We study two interacting quantum particles forming a bound state in $d$-dimensional free space, and constrain the $k$ directions to $(0,\infty)^k \times \mathbb{R}^{d-k}$, with Neumann boundary conditions. First, we prove that ground energy strictly decreases upon going from $k+1$. This shows stick corner where all planes intersect. Second, show for resulting Hamiltonian, after removing part of...

Let {X n ; n ≥ 1} be a strictly stationary negatively associated sequence which satisfies EX 1 = 0, V ar(X 1) < ∞. Set S n = n k=1 X k , n ≥ 1, σ 2 = EX 2 1 + 2 ∞ k=2 EX 1 X k. In this paper, we prove that, for b > −1, lim ε0 ε 2(b+1) ∞ n=1 (log log n) b n log n P{|S n | ≥ εσ n log log n} = 2 b+1 (b + 1) √ π Γ(b + 3 2) holds if EX 2 1 (1 + log log |X 1 |) b−1 < ∞. The result of Gut and Spˇataru...

Let V be a crystalline p-adic representation of the absolute Galois group GK of an finite unramified extension K of Qp and T a lattice of V stable by GK . We prove the following result : Let FilV be the maximal sub-representation of V with Hodge-Tate weights strictly positive and FilT = T ∩ FilV . Then, the projective limit of the H g (K(μpn), T ) is equal up to torsion to the projective limit ...

Let Rn = n k=1 1 k −log n + 1 2 , H(n) = n 2 (Rn −γ), n = 1, 2,. . ., where γ is the Euler-Mascheroni constant. We prove that for all integers n ≥ 1, H(n) and [(n + 1/2)/n] 2 H(n) are strictly increasing, while [(n + 1)/n] 2 H(n) is strictly decreasing. For all integers n ≥ 1, 1 24(n + a) 2 ≤ Rn − γ < 1 24(n + b) 2 with the best possible constants a = 1 24[−γ + 1 − log(3/2)] − 1 = 0.55106. .. a...

For LTI plant, SPR(Strictly Positive Real)/ASPR(Almost Strictly Positive Real) property was recently used to design a continuous-time (adaptive) multi-periodic repetitive control system that guarantees the Lyapunov stability of the whole system. However in discrete time, SPR/ASPR property requires the controlled plant to be proper and unfortunately in practice it is very rare to find a plant wh...

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. ...

We put forward a new family of computational assumptions, the Kernel Matrix DiffieHellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is the natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al....

In 1933 Karol Borsuk asked whether every compact subset of R can be decomposed into d + 1 subsets of strictly smaller diameter. The 0/1Borsuk conjecture asks a similar question using subsets of the vertices of a ddimensional cube. Although counterexamples to both conjectures are known, we show in this article that the 0/1-Borsuk conjecture is true when d is much larger than the diameter of the ...

let $omega_x$ be a bounded, circular and strictly convex domain of a banach space $x$ and $mathcal{h}(omega_x)$ denote the space of all holomorphic functions defined on $omega_x$. the growth space $mathcal{a}^omega(omega_x)$ is the space of all $finmathcal{h}(omega_x)$ for which $$|f(x)|leqslant c omega(r_{omega_x}(x)),quad xin omega_x,$$ for some constant $c>0$, whenever $r_{omega_x}$ is the m...