Related papers: On the Relationship between D'Angelo q-type and Ca…
We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.
The correspondence between two geometrical descriptions of the KP-hierarchy, one by discrete surface and another by difference analogue of differential geometry, is given.
In supersymmetric generalizations of the Standard Model, all stable Q-balls are associated with some flat directions. We show that, if the flat direction has both the baryon number and the lepton number, the scalar field inside the Q-ball…
We investigate theoretically the entanglement of two quantum dots (QDs) coupled to metallic nanowaveguide in the presence of the flip-flop interaction with the analytical solutions of eigenvalue equations of the coupled system. High…
We construct contact forms with constant $Q^\prime$-curvature on compact three-dimensional CR manifolds which admit a pseudo-Einstein contact form and satisfy some natural positivity conditions. These contact forms are obtained by…
In this work we deal with non-topological solutions of the Q-ball type in two space-time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls…
We prove an ultrametric q-difference version of the Maillet-Malgrange theorem, on the Gevrey nature of formal solutions of nonlinear analytic q-difference equations. Since \deg_q and \ord_q define two valuations on {\mathbb C}(q), we…
In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation…
We investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case we pay special…
We give a new proof of the classification of contact real hypersurfaces with constant mean curvature in the complex hyperbolic quadric ${Q^m}^* = SO_{m,2}^o/SO_mSO_2$, where $m\geq 3$. We show that a contact real hypersurface $M$ in…
We explore the $\textit{difference Langlands correspondence}$ using the four dimensional ${\mathcal{N}}=2$ super-QCD. Surface defects and surface observables play the crucial role. As an application, we give the first construction of the…
We prove, in a quantitative form, linear independence results for values of a certain class of q-series, which generalize classical q-hypergeometric series. These results refine our recent estimates.
We review some of the recent results on two-interacting particles (TIP) in low-dimensional disordered quantum models. Special attention is given to the mapping of the problem onto random band matrices. In particular, we construct two…
Properties and applications of a plasmonic cross-shaped nano-antenna is presented and compared to those of array of holes. A simple analytical model based on the superposition of waves are proposed and compared to the numerical results. A…
The quantum entanglement measures for $T{\overline{T}}$ deformed field theory on boundary, deformation coefficient $\mu$, with dual bulk geometry with finite radial cutoff $\rho_c$, for entangling region is single or disjoint intervals on…
In this paper we establish a new lattice description for superspecial abelian varieties over a finite field $\mathbb {F}_q$ of $q=p^a$ elements. Our description depends on the parity of the exponent $a$ of $q$. When $q$ is an odd power of…
We determine the additional structure which arises on the classical limit of a DQ-algebroid.
In this paper we establish sharp weighted Hardy type inequalities on the Carnot group with homogeneous dimension $Q\ge 3$.
We study how the category of $q$-connections depends on the choice of coordinates. We exploit Bhatt's and Scholze's $q$-crystalline site, which is based on a coordinate free formulation of $q$-PD structures, in order to relate $q$-crystals…
We examine the convergence of $q$-hypergeometric series when $|q|=1$.