Automorphisms of a Generic Jacobian Kummer Surface

For a generic quartic surface F in ³ with sixteen nodes, we shall prove that every birational automorphism of F is induced by a Cremona transformation of ³.     

Relaxed Hyperelastic Curves on a Non-Degenerate Surface

We study the variational problem belonging to a relaxed hyperelastic curve for non-null curve on a non-degenerate surface in Minkowski three-space \({E_{1}^{3}}\) . Firstly, we derive the intrinsic equations for a relaxed hyperelastic curve and we give the necessary condition for being relaxed hyperelastic curve of any non-null geodesic on the surface in \({E_{1}^{3}}\) . Then, we examine this formulation on non-null geodesics of pseudo-plane, pseudo-sphere \({S_{1}^{2}(r) }\) , hyperbolic space \({H_{0}^{2}(r)}\) and pseudo-cylinder \({C_{1}^{2}(r)}\) .     

On Σ1-definable Functions Provably Total in I ∏

We prove the following theorem: Let φ(x) be a formula in the language of the theory PA^? of discretely ordered commutative rings with unit of the form ?yφ′(x,y) with φ′ and let ∈ Δ₀ and let fφ: ? → ? such that f_φ(x) = y iff φ′(x,y) & (?z < y) φ′(x,z). If I ∏ ∈(?x ≥ 0), φ then there exists a natural number K such that I ∏ ? ?y?x(x > y ? ?φ(x) < x^K). Here I ∏₁^? denotes the theory PA^? plus the scheme of induction for formulas φ(x) of the form ?yφ′(x,y) (with φ′) with φ′ ∈ Δ₀.     

Rational Cuspidal Plane Curves of Type (d,d — 3)

In the previous paper [FlZa 2] we classified the rational cuspidal plane curves C with a cusp of multiplicity deg C — 2. In particular, we showed that any such curve can be transformed into a line by Cremona transformations. Here we do the same for rational cuspidal plane curves C with a cusp of multiplicity deg C — 3.     

Linear Series on 4 – Gonal Curves

Let C be the general 4 – gonal curve of genus g > 6. We investigate the complete linear series on C and the varieties W^r_d(C), and we study the birational models of C in ℙ^r (r ≥ 2) of minimal degree.     

2-Harmonic Curves Isometrially Immersed in a Surface

In this paper,the author proves the necessary and sufficient condition for the existenceof 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N■IE~3.     

Differential Modular Forms on Shimura Curves, I

The quotient of a Shimura curve by the isogeny equivalence relation is not an object of algebraic geometry. The paper shows how this quotient space becomes a geometric object in a more general geometry obtained from 'usual algebraic geometry', by adjoining a new operation; this operation looks like a 'Fermat quotient' and should be viewed as an arithmetic analogue of usual derivations.     

On first order congruences of lines in ℙ4 with irreducible fundamental surface

In this article we study congruences of lines in ?ⁿ, and in particular of order one. After giving general results, we obtain a complete classification in the case of ?⁴ in which the fundamental surface F is in fact a variety, i.e. it is integral, and the congruence is the irreducible set of the trisecant lines of F. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Family of Pearson discrete distributions generated by the univariate hypergeometric function 3F2(α1, α2, α3; γ1, γ2; λ)

In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function ₃F₂(α₁, α₂, α₃;γ₁, γ₂; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd.     

Difference between irregular chaotic patterns of second-order double-loop ΣΔ modulators and second-order interpolative bandpass ΣΔ modulators

In this paper, we find that, by computing the difference between two consecutive state vectors of second-order double-loop sigma-delta modulators (SDMs) and plotting one component of the subtracted vectors against the other component, irregular chaotic patterns will become two vertical lines. By multiplying a matrix on the subtracted vectors, it can be further transformed to two fixed points. However, second-order interpolative bandpass SDMs still exhibit chaotic behaviors after applying the same transformations. Moreover, it is found that the Lyapunov exponent of state vectors of second-order double-loop SDMs is higher than that of second-order interpolative bandpass SDMs, whereas the Lyapunov exponent of transformed vectors becomes negative infinity for second-order double-loop SDMs and increases for second-order interpolative bandpass SDMs. Hence, by examining the occurrence of chaotic behaviors of the transformed vectors of these two SDMs, these two SDMs can be distinguished from their state vectors and their transformed vectors without solving the state equations and knowing the information of input signals.     

Weak -property in Σ-products

It is shown that each Σ-product of paracompact p-spaces has the weak -property.     

Equivalent Separating Curves on Closed Surface of Genus 2

Let {A,B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to (A, B) if it is disjoint from A∪B and it cuts F into two once-punctured tori X, Y with A(?)X, B(?)Y. Letγbe a simple closed curve on F which is disjoint from A∪B and intersects C essentially in two points. In this paper, we show that up to isotopy, {hnγ(C):n∈Z} is the set containing all the simple closed curves on F which is separating with respect to (A,B), where hγis the Dehn twist alongγon F. This also shows how two simple closed curves on F which are separating with respect to (A,B) are related. The result can be applied to yield all Haken spheres of a Heegaard splitting V∪F W which are weakly equivalent to a given Heken sphere of the splitting.     

Terminal 3-fold Divisorial Contractions of a Surface to a Curve I

Let X be a smooth curve on a 3-fold which has only index 1 terminal singularities along . In this paper we investigate the existence of extremal terminal divisorial contractions E Y X, contracting an irreducible surface E to . We consider cases with respect to the singularities of the general hypersurface section S of X through . We completely classify the cases when S is A _i , i 3, and D _2n for any n.     

Fractional Calculus Operators Involving the Gauss Function on Spaces Fp,μand F'p,μ

This paper deals with the study of operators of fractional calculus introduced by Saigo in spaces of generalized functions considered by McBride.