The incomplete Gamma function γ(α, x) and its associated functions γ(α, x+) and γ(α, x−) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions x and x − are then found.

Definition 1.1. Let L be a line bundle on a normal, irreducible, projective variety. Then the Iitaka dimension of L is defined to be the maximum dimension of the image of πm for m ⊕ N(X, L) provided N(X, L) ∈= 0. If N(X, L) = 0, then the Iitaka dimension of L is defined to be −→. When X is smooth, the Kodaira dimension of X is defined to be the Iitaka dimension of its canonical bundle KX . If X...

We study Gauss maps of order k, associated to a projective variety X embedded in projective space via a line bundle L. We show that if X is a smooth, complete complex variety and L is a k-jet spanned line bundle on X , with k > 1, then the Gauss map of order k has finite fibers, unless X = Pn is embedded by the Veronese embedding of order k. In the case where X is a toric variety, we give a com...

This talk is based on work with N. Khuri and H. Ren.[1,2] The main new tools we use are theorems by Voronin on the universality properties of the Riemann Zeta function, ζ(s), in the critical strip, 1 2 < Re s < 1. Given any real continuous function, φ(x), 0 ≤ x ≤ L, we can choose a mapping, s(x), which maps the line, 0 ≤ x ≤ L, onto a line s(x) that lies in the strip 1 2 < Re s < 1, then given ...

!! Ui // X The modules Mi are “restrictions“ or pullbacks of M along Ui → X, and are compatible in that if Mi,j is the pullback of Mi over Ui along Ui ×X Uj → Ui, then we have isomorphisms Mi,j ∼= Mj,i that satisfy a coherence condition known as the cocycle condition. We say that modules over affine schemes have the property of descent for a family {Ui → X} if any family of compatible modules M...

This formula, derived largely from the work of Talbot, Berman, and MacLachlan (1942), can easily be converted into the form x=mly+m2z which allows the construction of a simple nomogram (Feldman, 1935). The latter greatly accelerates calculation when several estimations are being done together, and reduces the risk of arithmetical error. Thus if the observed extinction at 430 mu=E430=x, the obse...

We present photoionization models accounting for both photoelectric and resonant absorption. Resonance absorption lines from C, O, Ne, Mg, Si S and Fe between 0.1 and 10 keV are treated. In particular we consider the complex of almost 60 strong Fe L absorption lines around 1 keV. We calculate profiles, intensities and equivalent widths of each line, considering both Doppler and natural broadeni...

background: radiation therapy is among the most conventional cancer therapeutic modalities with effective local tumor control. however, due to the development of radio-resistance, tumor recurrence and metastasis often occur following radiation therapy. in recent years, combination of radiotherapy and gene therapy has been suggested to overcome this problem. the aim of the current study was to e...

Let f : X → Spec(Z) be an arithmetic variety of dimension d ≥ 2 and (H, k) an arithmetically ample Hermitian line bundle on X, that is, a Hermitian line bundle with the following properties: (1) H is f -ample. (2) The Chern form c1(H∞, k) gives a Kähler form on X∞. (3) For every irreducible horizontal subvariety Y (i.e. Y is flat over Spec(Z)), the height ĉ1( (H, k)|Y ) dim Y of Y is positive. ...

The paper considers a two-dimensional mathematical model of the filtration viscous, incompressible fluid in deformable porous medium. article describes problem at “oil-water” interface with system parabolic differential equations. posed is solved numerically using differential-difference method based on longitudinal-transverse scheme and sweep to determine unknown boundary. To obtain problem, a...