Abstract Minimizers of functionals the type $$\begin{aligned} w\mapsto \int _{\Omega }[|Dw|^{p}-fw]\,\textrm{d}x+\int _{{\mathbb {R}}^{n}}\int {R}}^{n}}\frac{|w(x)-w(y)|^{\gamma }}{|x-y|^{n+s\gamma }}\,\textrm{d}x\,\textrm{d}y\end{aligned}$$ w ↦ <mml...

and Applied Analysis 3 (1) V is continuous in ((n − 1)T, (n + τ − 1)T] × R + , ((n + τ − 1)T, nT] × R + and for each x ∈ R + , n ∈ N, lim (t,y)→ ((n+τ−1)T + ,x) V(t, y) = V((n + τ − 1)T + , x) and lim (t,y)→ (nT + ,x) V(t, y) = V(nT, x) exist. (2) V is locally Lipschitzian x. Definition 1. Letting V ∈ V 0 , one defines the upper right derivative of V with respect to the impulsive differential s...

A system of n linear differential equations xy'{x) =x~8B{x)y(x) is considered, in which s is a positive integer and B(x) is a formal power series. In a preceding paper [6] the author has developed a method for evaluating a formal fundamental matrix solution to the system. This method leads to the algebraic treatment of certain singular matrix pencils. In the present paper the author provides so...

tumors of t h e male u ret h ra are r a re, co m prising <1% of urolo g ic malignancies. this is a re po rt of a 44-ye a r-old man pre s ented with a 4 -month history of gross initi a l h e maturia and d y s u ri a . af t e r exami n ing the pa t ien t , we found a firm mass ex t ending 1 c m within the p roxim a l bulb a r uret h ra and a pathologic report of moderately differen t iated sq u a...

Sunto: Questo articolo considera una successione di equazioni diieren-ziali a derivate parziali non lineari in forma di divergenza del tipo ?div (Q " G(x; N " ru)) = f " ; in un dominio limitato dello spazio n-dimensionale; Q " = Q " (x) e N " = N " (x) sono matrici con coeecenti limitati, N " e' invertibile e la sua matrice inversa R " ha anche coeecenti limitati. La non linearita' e' dovuta a...

Let X be a nonsingular algebraic curve of genus g ≥ 3, and M ξ the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d coprime and d > n(2g − 2). We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3. Let W ξ (L) denote the vector bundle over M ξ defined as the direct image π * (U ξ ⊗ p * 1 L) where U ξ is a universal vector bu...

IT WAS established by Brown[2] that any locally-fiat imbedding of S "-~ in S" divides S" into two domains, each of whose closures is an n-ball. Somewhat later[5] the h-eobordism theorem further established that if S"1 is a smooth of P L submanifold of S" then so are the resulting n-balls, provided that n > 5. (The case n < 3 had been known since Alexander[l].) For n = 4 little is known. The goa...

Let S(n, k) denote the Stirling number of the second kind, and let Kn be such that S(n,Kn − 1) < S(n,Kn) ≥ S(n,Kn + 1). Using a probabilistic argument, we show that, for all n ≥ 2, ⌊e⌋ − 2 ≤ Kn ≤ ⌊e ⌋+ 1, where ⌊x⌋ denotes the integer part of x, and w(n) denotes Lambert’s W function.

Let D be a real function such that D(z) is analytic and D(z) ± 0 for \z\ < 1. Furthermore, put W(x) = \J\ x2\D(e'v)\2 , x = costp , tp e [0, 71 ], and denote by pn(', rV) the polynomial which is orthogonal on [-1, +1] to Pn_[ (P„_! denotes the set of polynomials of degree at most n 1 ) with respect to W . In this paper it is shown that for each sufficiently large n the polynomial En+X(-, W) (ca...