Related papers: Secant degeneracy index of the standard strata in …

The discriminant, $D$, in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equivalently, by the sum of the delta invariants of the singular…

For essential reduced hyperplane arrangements of 4 variables, we show that the pole order spectral sequence degenerates almost at $E_2$, and completely at $E_3$, generalizing the 3 variable case where the complete $E_2$-degeneration is…

The semileptonic decay channel B -> D tau nu is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently the BaBar experiment reported the first observation of the exclusive semileptonic decay…

The spectral properties of p-forms on the fundamental domains of regular tesselations of the d-dimensional sphere are discussed. The degeneracies for all ranks, p, are organised into a double Poincare series which is explicitly determined.…

By using a characterization of the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem given in a previous paper, we give a lower bound for the Morse index of radial solutions to H\'enon type problems \[…

We prove that a product of $m>5$ copies of $\PP^1$, embedded in the projective space $\PP^r$ by the standard Segre embedding, is $k$-identifiable (i.e. a general point of the secant variety $S^k(X)$ is contained in only one $(k+1)$-secant…

Building on results developed in https://doi.org/10.48550/arXiv.2404.14902, where It\^{o}-SDEs with possibly degenerate and discontinuous dispersion coefficient and measurable drift were analyzed with respect to a given (sub-)invariant…

We give formulas for the degrees of the spaces of foliations in P2 with a dicritical singularity of prescribed order. Blowing up such singularity induces, generically, a foliation with all but finitely many leaves transversal to the…

The semileptonic decays $\bar{B}\to D(D^*)\pi\ell\bar{\nu}$ are analyzed by heavy quark and chiral symmetries. The branching ratio is of order of a few percent for $\dpi$, but it is much smaller for $\dstar$, of order $10^{-4}-10^{-5}$. The…

We study the differential branching ratio, branching ratio and the CP-violating asymmetry for the exclusive $B_{d}->(\eta, \eta^{\prime}) \ell^+ \ell^-$ decays in the standard model. We deduce the $B_{d}->(\eta, \eta^{\prime})$ form factors…

We give positivity conditions on the embedding of a smooth variety which guarantee the normality of the secant variety, generalizing earlier results of the author and others. We also give classes of secant varieties satisfying the Hodge…

In this work, we have conducted a comprehensive and systematic theoretical investigation of the full cascade decays of charged pseudoscalar mesons, specifically $D_s$, $D$, $B$, and $B_c$, into $\tau \nu_\tau$, followed by the subsequent…

In this contribution we present a novel, model-independent description of semileptonic $B\rightarrow D \pi \ell \nu$ decays. In addition, we discuss recent developments in the understanding of coupled-channel $D \pi$-$D \eta$-$D_s K$ S-wave…

We investigate the decays $B_c^- \rightarrow D_{s}^{(*)-}\ell^+\ell^-$ and $B_c^- \rightarrow D_{s}^{(*)-}\nu\bar{\nu}$ within the Standard Model (SM), employing perturbative QCD form factors that are sensitive to the wave functions of…

Based on the predictions of the relevant form factors from the covariant light-front quark model, we show the branching fractions for the $D (D_s) \to (P,\,S,\,V,\,A)\,\ell\nu_\ell$ ($\ell=e$ or $\mu$) decays, where $P$ denotes the…

We investigate the decays $B_c^- \rightarrow \bar{D}^{(*)0}\ell^-\bar{\nu}_{\ell}$ and $B_c^- \rightarrow D^{(*)-}\ell^+\ell^-$ within the Standard Model (SM), employing perturbative QCD (pQCD) form factors that are sensitive to the wave…

Given a natural number $k \geq 2$, we construct a hereditarily indecomposable, $\mathscr{L}_{\infty}$ space, $X_k$ with dual isomorphic to $\ell_1$. We exhibit a non-compact, strictly singular operator $S$ on $X_k$, with the property that…

We introduce a new parameterization of $B\rightarrow D \pi \ell \nu$ form factors using a partial-wave expansion and derive bounds on the series coefficients using analyticity and unitarity. This is the first generalization of the…

Model-independent bounds are presented for the form-factors describing the semileptonic decay $\Lambda_b\to\Lambda_ce\bar\nu_e$ at the end-point of the lepton energy spectrum. For the axial-vector form-factor $f_1^A(1)$ we obtain…

We calculate the decay constant of $D_s$ and $D_s^{*}$ with $\bar{B}^0 \ra D^{+}\ell^{-}\nu$ and $\bar{B}^0 \ra D^{+}D_s^{-(*)}$ decays. In our analysis we assume that factorization ansatz works and used two different form factor behaviours…