In the present article, we study conjecture of Sharifi on surjectivity map $\varpi_{\theta}$. Here $\theta$ is a primitive even Dirichlet character conductor $Np$, which exceptional in sense Ohta. After localizing at prime ideal $\mathfrak{p}$ Iwasawa algebra related to trivial zero Kubota\textendash Leopoldt $p$-adic $L$-function $L_p(s,\theta^{-1}\omega^2)$, compute image $\varpi_{\theta,\mat...

Abstract We study, from a quite general point of view, the family all extensions positive hermitian linear functional $$\omega $$ ? , defined on dense *-subalgebra $${\mathfrak {A}}_0$$ A 0 topological *-algebra {A}}[\tau ]$$ [</mml:m...

We introduce the family of Theta operators $\Theta_f$ indexed by symmetric functions $f$ that allow us to conjecture a compositional refinement Delta Haglund, Remmel and Wilson for $\Delta_{e_{n-k-1}}'e_n$. show $4$-variable Catalan theorem Zabrocki is precisely Schr\"{o}der case our conjecture, we how relate this Dyck path algebra introduced Carlsson Mellit, extending one their results. Again ...

A weakly nonlinear oscillator of natural frequency omega(0) and damping ratio delta is driven by an amplitude-modulated force of dimensionless amplitude epsilon, carrier frequency omega, and modulation frequency omega(1). Each of (omega - omega(0))/omega(0), omega(1)/omega(0), and delta is O(epsilon(2/3)) as epsilon --> 0. The response in this resonant neighborhood is a slowly modulated sine wa...

We use the Tomita-Takesaki modular theory and Kubo-Ando operator mean to write down a large class of multi-state quantum $f$-divergences prove that they satisfy data processing inequality. For two states, this includes $(\alpha,z)$-R\'enyi divergences, Petz, measures in \cite{matsumoto2015new} as special cases. The method used is interpolation non-commutative $L^p_\omega$ spaces result applies ...

We study the regular surface defect in $$\Omega $$ -deformed four-dimensional supersymmetric gauge theory with group SU(N) 2N hypermultiplets fundamental representation. prove its vacuum expectation value obeys Knizhnik–Zamolodchikov equation for 4-point conformal block of $$\widehat{{\mathfrak {sl}}}_{N}$$ -current algebra, originally introduced context two-dimensional field theory. The level ...