We consider Bourgain's ergodic theorem regarding arithmetic averages in the cases where quantitative mixing is present dynamical system. Focusing on case of horocyclic flow, those estimates allow us to bound from above Hausdorff dimension exceptional set, providing evidence towards conjectures by Margulis, Shah, and Sarnak equidistribution homogeneous spaces. also prove existence a uniform uppe...

Abstract We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy polynomial growth condition on the real axis. This leads to an improved upper estimate in recent work of Culiuc Treil (Int. Math. Res. Not. 2019: 3301–3312, 2019) weighted martingale Carleson embedding theorem with matrix weights. In scalar case this new bound is optimal.

Abstract We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that is non-negative potential function proper. Upper expander with nonpositive will also be given. Furthermore, we provide sufficient condition being non-negative. Curvature estimates solitons in dimensions three four established. As an application, prove gap th...

In this essay, we show that quantum gravity and the spin-statistics theorem have very interesting consequences for dark matter candidates. Quantum can lead to fifth force type interactions a lower bound on masses of bosonic case fermions, leads fermion masses. For both fermionic candidates, decay particles. A comparison their lifetime with age universe an upper singlet scalar fields, find [Form...

Using Mazur’s theorem on torsions of elliptic curves, an upper bound 24 for the order finite Galois group ℋ associated with weighted walks in quarter plane ℤ + 2 is obtained. The explicit criterion to have 4 or 6 rederived by simple geometric arguments. division polynomials, a recursive 4m 4m+2 also As corollary, 8 given through method simpler than existing one.

The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem (Theorem 18 below) gives a necessary and sufficient condition for the existence of an exact upper bound / for a \A\~*~ is regular: an eub / with liminf/cf/(a) = /x exists if and only if for every regular K E (|^4...

The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem (Theorem 18 below) gives a necessary and suucient condition for the existence of an exact upper bound f for a < I-increasing sequence f = hf : < i On A where > jAj + is regular: an eub f with lim inf I cff(a) = exists if and only if for every regular 2 (jAj;) the set ...

Green’s general hyperplane restriction theorem gives a sharp upper bound for the Hilbert function of standard graded algebra over an infinite field K K <...

A keystone in the classical theory of diophantine approximation is the construction of an auxilliary polynomial. The polynomial is constructed so that it is forced (for arithmetic reasons) to vanish at certain approximating points and this contradicts an upper bound on the order of vanishing obtained by other (usually geometric) techniques; the contradiction then allows one to prove finiteness ...

Althdfer, I. and K.-U. Koschnick, On the deterministic complexity of searching local maxima, Discrete Applied Mathematics 43 (1993) 111~113. Lower and upper bounds for the deterministic complexity of searching local maxima in n-dimensional grids are given. The lower bound is based on an isoperimetric theorem of Bollob& and Leader.