Throughout this paper, G denotes a fixed, not necessarily connected, reductive algebraic group over an algebraically closed field k. This paper is a part of a series [L9] which attempts to develop a theory of character sheaves on G. The numbering of the sections and references continues that of the earlier Parts. Section 23 is a generalization of results in [L3, II,§7]. It is a preparation for ...

Let Y be the zero loci of a regular section of a convex vector bundle E over X . We provide a proof of a conjecture of Cox, Katz and Lee for the virtual class of the genus zero moduli of stable maps to Y . This in turn yields the expected relationship between Gromov-Witten theories of Y and X which together with Mirror Theorems allows for the calculation of enumerative invariants of Y inside of...

BACKGROUND The rate of caesarean deliveries has increased 10-fold worldwide during the past decades. OBJECTIVE To evaluate differences in the establishment of gut microbiota in infants born by vaginal or caesarean delivery and its impact on mucosal immunity. METHODS Altogether, 165 consecutive children, prospectively followed from birth at our clinic in Turku, Finland, were gathered; 141 (8...

Let O K be a Dedekind domain with eld of fractions K. Let f : X ! Y be a nite morphism of projective, smooth, and geometrically connected curves over Spec(K). In this paper, we study some possible relationships between the models of X and of Y. In the rst part of the paper, we look at semi-stable and stable models, while in the second part we investigate regular models. Let us describe the cont...

Let (M,I,Ω) be a holomorphically symplectic manifold equipped with holomorphic Lagrangian fibration π:M↦X, and η closed form of Hodge type (1,1)+(2,0) on X. We prove that Ω′:=Ω+π⁎η is again form, for another complex structure I′, which uniquely determined by Ω′. The corresponding deformation structures called “degenerate twistorial deformation”. map π respect to this new structure, X the fibers...

There are a number of subsets of primes with a conjectured density of a constant times x/ log x. These include the primes separated by a fixed even integer, Sophie Germain primes and the so-called “thin primes”, i.e. primes of the form 2q − 1 where q is prime [3]. In order to gain some familiarity with sequences of this density we undertook an investigation of the set of primes of prime order, ...

We consider integral equations on the halfline of the form x(s) − ∫∞ 0 k(s, t)x(t) dt = y(s) and the finite section approximation xβ to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e., xβ exists and is uniformly bounded in the space of bounded con...

and Applied Analysis 3 Remark 1.2. In 1.6 ; we easily see that lim q→ 1 F r q t, x 2 ∞ ∑ m 0 −1 m ( m r − 1 m ) e m x t 2e ∞ ∑ m 0 −1 m ( m r − 1 m ) e 2e 1 et r F r t, x . 1.7 From the above, we obtain generating function of the Nörlund Euler numbers of higher order. That is F r t, x 2e 1 et r ∞ ∑ n 0 E r n x t n! . 1.8 Thus, we have lim q→ 1 E r n,q x E r n x . 1.9 cf. 21 . Hence, we have F r...

The purpose of this paper is to extend the Buneman construction of partially labelled trees to the general case. This extension is related with the characterization of median graphs by Mulder and Schrijver. In the first section, we construct a graph G(H) associated with a copair hypergraph H on a finite set X and define the notion of a median graph with latent vertices (called X-median graph). ...

Figure 1: The unintegrated gluon distribution at a scale q̄ = 4 GeV for different values of μ and σ of the intrinsic k⊥ distribution as a function of x for fixed k⊥(top) and as a function of k⊥ (bottom) for fixed x Unintegrated parton density functions (uPDFs) are best suited to study details of the hadronic final state in high energy ep and also in pp collisions (for a review see [2–8]). In gen...