Curves on threefolds and a conjecture of Griffiths–Harris

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in . We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.     

Koszul–Sullivan Models and the Cohomology of Certain Solvmanifolds

In this paper we develop a technique of working with graded differential algebra models of solvmanifolds, overcoming the main difficulty arising from the non-nilpotency of the corresponding Mostow fibrations. A graded differential model for solvmanifolds of the form G/ with G=RN is presented (N is a nilpotent Lie group, G is a semi-direct product). As an application, we prove the Benson–Gordon conjecture in dimension four.     

The Relation Between the Petits Integral and the McShane Integral of Banach-valued Functions Defined on R~n

R.A.Gordon[1]generalizedthedefinitionoftheMcShaneintegralforrealvaluedfunctionstotheabstractfunctionsfromR1toBanachspaces.Inthispaper,wedefinetheMcShaneintegralforabstractfunctionsfromRntoBanachspacesandprovethatifeveryfunctionffromIoinRntoBanachspacesisMcShaneintegrablethenfisPettisintegrable,andiftheunitballB(X)inX*isrelativelyweaklycompact,fisPetitsintegrablethenfisMcShaneintegrableonIo.ThisgivesapositiveanswertoanopenproblemleftbyR.A.Gordonin[1].ThroughoutthispaperXwilldenoteare…     

The Cartesian Closedness of the Category CDL and Function Spaces on Topological CDL''''s

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Monomial Gorenstein algebras and the stably Calabi–Yau property

A celebrated result by Keller–Reiten says that 2-Calabi–Yau tilted algebras are Gorenstein and stably 3-Calabi–Yau. This note shows that the converse holds in the monomial case: a 1-Gorenstein monomial algebra and stably 3-Calabi–Yau is 2-Calabi–Yau tilted, moreover is Jacobian. We study the case of other stably Calabi–Yau Gorenstein monomial algebras.

     

Singular Integral Equations on Non-Smooth Curves in Hölder–Frechét Space

We consider singular integral equations on non-smooth rectifiable curves and on certain classes of curves of infinite length.     

Integral representation and computational properties of the incomplete Fox–Wright function

The Ramanujan Journal - The main focus of this paper is to investigate some new properties of the incomplete Fox–Wright function. We derive an integral representation of the incomplete...     

The Integral of Mean Curvatures on the Tube Hypersurfaces

The calculation on the tube hypersurfaces is very interesting and important,especially H.Weyl gave a formula of the volume of tubes which contains a seriesof curvature invariants of submanifolds. Let N be an oriented compact n-dimensional submanifold in the m-dimensional     

One Loop Approximation of the Chern–Simons Integral

It is proven that the one loop approximation of the Wilson line integral in a perturbative SU(2) Chern–Simons theory is localized around the critical point in the large level.     

A Construction of the Rational Function Sheaves on Elliptic Curves

Abstract The authors introduce an effective method to construct the rational function sheaf κ on an elliptic curve E, and further study the relationship between κ and any coherent sheaf on E. Finally, it is shown that the category of all coherent sheaves of finite length on E is completely characterized by κ.     

On the Volterra Factorization of the Wiener–Hopf Integral Operator

Mathematical Notes - The problem of the factorization of the Wiener–Hopf integral operator in the form of the product of the upper and lower Volterra operators is considered. Conditions for...     

Green’s Function of Ordinary Differential Operators and an Integral Representation of Sums of Certain Power Series

The eigenvalues and eigenfunctions of certain operators generated by symmetric differential expressions with constant coefficients and self-adjoint boundary conditions in the space of Lebesgue squareintegrable functions on an interval are explicitly calculated, while the resolvents of these operators are integral operators with kernels for which the theorem on an eigenfunction expansion holds. In addition, each of these kernels is the Green’s function of a self-adjoint boundary value problem, and the procedure for its construction is well known. Thus, the Green’s functions of these problems can be expanded in series in terms of eigenfunctions. In this study, identities obtained by this method are used to calculate the sums of convergent number series and to represent the sums of certain power series in an intergral form.