Related papers: Weighted Yosida Mappings of Several Complex Variab…

In this paper, we introduce a new energy density function $\mathscr Y$ on the projective bundle $\mathbb{P}(T_M)\>M$ for a smooth map $f:(M,h)\>(N,g)$ between Riemannian manifolds $$\mathscr Y=g_{ij}f^i_\alpha f^j_\beta \frac{W^\alpha…

Given a map $f: X\rightarrow Y$ of simply connected spaces of finite type such. The space of based loops at $f$ of the space of maps between $X$ and $Y$ is denoted by $\Omega_{f} Map(X,Y)$. For $n> 0$, we give a model categorical…

Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strictly increasing f : D(Y) \to D(X) such that dX = f \circ dY…

Given an assignment of weights w to the edges of a graph G, a matching M in G is called strongly w-maximal if for any matching N the sum of weights of the edges in N\M is at most the sum of weights of the edges in M\N. We prove that if w…

Let $\psi$ be a holomorphic function on the open unit ball $\BB \subset \C^N$, and let $\varphi$ be a holomorphic self-map of $\BB$, associated with normal weights $\nu$ and $\mu$. We consider the weighted composition operator $…

Let's consider a control system described by the implicit equation $F(x,\dot x) = 0$. If this system is differentially flat, then the following criterion is satisfied : For some integer $r$, there exists a function $\varphi(y_0, y_1,…

Let $M$ be a quantizable symplectic manifold acted on by $T=(S^1)^r$ in a Hamiltonian fashion and $J$ a moment map for this action. Suppose that the set $M^{T}$ of fixed points is discrete and denote by ${\alpha}_{pj}\in{\mathbb Z}^r$ the…

We prove holomorphy E sqcap C(I,varPi) to C(I,varPi) of the map (x,y) mapsto x circ [id,y] where [id,y]:I owns t mapsto (t,y(t)) for a real compact interval I, and where varPi is a complex Banach space and E is a certain locally convex…

We give all possible holomorphic Eisenstein series on $\Gamma_0(p)$, of rational weights greater than $2$, and with multiplier systems the same as certain rational-weight eta-quotients at all cusps. We prove they are modular forms and give…

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we assume…

If $f$ is a symmetric complex-valued function on the $m$-fold Cartesian product of the set of non-negative reals and $A$ is a positive semi-definite $m\times m$ matrix with eigenvalues $\lambda_j$, we set…

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…

We prove an analogue of E. Levi's Continuity Principle for meromorphic mappings with values in arbitrary compact complex manifolds in place of the Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new extension method for…

Let ${\cal G}=(G,w)$ be a weighted simple finite connected graph, that is, let $G$ be a simple finite connected graph endowed with a function $w$ from the set of the edges of $G$ to the set of real numbers. For any subgraph $G'$ of $G$, we…

If M is a compact oriented manifold-with-boundary whose fundamental group is virtually nilpotent or Gromov-hyperbolic, we show that the higher signatures of M are oriented-homotopy invariants.

For a linear code $\mathcal{C} \subseteq \mathbb{F}_2^n$ and $\alpha \in [0,1]$, call a set $S \subseteq [n]$ an (unweighted) one-sided $\alpha$-sparsifier of $\mathcal{C}$ if for all $c \in \mathcal{C}$, $\mathrm{wt}(c_S)\geq \alpha \cdot…

We define a subset of an almost complex manifold (M,J) to be a holomorphic shadow if it is the image of a J-holomorphic map from a compact complex manifold. Notice that a J-holomorphic curve is a holomorphic shadow, and so is a complex…

The singular set of a generic map $f: M\to F$ of a manifold $M$ of dimension $m\ge 2$ to an oriented surface $F$ is a closed smooth curve $\Sigma(f)$. We study the parity of the number of components of $\Sigma(f)$. The image $f(\Sigma)$ of…

The functional equation $\varphi(Fx) - \varphi(x) = \gamma(x)$ is considered in topological, measurable and related categories from the point of view of functional analysis and general theory of dynamical systems. The material is presented…

Given a map $\phi:X\rightarrow Y$ between $F$-analytic manifolds over a local field $F$ of characteristic $0$, we introduce an invariant $\epsilon_{\star}(\phi)$ which quantifies the integrability of pushforwards of smooth compactly…