Displaying similar documents to “Subclasses of typically real functions determined by some modular inequalities”

Further generalized versions of Ilmanen’s lemma on insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2021)

Commentationes Mathematicae Universitatis Carolinae

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The author proved in 2018 that if G is an open subset of a Hilbert space, f 1 , f 2 : G continuous functions and ω a nontrivial modulus such that f 1 f 2 , f 1 is locally semiconvex with modulus ω and f 2 is locally semiconcave with modulus ω , then there exists f C loc 1 , ω ( G ) such that f 1 f f 2 . This is a generalization of Ilmanen’s lemma (which deals with linear modulus and functions on an open subset of n ). Here we extend the mentioned result from Hilbert spaces to some superreflexive spaces, in particular to L p spaces, p [ 2 , ) . We...

2-Cohomology of semi-simple simply connected group-schemes over curves defined over p -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

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Let X be a proper, smooth, geometrically connected curve over a p -adic field k . Lichtenbaum proved that there exists a perfect duality: Br ( X ) × Pic ( X ) / between the Brauer and the Picard group of X , from which he deduced the existence of an injection of Br ( X ) in P X Br ( k P ) where P X and k P denotes the residual field of the point P . The aim of this paper is to prove that if G = G ˜ is an X e t - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results...

A density version of the Carlson–Simpson theorem

Pandelis Dodos, Vassilis Kanellopoulos, Konstantinos Tyros (2014)

Journal of the European Mathematical Society

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We prove a density version of the Carlson–Simpson Theorem. Specifically we show the following. For every integer k 2 and every set A of words over k satisfying lim sup n | A [ k ] n | / k n > 0 there exist a word c over k and a sequence ( w n ) of left variable words over k such that the set c { c w 0 ( a 0 ) . . . w n ( a n ) : n and a 0 , . . . , a n [ k ] } is contained in A . While the result is infinite-dimensional its proof is based on an appropriate finite and quantitative version, also obtained in the paper.

Modular symbols, Eisenstein series, and congruences

Jay Heumann, Vinayak Vatsal (2014)

Journal de Théorie des Nombres de Bordeaux

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Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k 2 and of the same level N , both eigenfunctions of the Hecke operators, and both normalized so that a 1 ( f ) = a 1 ( E ) = 1 . The main result we prove is that when E and f are congruent mod a prime 𝔭 (which we take in this paper to be a prime of ¯ lying over a rational prime p > 2 ), the algebraic parts of the special values L ( E , χ , j ) and L ( f , χ , j ) satisfy congruences mod the same prime. More explicitly, we prove that, under certain conditions, ...

On behavior of solutions to a chemotaxis system with a nonlinear sensitivity function

Senba, Takasi, Fujie, Kentarou

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In this paper, we consider solutions to the following chemotaxis system with general sensitivity τ u t = Δ u - · ( u χ ( v ) ) in Ω × ( 0 , ) , η v t = Δ v - v + u in Ω × ( 0 , ) , u ν = u ν = 0 on Ω × ( 0 , ) . Here, τ and η are positive constants, χ is a smooth function on ( 0 , ) satisfying χ ' ( · ) > 0 and Ω is a bounded domain of 𝐑 n ( n 2 ). It is well known that the chemotaxis system with direct sensitivity ( χ ( v ) = χ 0 v , χ 0 > 0 ) has blowup solutions in the case where n 2 . On the other hand, in the case where χ ( v ) = χ 0 log v with 0 < χ 0 1 , any solution to the system exists globally in time and is bounded. We present a sufficient condition for the boundedness...

On a sequence formed by iterating a divisor operator

Bellaouar Djamel, Boudaoud Abdelmadjid, Özen Özer (2019)

Czechoslovak Mathematical Journal

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Let be the set of positive integers and let s . We denote by d s the arithmetic function given by d s ( n ) = ( d ( n ) ) s , where d ( n ) is the number of positive divisors of n . Moreover, for every , m we denote by δ s , , m ( n ) the sequence d s ( d s ( ... d s ( d s ( n ) + ) + ... ) + ) m -times = d s ( n ) for m = 1 , d s ( d s ( n ) + ) for m = 2 , d s ( d s ( d s ( n ) + ) + ) for m = 3 , We present classical and nonclassical notes on the sequence ( δ s , , m ( n ) ) m 1 , where , n , s are understood as parameters.

Explicit birational geometry of threefolds of general type, I

Jungkai A. Chen, Meng Chen (2010)

Annales scientifiques de l'École Normale Supérieure

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Let V be a complex nonsingular projective 3-fold of general type. We prove P 12 ( V ) : = dim H 0 ( V , 12 K V ) &gt; 0 and P m 0 ( V ) &gt; 1 for some positive integer m 0 24 . A direct consequence is the birationality of the pluricanonical map ϕ m for all m 126 . Besides, the canonical volume Vol ( V ) has a universal lower bound ν ( 3 ) 1 63 · 126 2 .

Contracting endomorphisms and dualizing complexes

Saeed Nasseh, Sean Sather-Wagstaff (2015)

Czechoslovak Mathematical Journal

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We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R . Our focus is on homological properties of contracting endomorphisms of R , e.g., the Frobenius endomorphism when R contains a field of positive characteristic. For instance, in this case, when R is F -finite and C is a semidualizing R -complex, we prove that the following conditions are equivalent: (i) C is a dualizing R -complex; (ii) C 𝐑 Hom R ( n R , C ) for some n > 0 ; (iii) G C -dim n R < and C is derived...

On the birational gonalities of smooth curves

E. Ballico (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let C be a smooth curve of genus g . For each positive integer r the birational r -gonality s r ( C ) of C is the minimal integer t such that there is L Pic t ( C ) with h 0 ( C , L ) = r + 1 . Fix an integer r 3 . In this paper we prove the existence of an integer g r such that for every integer g g r there is a smooth curve C of genus g with s r + 1 ( C ) / ( r + 1 ) > s r ( C ) / r , i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails.