in cite{p}, park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|andbegin{eqnarray}&& left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}r...

Among probability measures on d-dimensional real projective space, one which maximizes the expected angle $$\arccos (\frac{x}{|x|}\cdot \frac{y}{|y|})$$ between independently drawn points x and y was conjectured to equidistribute its mass over standard Euclidean basis $$\{e_0,e_1,\ldots , e_d\}$$ by Fejes Tóth (Acta Math Acad Sci Hung 10:13–19, 1959. https://doi.org/10.1007/BF02063286 ). If tru...

We have studied the ground state of a fullerene-based magnet, the alpha;{'}-phase tetra-kis-(dimethylamino)-ethylene-C60 (alpha'-TDAE-C(60)), by electron spin resonance and magnetic torque measurements. Below T(N) = 7 K, nonparamagnetic field dependent resonances with a finite excitation gap (1.7 GHz) are observed along the a axis. Strong enhancement in their intensity as temperature is decreas...

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

Let G be a finite group, and ? nontrivial character of G. The McKay graph $${\cal M}\left({G,\alpha } \right)$$ has the irreducible characters as vertices, with an edge from ?1 to ?2 if is constituent ??1. We study diameters graphs for simple groups Lie type. show that any ?, diameter bounded by quadratic function rank, obtain much stronger bounds = PSLn(q) or PSUn(q).

We perform a study of gravitational waves emitted by inspiraling black holes in the context quadratic gravity. By linearizing field equations around flat background, we demonstrate that all degrees freedom satisfy wavelike equations. These split into three modes: massive spin-2 mode, spin-0 and expected massless mode. construct energy-momentum tensor show that, due to it presents Ostrogradsky i...