Isotopic Space, Complex Conjugation, and U3 Symmetry for Particles

1965 ◽  
Vol 6 (12) ◽  
pp. 1976-1979 ◽  
Author(s):  
S. Teitler
Keyword(s):  
Complex Conjugation ◽  
Isotopic Space

ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER

2016 ◽  
Vol 94 (1) ◽  
pp. 15-19 ◽  
Author(s):  
DIEGO MARQUES ◽  
JOSIMAR RAMIREZ
Keyword(s):  
Entire Functions ◽  
Complex Conjugation ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Transcendental Numbers ◽  
Lecture Notes ◽  
Transcendental Entire Functions

In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].

Niche structure of marine sponges from temperate hard-bottom habitats within Gray's Reef National Marine Sanctuary

2015 ◽  
Vol 96 (2) ◽  
pp. 559-565 ◽  
Author(s):  
Christopher J. Freeman ◽  
Cole G. Easson ◽  
David M. Baker
Keyword(s):  
Sympatric Species ◽  
Marine Sponges ◽  
Latitudinal Gradients ◽  
Isotopic Niche ◽  
Microbial Abundance ◽  
Ecological Benefit ◽  
Relative Placement ◽  
Metabolic Capability ◽  
The Tropics ◽  
Isotopic Space

Many species of marine sponges on tropical reefs host abundant and diverse symbiont communities capable of varied metabolic pathways. While such communities may confer a nutritional benefit to some hosts (termed High Microbial Abundance (HMA) sponges), other sympatric species host only sparse symbiont communities (termed Low Microbial Abundance (LMA) sponges) and obtain a majority of their C and N from local sources. Sponge communities are widespread across large latitudinal gradients, however, and recent evidence suggests that these symbioses may also extend beyond the tropics. We investigated the role that symbionts play in the ecology of sponges from the temperate, hard-bottom reefs of Gray's Reef National Marine Sanctuary by calculating the niche size (as standard ellipse area (SEAc)) and assessing the relative placement of five HMA and four LMA sponge species within bivariate (δ13C and δ15N) isotopic space. Although photosymbiont abundance was low across most of these species, sponges were widespread across isotopic niche space, implying that microbial metabolism confers an ecological benefit to temperate sponges by expanding host metabolic capability. To examine how these associations vary across a latitudinal gradient, we also compared the relative placement of temperate and tropical conspecifics within isotopic space. Surprisingly, shifts in sponge δ13C and δ15N values between these regions suggest a reduced reliance on symbiont-derived nutrients in temperate sponges compared with their tropical conspecifics. Despite this, symbiotic sponges in temperate systems likely have a competitive advantage, allowing them to grow and compete for space within these habitats.

scholarly journals On the image of complex conjugation in certain Galois representations

2016 ◽  
Vol 152 (7) ◽  
pp. 1476-1488 ◽  
Author(s):  
Ana Caraiani ◽  
Bao V. Le Hung
Keyword(s):  
Symmetric Spaces ◽  
Galois Representations ◽  
Real Field ◽  
Complex Conjugation ◽  
Automorphic Representations ◽  
Locally Symmetric Spaces ◽  
Cuspidal Automorphic Representations ◽  
Totally Real ◽  
Totally Real Field

We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $\text{GL}_{n}$ over a totally real field $F$.

Trace functions on the algebras of certain E-unitary inverse semigroups

1995 ◽  
Vol 125 (5) ◽  
pp. 1077-1084 ◽  
Author(s):  
M. J. Crabb ◽  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebra ◽  
Inverse Semigroups ◽  
Trace Function ◽  
Complex Field ◽  
Semigroup Algebras ◽  
Complex Conjugation ◽  
Arbitrary Rank

A construction is given for a trace function on the semigroup algebra of a certain type of E-unitary inverse semigroup over any subfield of the complex field that is closed under complex conjugation. In particular, the method applies to the semigroup algebras of free inverse semigroups of arbitrary rank.

A remark on Zilber's pseudoexponentiation

2006 ◽  
Vol 71 (3) ◽  
pp. 791-798 ◽  
Author(s):  
David Marker
Keyword(s):  
Baire Category ◽  
Positive Answer ◽  
Complex Conjugation ◽  
Closed Set ◽  
Definable Set ◽  
Open Questions ◽  
Novel Approach ◽  
Definable Sets ◽  
Order Arithmetic ◽  
Image Position

When studying the model theory ofthe first observation is that the integers can be defined asSince ∂exp is subject to all of Gödel's phenomena, this is often also the last observation. After Wilkie proved that ℝexp is model complete, one could ask the same question for ∂exp, but the answer is negative.Proposition 1.1. ∂expis not model completeProof. If ∂exp is model complete, then every definable set is a projection of a closed set. Since ∂ is locally compact, every definable set is Fσ. The same is true for the complement, so every definable set is also Gδ. But, since ℤ is definable, ℚ is definable and a standard corollary of the Baire Category Theorem tells us that ℚ is not Gδ.Still, there are several interesting open questions about ∂exp.• Is ℝ definable in ∂exp?• (quasiminimality) Is every definable set countable or co-countable? (Note that this is true in the structure (∂, ℤ, +, ·) where we add a predicate for ℤ).• (Mycielski) Is there an automorphism of ∂exp other than the identity and complex conjugation?1A positive answer to the first question would tell us that ∂exp is essentially second order arithmetic, while a positive answer to the second would say that integers are really the only obstruction to a reasonable theory of definable sets.A fascinating, novel approach to ∂exp is provided by Zilber's [6] pseudoexponentiation. Let L be the language {+, · E, 0, 1}.

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