We investigate the question of whether or not the orbit of a point in A/Q, under the natural action of a subset Σ ⊆ Q, is dense in A/Q. We prove that if the set Σ is a multiplicative semigroup of Q× which contains at least two multiplicatively independent elements, one of which is an integer, then the orbit Σα of any point α with irrational real coordinate is dense.

We propose a novel q-space imaging method called generalized q-space imaging (GQI), which is derived from the Fourier transform relationship between the MR signals and underlying diffusion displacement [1]. The method is characterized by being independent of the q-space sampling schemes, enabling us to use either q-ball imaging (QBI) [2] or diffusion spectrum imaging (DSI) dataset [3]. The accu...

Let q be a power of a prime p. Matrices over Fq in which every subset of basis size of the columns are independent, are of interest in coding theory, matroid theory, and projective geometry. For any positive integer m ≤ p and bijection σ : N≤q−1 ∪ {0} → Fq, we show that the m× (q + 1) matrix Hq,m, with {Uq}i,j = 

We present a new non-Archimedean realization of the Fock representation q-oscillator algebras where creation and annihilation operators act on complex-valued functions, which are defined local field arbitrary characteristic, for instance, p-adic numbers. This implies that many quantum models constructed using models, in particular, models. In this framework, we select q-deformation Heisenberg u...

We investigate the homology of a congruence subgroup Γ SL3(Z) with coefficients in Steinberg modules St(Q3) and St(E3), where E is real quadratic field are Q. By Borel-Serre duality, H0(Γ,St(Q3)) isomorphic to H3(Γ,Q). Taking image connecting homomorphism H1(Γ,St(E3)/St(Q3))→H0(Γ,St(Q3)), followed by isomorphism, we obtain naturally defined Hecke-stable subspace H(Γ,E) conjecture that independe...

The objective of this paper is to study an integrated two-supplier supply chain whose suppliers are unreliable. An unreliable supplier is alternative between available (ON) and unavailable (OFF) states which are considered to be independent exponential variables. The suppliers apply a continuous review policy and the retailer uses an adapted continuous review base on an(R,Q) policy. Transportat...

We prove estimates for the expected value of operator norms of Gaussian random matrices with independent (but not necessarily identically distributed) and centered entries, acting as operators from `p∗ to ` m q , 1 ≤ p∗ ≤ 2 ≤ q <∞.

OBJECTIVE To determine the extent to which select lower extremity alignment characteristics of the pelvis, hip, knee, and foot are related to the Q angle. DESIGN Descriptive cohort study design. SETTING Applied Neuromechanics Research Laboratory. PARTICIPANTS Two hundred eighteen participants (102 males, 116 females). ASSESSMENT OF RISK FACTORS Eight clinical measures of static alignmen...

Rapp [5] proves that the theory of the field N of reals in the language with Magidor-Malitz quantifiers Qi, QZ,... is decidable. The quantifier Q] is interpreted in a structure M by: M~Q",xl . . . . ,x,q) iff there exists a set Be=M, card(B)>~% such that for all distinct b 1 . . . . , b ,e B: M ~ q~[b~, ..., b,]; such a set B is called homogeneous for tp. Using Tarski's classical result on real...