purpose: to evaluate changes in tear condition following unilateral ptosis surgery. methods: in this case series all patients with unilateral ptosis who underwent ptosis surgery over a two-year period were studied. the patients did not have history of previous eye surgery or other eye problems. eyelid and lacrimal evaluation included schirmer’s test with and without anesthesia and tear break up...

Abstract We apply capacities to explore the space–time fractional dissipative equation: (0.1) $$ \begin{align} \left\{\begin{aligned} &\partial^{\beta}_{t}u(t,x)=-\nu(-\Delta)^{\alpha/2}u(t,x)+f(t,x),\quad (t,x)\in\mathbb R^{1+n}_{+},\\ &u(0,x)=\varphi(x),\ x\in\mathbb R^{n}, \end{aligned}\right. \end{align} where $\alpha>n$ and $\beta \in (0,1)$ . In this paper, we focus on regulari...

1 Dirichlet’s theorem — set up Dirichlet’s famous theorem from 1837 asserts that if k is a positive integer and a is an integer coprime to k, then there are infinitely many primes p with p ≡ a (mod k). In this unit we will prove the stronger assertion that the sum of the reciprocals of the primes p ≡ a (mod k) is divergent. Important in the proof is the use of the orthogonality relations for th...