We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold smooth reflexive polytopes with barycenter at the origin. Our proof involves considering slope stability canonical extension tangent bundle by trivial line class $c_1(\mathcal{T}_X)$ on Fano toric varieties.

We answer an open problem raised by Chen and Zhang in 2008 prove that, for any minimal projective 3-fold $X$ of general type with the geometric genus $\geq 5$, is birationally fibred a pencil $(1,2)$-surfaces (i.e. $c_1^2=1$, $p_g=2$) if only $4$-canonical map $\varphi_{4,X}$ non-birational. The statement does not hold those $\leq 4$ according to our examples.

We shall study minimal complex surfaces with $c^2 = 9$ and $\chi=5$ whose canonical classes are divisible by $3$ in the integral cohomology groups, where $c_1^2$ $\chi$ denote first Chern number of an algebraic surface Euler characteristic structure sheaf, respectively. The main results a theorem for such surfaces, unirationality moduli space, description behavior map. As byproduct, we also rul...

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ f_c(z) = z^2+c $\end{document}</tex-math></inline-formula> for id="M2">\begin{document}$ c \in {\mathbb C} $\end{document}</tex-math></inline-formula>. We show there exists a uniform upper bound on the number of points in id="M3">\begin{document}$ P}^1( C}) that c...

In this paper we study the following torsion problem $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=1~&{}\quad \text{ in }\ \Omega ,\\ u=0~&{}\quad on \partial . \end{array}\right. } \end{aligned}$$ Let $$\Omega \subset \mathbb R^2$$ be a bounded, convex domain and $$u_0(x)$$ solution of above with its maximum $$y_0\in $$ Steinerberger (J Funct Anal 274:1611–1630, 2018) proved that ther...

غلاف سوخت‌های هسته‌ای یکی از مهم‌ترین اجزا رآکتور محسوب می‌شود. این غلاف‌ها آلیاژ زیرکونیم ساخته می‌شوند؛ اما خواص ترمومکانیکی چندان مناسبی ندارند؛ لذا در پژوهش سعی شده با تغییر مواد به‌کاررفته NuScale به یک نوترونیکی و مناسب دست پیدا شود. قلب موجب ضریب تکثیر مؤثر طول بازه سوخت‌گذاری می‌گردد. شبیه‌سازی که M5 بهره می‌برد به‌عنوان معیار هم‌­چنین همراه سه نوع دیگر آلیاژهای رایج دو آن FeCrAl است، د...

A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix dimension n . The uses quadratic multiplication and cubic has running time bounded by O ( 3 (log + log || ||) 2 ) bit operations, where = max ij | denotes largest entry in absolute value. variant that pseudo-linear 1 o (1) exponent `` (1)′′ captures additional factors \(c_1 (\log n)^{c_2...

Analysis of stress distributions under lightweight wheeled vehicles Report Title In recent years, the need for reliable modeling tools for lightweight robotic systems deployed on various terrains has spurred research efforts into development of vehicle terrain interaction (VTI) models. This paper presents an analysis of rigid wheels dry sand interaction and compares experimental results with pr...