This Article contains a typographical error in Equation (7). ρ ω ψ ρ ψ ρ () = () ∑ () , = i a i a j n i a 1 l should read: ρ ω ψ ρ ψ ρ () = () ∑ () , = i a i a j n j a 1 l

Let p≥5 be a prime number, F finite field of characteristic p and let χ¯ the mod-p cyclotomic character. ρ¯:GQ→GL2(F) Galois representation such that local ρ¯↾GQp is flat irreducible. Further, assume detρ¯=χ¯. The celebrated theorem Khare Wintenberger asserts if ρ¯ satisfies some natural conditions, there exists normalized Hecke-eigencuspform f=∑n≥1anqn p|p in its Fourier coefficients associate...

Let D be a strongly connected digraph. The average distance σ̄(v) of vertex v is the arithmetic mean distances from to all other vertices D. remoteness ρ(D) and proximity π(D) are maximum minimum D, respectively. We obtain sharp upper lower bounds on as function order n describe extreme digraphs for bounds. also such strong tournaments. show that tournament T, we have π(T)=ρ(T) if only T regular...

• ρ ramifies at only finitely many places. • ρ is odd, i.e., det ρ(c) = −1 for all complex conjugations c ∈ GF . • ρ is potentially crystalline and ordinary at all places above p. • ρ|GF (ζp) is absolutely irreducible. • There exists a parallel weight two Hilbert modular form f such that ρf is potentially crystalline and ordinary at all places above p and ρ = ρf . Then there exists a Hilbert mo...

Let R be a prime ring of char R = 2, d a nonzero derivation of R, ρ a nonzero right ideal of R and 0 = b ∈ R such that b[[d2[x, y], [x, y]]n = 0 for all x, y ∈ ρ, n ≥ 1 fixed integer. If [ρ, ρ]ρ = 0 then either bρ = 0 or d(ρ)ρ = 0. Mathematics Subject Classification: 16W25, 16R50, 16N60

limit to the tension reinforcement ratio ( ρ) in flexural high strength reinforced concrete (hsrc) members is based on the requirement that tension failure as sufficient rotation capacity are ensured at ultimate limit state. however, the provisions for the total amount of longitudinal reinforcement ratio ( ρ and ρ’) are not associated with any rational derivation. in this paper, a quantitative ...

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...

Given a finite group G and its representation ρ, the corresponding McKay graph is Γ(G,ρ) whose vertices are irreducible representations of G; number edges between two π,τ dimHom (π⊗ρ,τ). The collection all graphs for given encodes, in sense, character table. Such were also used by to provide bijection subgroups SU(2) affine Dynkin diagrams types A,D,E, considering appropriate graphs.

In this paper, we offer a proof for family of functional inequalities interpolating between the Poincaré and logarithmic Sobolev (standard weighted) inequalities. The proofs rely both on entropy flows CD(ρ,n) condition, either with ρ=0 n>0, or ρ>0 n∈R. As such, results are valid in case Riemannian manifold, which constitutes generalization what was previously proved.