Abstract. Let x0 ∈ Ω ⊂ R, n ≥ 2, be a domain and let m ≥ 2. We will prove that a solution u of the polyharmonic equation ∆u = 0 in Ω \ {x0} has a removable singularity at x0 if and only if |∆u(x)| = o(|x − x0|) ∀k = 0, 1, 2, . . . , m − 1 as |x − x0| → 0 for n ≥ 3 and = o(log(|x−x0|)) ∀k = 0, 1, 2, . . . , m− 1 as |x−x0| → 0 for n = 2. For m ≥ 2 we will also prove that u has a removable singula...

We present KaRMMa, a novel method for performing mass map reconstruction from weak-lensing surveys. employ fully Bayesian approach with physically motivated lognormal prior to sample the posterior distribution of convergence maps. test KaRMMa on suite dark matter N-body simulations simulated DES Y1-like shear observations. show that outperforms basic Kaiser-Squires in two key ways: 1) our best ...

Using the technique of evolving sets, we explore connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular show that a walk starting at vertex x0, if after n steps, En is least Cn where C independent then transient. We also give an example which demonstrates condition being x0 necessary.

Let A and B be closed, convex bounded subsets of a weakly sequentially complete Banach space E which both are not compact. Then there is linear form x0⁎∈E⁎ does attain its supremum on B. In particular, given any subset A⊂E, if every x⁎∈E⁎ either attains or infimum A, then relatively The same happens for finite family but compact subsets. result only remains true in arbitrary assuming, two σ(E⁎⁎...

introduction: tt virus (ttv) is an unenveloped single-stranded circular dna virus. sensitive pcr (polymerase chain reaction) methods with primers designed for very conserved regions of the viral genome (utr) indicate high prevalence (> 90%) of ttv infection in general population of many countries world-wide. although there has been no evidence of its relation to any liver or other specific dise...