Related papers: Areas Between Cosines
We obtain analytical expressions for the generating function $\xi_d(\lambda)$ of the sum of $d$-squares arithmetical function $r_d(n)$ where $\lambda$ is a free parameter. The original $d$-dimensional infinite sum is reduced to a formula…
The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. This extremal surface can be obtained by a maximin construction, allowing many new…
Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…
Based on a suitable improvement of a triangle inequality, we derive new mutual bounds for $p$-angular distance $\alpha_p[x,y]=\big\Vert \Vert x\Vert^{p-1}x- \Vert y\Vert^{p-1}y\big\Vert$, in a normed linear space $X$. We show that our…
We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of…
Let $s(n)$ be the number of different remainders $n \bmod k$, where $1 \leq k \leq \lfloor n/2 \rfloor$. This rather natural sequence is sequence A283190 in the OEIS and while some basic facts are known, it seems that surprisingly it has…
In this paper, the existence of $L^p(p>1)$ solutions for one-dimensional backward stochastic differential equations will be shown directly by proving that an approximation sequence is a Cauchy one in the $L^p$ sense.
We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first-order, in the Lebesgue space L^p(R^d;R^m) with p in (1,\infty). Sufficient conditions to prove generation results of an analytic…
The intersection numbers of p-spin curves are computed through correlation functions of Gaussian ensembles of random matrices in an external matrix source. The p-dependence of intersection numbers is determined as polynomial in p; the large…
We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D>5 dimensional supergravities. The scalar flow towards the horizon is described in terms an effective potential given by…
Cosmic internal symmetry (COINS) relates cosmic vacuum, dark matter, baryons and radiation, in a finite universe. Evidence for COINS comes from the concordance data, including the WMAP data. COINS is behind 1)the cosmic coincidence, 2)the…
There is no source for cosmic vorticity within the cold dark matter cosmology. However, vorticity has been observed in the universe, especially on the scales of clusters, filaments, galaxies, etc. Recent results from high-resolution general…
We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $L^p$ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient.…
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory…
Saxino decay can generate significant cosmological entropy, and hence dilute theoretical estimates of the present mass density of a given particle species. The dilution factor depends on the saxino and axion masses, and is constrained by…
An introduction to solutions of the Einstein equations defining cosmological models with accelerated expansion is given. Connections between mathematical and physical issues are explored. Theorems which have been proved for solutions with…
Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict…
In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…
I will discuss some recent results on marginally outer trapped surfaces, apparent horizons, and the trapped region. A couple of applications of the results developed for marginally outer trapped surfaces to coalescence of black holes and to…
Let (X,\mu) be a measure space. For p, q\in (0,\infty] and arbitrary subsets P,Q of (0,\infty], we introduce and characterize some intersections of Lorentz spaces, denoted by ILp,Q(X,\mu), ILJ,q(X,\mu) and ILJ,Q(X,\mu).