The paper is devoted to a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential
The paper is devoted to a family of discrete one-dimensional Schrödinger operators with power-like decaying potentials with rapid oscillations. In particular, for the potential
On the basis of a prescribed quadratic Lagrangian, an algorithm of synthesis for an electric circuit is suggested here. That is, the circuit evolution equations are equivalent to the relevant Euler–Lagrange equations. The proposed synthesis is a systematic approach that allows one to realize any finite-dimensional physical system described by a quadratic Lagrangian in a lossless electric circuit so that their evolution equations are equivalent. The synthesized circuit is composed of (i) capacitors and inductors of positive or negative values for the respective capacitances and inductances, and (ii) gyrators. The circuit topological design is based on the set of
A family
Let
让 f f 是非均匀贝索夫空间 {text textit {Russian {B}}}_{infty ,1}^{1}(mathbb {R}^2) 中 R 2 mathbb {R}^2 上的函数。对于一对 ( A , B ) (A,B) 不一定有界且不一定相交的自相交算子，A A 和 B B 的函数 f ( A , B ) f(A,B) 被引入为密集定义的线性算子。结果表明，如果 1 ≤ p ≤ 2 1le ple 2 ， ( A 1 , B 1 ) (A_1,B_1) 和 ( A 2 , B 2 ) (A_2. B_2) 是成对的、B_2) 是一对不一定有界且不一定相交的自并算子，使得 A 1 - A 2 A_1-A_2 和 B 1 - B 2 B_1-B_2 都属于 Schatten-von Neumann 类 S p {boldsymbol {S}}_p 且 fin {text textit {Russian {B}}}_{infty ,1}^{1}(mathbb {R}^2)，那么下面的 Lipschitz 类型估计成立： 开始|f(A_1,B_1)-f(A_2,B_2)|_{{boldsymbol {S}}_p}最大值（big）：||A_1-A_2|_{{boldsymbol {S}_p}, |B_1-B_2|_{{boldsymbol {S}_p}big }。end{equation*}
The paper is devoted to the study of deformations of Artinian algebras and zero-dimensional germs of varieties. In particular, an approach is developed to solving the open problem about the nonexistence of rigid Artinian algebras; it is based essentially on the use of the canonical duality in the cotangent complex. Thus, it is shown that there are no rigid Gorenstein Artinian algebras and rigid almost complete intersections. The proof of the latter statement is based on the properties of the torsion functors. More precisely, the tensor product of the conormal and canonical modules of the corresponding Artinian algebra is calculated. In this case, the homology and cohomology groups of higher degrees are also found. Among other things, some estimates are obtained for the dimension of the spaces of the first lower and upper cotangent functors of Artinian algebras, and the relationship between them is described. In conclusion, several examples of nonsmoothable Artinian noncomplete intersections are examined, and some unusual properties of such algebras are discussed.
A version of the extra-zero conjecture, formulated by the first named author, is proved for
An alternative approach to the classical Morel–Voevodsky stable motivic homotopy theory
本文提出了经典莫雷尔-伏沃斯基稳定动机同调理论 S H ( k ) SH(k) 的另一种方法。文中介绍了有框双谱 S H nis fr ( k ) SH_{operatorname {nis}}^{operatorname {fr}}(k) 和有效有框双谱 S H nis fr , eff ( k ) SH_{operatorname {nis}}^{operatorname {fr},operatorname {eff}}(k) 的三角范畴。这两个三角范畴都只涉及尼斯内维奇局部等价，而与任何一种动机等价无关。研究表明，S H nis fr ( k ) SH_{operatorname {nis}}^{operatorname {fr}}(k) 和 S H nis fr , eff ( k ) SH_{operatorname {nis}}^{operatorname {fr}、operatorname {eff}}(k) 分别恢复了经典的莫雷尔-伏伊伏丁斯基三角范畴的双谱 S H ( k ) SH(k) 和有效双谱 S H eff ( k ) SH^{operatorname {eff}}(k) 。还有 S H ( k ) SH(k) 和 S H eff ( k ) SH^{operatorname {eff}}(k) 被复原为有框动机谱函子 S H S 1 fr [ F r 0 ( k ) ] SH_{S^1 fr [ F r 0 ( k ) ] 的三角范畴。) ] SH_{S^1}^{operatorname {fr}}[mathcal {F}r_0(k)] 和本文构建的有框动机三角范畴 S H fr ( k ) mathcal {SH}^{operatorname {fr}}(k).
Atsuyama’s result on the geometry of symmetric spaces of type EIII is generalized to the case of arbitrary fields of characteristic not 2 or 3. As an application, a variant of the “chain lemma” for microweight tori in groups of type
A necessary and sufficient Blaschke-type condition is obtained for the zeros of derivatoves of Nevanlinna class functions.
A hierarchy of Lax pairs with
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：