In this work we introduce a Poincaré determinant type for operators on the torus $${\mathbb {T}}^n$$ . As an application establish existence of nontrivial solutions elliptic equations form $$(-\Delta )^{\frac{\nu }{2}}u+Qu=0$$ by using Hill’s method.

conclusions results of the present study showed that the tst and sea genes had high frequencies among the mrsa isolates. the increased prevalence of mrsa isolates containing different virulence genes, probably accompanied by antimicrobial resistance, can complicate the therapy of mrsa isolates. results all the tested isolates were susceptible to vancomycin, but resistant to penicillin (100%), e...

This is a complement to my previous article “Advanced Determinant Calculus” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441– ...

Let Ck = ( 2k k ) /(k+1) denote the k-th Catalan number and put ak(x) = Ck+Ck−1x+· · ·+C0x . Define the (n+1)×(n+1) Hankel determinant by setting Hn(x) = det[ai+j(x)]0≤i,j≤n. Even though Hn(x) does not admit a product form evaluation for arbitrary x, the recently introduced technique of γ-operators is applicable. We illustrate this technique by evaluating this Hankel determinant as Hn(x) = n ∑

introduction: certain types of human papillomavrus (hpv) are associated with cervical intraepithelial neoplasia (cin) and squamous cell carcinoma (scc). the aim of theobservations reported here was to determine whether the prognosis for invasive cancers of the uterine cervix is related to the type of human papillomavirus asociated with the tumor. material and methods: twenty patients with invas...