We demonstrate the role of ${D}_{(s)}^{*}$ and their contributions in quasi-two-body decays ${B}_{(s)}\ensuremath{\rightarrow}{D}_{(s)}h{h}^{\ensuremath{'}}$ ($h,{h}^{\ensuremath{'}}={\ensuremath{\pi},K}$) perturbative QCD approach, stemming from quark flavor changing $\overline{b}\ensuremath{\rightarrow}\overline{c}{q}_{2}{\overline{q}}_{1}$ $\overline{b}\ensuremath{\rightarrow}c\overline{{q}_...

In this paper, we resolve a conjecture of Green and Liebeck (2019) [3] on codes in PGL(2,q). To be specific, show that: if D is dihedral subgroup order 2(q+1) G=PGL(2,q), A={g∈G:gq+1=1,g2≠1}, then λG=A⋅D, where λ=q or q−1 according as q even odd.

1. The vestibuloocular reflex (VOR) was examined in four alert monkeys during rotations of the head about torsional, vertical, horizontal, and intermediate axes. Eye positions and axes were recorded in three dimensions (3-D). Visual targets were used to optimize gaze stabilization. 2. Axes of eye rotation during slow phases showed small but systematic deviations from collinearity with the axes ...

We give four new extension theorems for linear codes over Fq: (a) For q = 2, h ≥ 3, every [n, k, d]q code with d odd whose weights are congruent to 0 or d (mod q/2) is extendable. (b) For q = 2, h ≥ 3, every [n, k, d]q code with gcd(d, q) = 2 whose weights are congruent to 0 or d (mod q) is doubly extendable. (c) For integers h,m, t with 0 ≤ m < t ≤ h and prime p, every [n, k, d]q code with gcd...

In this paper, we study the number of $\mathbb F_{q^n}$-rational points on affine curve $\mathcal{X}_{d,a,b}$ given by equation $$ y^d=ax\text{Tr}(x)+b,$$ where $\text{Tr}$ denote trace function from F_{q^n}$ to F_{q}$ and $d$ is a positive integer. particular, present bounds for F_{q}$-rational and, cases satisfies natural condition, explicit formulas rational are obtained. Particularly, compl...

There are a number of results concerning the generation of a collineation group by two of its elements. A. A. Albert and J. Thompson [1] were the first to exhibit two elements generating the little projective group PSL(d, q) of PG(d − 1, q) (for each d and q). According to a theorem of W. M. Kantor and A. Lubotzky [8], “almost every” pair of its elements generates PSL(d, q) as qd→∞ (asymptotica...

Proof of Lemma 5: Because both D(q||u) = D(1− q||1− u) and GF(q||u) = GF(1− q||1− u), we can assume u ≥ q without loss of generality. Keeping q fixed, we want to show that the result holds for all u. Note that D(q||q) = GF(q||q) = 0. Thus, differentiating with respect to u, it is sufficient to prove that GF ′(q||u) ≥ D′(q||u)/2 for all u ≥ q,u ≤ 1. We change variables by setting y = u−q. We use...

We prove that | ∑{ d≤x, (d,q)=1 μ(d)/d| ≤ 2.4 (q/φ(q))/ log(x/q) for every x > q ≥ 1 and similar estimates for the Liouville functions. We give also better constants when x/q is larger.

We study momentum dependence of static magnetic susceptibility $\chi(q)$ in paramagnetic phase Heisenberg magnets and its relation to critical behavior within nonlinear sigma model (NLSM) at arbitrary dimension $2<d<4$. In the first order $1/N$ expansion, where $N$ is number spin components, we find $\chi(q)\propto[q^{2}+\xi^{-2}(1+f(q\xi ))]^{-1+\eta /2}$, $\xi $ correlation length, $q$ moment...