发表机构
Instituto Politécnico Nacional; University of Ostrava; Charles University; VSB–Technical University of Ostrava（国立理工学院; 俄斯特拉发大学; 查理大学; 俄斯特拉发工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将径向代数上的右q向量导数用于积分超维，通过系数特化得到形式径向超空间及相关微积分。确定特殊单向量微积分，证明菲舍尔算子性质，分类支撑共振值并给出核秩公式，区分超维缺陷与q共振，还记录了相关投影性质。
AI 中文摘要
我们将径向代数上的固有右q向量导数专门应用于积分超维。形式维数由一个独立系数Q编码，通过系数特化Q→q^M得到超维M = m - 2n的形式径向超空间。这给出了一个严格的通用微积分，并在最多包含m个抽象向量的有限块上，在R^{m|2n}上有一个忠实的坐标实现。局部外积结果通过互补投影图像表示为格林分解。当专门化的有限行列式非零时，完全左乘产生一个行列式局部化的右单演菲舍尔分解。除了这种基变换理论，我们还完全确定了特殊的单向量微积分：对于M = -2ℓ，有一个额外的奇异单项式和一个缺失的图像单项式，而所有其他积分超维给出一个满射导数，其核为常数。然后我们证明零次菲舍尔算子在外部叶片上恰好是对角的，明确得到其行列式，对0 < q < 1中的所有支撑共振值进行分类，并给出一个精确的核秩公式作为支撑重数的和。在一个有N个辅助向量的块上，偶数支撑秩p在支撑截断上具有纯重数binom Np。在奇支撑根处，每个较低的奇因子非零，任何同时的较低共振是唯一的、偶数的，并由一个严格单调的标量方程表征。这些结果区分了持续的非正偶数超维缺陷与孤立的支撑相关q共振。附录记录了两个独立正交右q向量导数的常标量投影不会下降到埃尔米特商。
英文摘要
We specialize the intrinsic right $q$-vector derivative on radial algebras to integral superdimension. The formal dimension is encoded by an independent coefficient $Q$, and formal radial superspace of superdimension $M=m-2n$ is obtained by the coefficient specialization $Q\mapsto q^M$. This gives a rigorous universal calculus and, on finite blocks containing at most $m$ abstract vectors, a faithful coordinate realization on $\mathbb R^{m|2n}$. The localized exterior result is formulated as a Green decomposition by complementary projector images. Whenever the specialized finite determinant is nonzero, full left multiplication yields a determinant-localized right-monogenic Fischer decomposition. Beyond this base-change theory, we determine the exceptional one-vector calculus completely: for $M=-2\ell$ there is one additional singular monomial and one missing image monomial, whereas all other integral superdimensions give a surjective derivative with constants as its kernel. We then prove that the degree-zero Fischer operator is exactly diagonal on exterior blades, obtain its determinant explicitly, classify all support-resonance values in $0<q<1$, and give an exact kernel-rank formula as a sum of support multiplicities. On a block with $N$ auxiliary vectors, an even support rank $p$ has pure multiplicity $\binom Np$ on the support truncation. At an odd-support root, every lower odd factor is nonzero and any simultaneous lower resonance is unique, even, and characterized by one strictly monotone scalar equation. These results distinguish persistent nonpositive-even-superdimension defects from isolated support-dependent $q$-resonances. An appendix records that constant scalar projection of two independent orthogonal right $q$-vector derivatives does not descend to the Hermitian quotient.
