0s have steeper velocity dispersion profiles than fast-rotating elliptical galaxies (E-FRs) of the same luminosity and velocity dispersion. The kinematic profiles and SP gradients of E-FRs are both more similar to those of slow-rotating ellipticals (E-SRs) than to S0s, suggesting that E-FRs are not simply S0s viewed face-on. (3) At fixed σ0, more luminous S0s and E-FRs are younger, more metal rich and less α-enhanced. Evidently for these galaxies, the usual statement that ‘massive galaxies are older’ is not true if σ0 is held fixed.

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

scholarly journals A z = 2.5 protocluster associated with the radio galaxy MRC 2104-242: star formation and differing mass functions in dense environments

2014 ◽  
Vol 440 (4) ◽  
pp. 3262-3274 ◽  
Author(s):  
E. A. Cooke ◽  
N. A. Hatch ◽  
S. I. Muldrew ◽  
E. E. Rigby ◽  
J. D. Kurk
Keyword(s):  
Star Formation ◽  
Radio Galaxy ◽  
Mass Functions
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