Related papers: $delta$-Quasi Cauchy Sequences
We announce conditions under which a given sequence of points on the complex plane is a subsequence of zeros of an entire function with weight restrictions on growth.
We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…
Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $\phi(v; \cdot)$ be the density of the absolutely…
A metric space $\mathbf{X}$ is called densely complete if there exists a dense set $D$ in $\mathbf{X}$ such that every Cauchy sequence of points of $D $ converges in $\mathbf{X}$. One of the main aims of this work is to prove that the…
Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…
J. Elton proved that every normalized weakly null sequence in a Banach space admits a subsequence that is nearly unconditional which is a weak form of unconditionality. The notion of near-unconditionality is quantified by a constant…
The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multiple natural definitions of capacity are possible). Motivated…
Let $(r_k)$ be an increasing sequence and $(w_k)$ a positive sequence. We study the following question: is it true that for every sequence $(a_k)$ satisfying $\sum_{k=0}^\infty |a_k|^2 w_k^2 < \infty$ there exists a function $f\in…
In this paper we introduce a new semicontinuity notion, which is weaker than upper semicontinuity, and assures the closedness of the sets $G(y)=\{x\in K: f(x,y)\not\in -\inte C\}.$ Furhter, this semicontinuity is also closed under addition.…
We demonstrate analytically and numerically the existence of geodesically complete singularities in quintessence and scalar tensor quintessence models with scalar field potential of the form $V(\phi)\sim \vert \phi\vert^n$ with $0<n<1$. In…
For topological spaces $X$ and $Y$, a (not necessarily continuous) function $f:X \rightarrow Y$ naturally induces a functor from the category of closed subsets of $X$ (with morphisms given by inclusions) to the category of closed subsets of…
We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
In a metric space, such as the real numbers with their standard metric, a set A is open if and only if no sequence with terms outside of A has a limit inside A. Moreover, a metric space is compact if and only if every sequence has a…
We characterize lower semicontinuity of integral functionals with respect to weak$^*$ convergence in $\mathrm{BV}$, including integrands whose negative part has linear growth. In addition, we allow for sequences without a fixed trace at the…
Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain…
A relation giving a minimum for the irreversible work in quasi-equilibrium processes was derived by Sekimoto et al. (K. Sekimoto and S. Sasa, J. Phys. Soc. Jpn. {\bf 66} (1997), 3326) in the framework of stochastic energetics. This relation…
In this note we establish several versions of a compactness theorem for submanifolds. In particular we require only bounds on the second fundamental form and do not assume volume or diameter bounds. As an application we prove a compactness…
One of the consequences of the Compactness Principle in structural Ramsey theory is that the small Ramsey degrees cannot exceed the corresponding big Ramsey degrees, thereby justifying the choice of adjectives. However, it is unclear what…
We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…