Related papers: On the C-projective vector fields on Randers space…

Let F be a field of characteristic different from 2. The u-invariant and the Hasse number of a field F are classical and important field invariants pertaining to quadratic forms. These invariants measure the suprema of dimensions of…

Projectivity and injectivity are fundamental notions in category theory. We consider natural weakenings termed semiprojectivity and semiinjectivity, and study these concepts in different categories. For example, in the category of metric…

Two K\"ahler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit…

We propose a method to give a $d+1$ geometry from a $d$ dimensional quantum field theory in the large N expansion. We first construct a $d+1$ dimensional field from the $d$ dimensional one using the gradient flow equation, whose flow time…

Let $\mathscr{C}_n=\{-1,1\}^n$ be the discrete hypercube equipped with the uniform probability measure $\sigma_n$. Talagrand's influence inequality (1994) asserts that there exists $C\in(0,\infty)$ such that for every $n\in\mathbb{N}$,…

Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…

We work on the classification of isomorphism classes of finitely generated projective modules over the C*-algebras $C\left( \mathbb{P}^{n}\left( \mathcal{T}\right) \right) $ and $C\left( \mathbb{S}_{H}^{2n+1}\right) $ of the quantum complex…

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates X^{\mu_1 ... \mu_n} encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which…

Let $X$ be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of $C(X)$-algebras by $C(X)$-subalgebras with controlled complexity. The following…

Let $B_n$ be the Euclidean unit ball in ${\mathbb R}^n$ given by the inequality $\|x\|\leq 1$, $\|x\|:=\left(\sum\limits_{i=1}^n x_i^2\right)^{\frac{1}{2}}$. By $C(B_n)$ we mean the space of continuous functions $f:B_n\to{\mathbb R}$ with…

We study the scaling behavior of Randers-Finsler massless scalar field theories in the infrared regime. For that, we compute analytically the radiative corrections to the corresponding anomalous dimensions, related to the critical exponents…

We consider a deviation of the physical length from the Riemann geometry toward the Randers'. We construct a consistent second-order relativistic theory of gravity that dynamically reduces to the Einstein-Hilbert theory for the strong and…

We generalize the classical Multidimensional Scaling procedure to the setting of general metric measure spaces. We develop a related spectral theory for the generalized cMDS operator, which provides a more natural and rigorous mathematical…

In this paper, the isoperimetric problem in Randers planes, $(\mathbb{R}^2,F=\alpha +\beta)$, which are slight deformation of the Euclidean plane $(\mathbb{R}^2,\alpha)$ by suitable one forms $\beta$, have been studied. We prove that the…

We study the noncommutative topology of the $C^*$-algebras $C(\mathbb{C}P_q^{n})$ of the quantum projective spaces within the framework of Kasparov's bivariant K-theory. In particular, we construct an explicit KK-equivalence with the…

Let $\lambda_1(G)\ge \lambda_2(G)\ge \cdots \ge \lambda_n(G)$ denote the adjacency eigenvalues of a graph $G$ of order $n$. We prove that for every $k\geq 2$ and every graph $G$ on $n\geq k$ vertices, $$ \lambda_k(G)\le…

Wigner's theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In metric geometry nonexpansive maps and noncontractive maps are well studied generalizations of isometries. We show that under certain…

We establish the vector-valued Wiener type theorems for countable projective and inductive limits of quasi-Banach algebras in a weighted setting for both finite and infinite dimensional cases. As an application, we extend the notions of…

We characterize the modules of infinite projective dimension over the endomorphism algebras of Opperman-Thomas cluster tilting objects $X$ in $(n+2)$-angulated categories $(\mathcal C,\Sigma^n,\Theta)$. For an indecomposable object $M$ of…

Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively…