We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of a domain lying across the boundary of the hyperbolic space using an analytic continuation argument. In this paper we show this method can be further generalized to find the volume of a domain with smooth boundary with suitable regularity in dimension 2 and 3. We also discuss that this volume is invariant under the group of hyperbolic isometries and that this regularity condition is sharp.ᰉ匀̀歭猏ë貀鳬袘駭验

An efficient method for reanalysis of a damaged structures is presented. Perturbation analysis for the equality constrained least squares problem is adapted to handle structural reanalysis, and related theoretical and numerical results are presented.

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

Let X be a smooth, closed, connected spin 4-manifold with and signature . In this paper we use Seiberg-Witten theory to prove that if X admits a spin alternating action, then ||/8+3 under some non-degeneracy conditions.

The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the T-th hyper-Kloosterman sums Kl(h, k+1, r;q) and the hyper Cochrane sums C(h, q; m, k), and give an interesting mean value formula.

Let X be a separable Banach space. We give sufficient conditions under which is hereditarily hypercyclic. Also, we prove that hereditarily hypercyclicity with respect to a special sequence implies the hereditarily hypercyclicity with respect to the entire sequence.

In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichmiiller space into the Goldman space g(M). From this algebraic presentation, we shall show that the Goldman's length parameter on g(M) is an isometric extension of the Fenchel-Nielsen's length parameter on .

We develop the upper and lower solutions method for the four point problem relative to second order differential equations in order to obtain the existence of solution.

As a continuation of computing the zeta function of a regular covering graph by Mizuno and Sato in [9], we derive in this paper computational formulae for the zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the voltages to derive them lie in an abelian or dihedral group and its fibre is a regular graph, those formulae can be simplified. As a by-product, the zeta function of the cartesian product of a graph and a regular graph is obtained. The same work is also done for a discrete torus and for a discrete Klein bottle.

It is well known that the twistor, section of twistor space, classify the orthogonal almost complex structure on even dimensional Riemannian manifold (X, g). We will show that existence of a harmonic and anti-holomorphic twistor is equivalent to having a symplectic structure on (X, g).

The affine homogeneous hypersurface in , which is a graph of a function with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

For double arrays of constants and sequences of negatively orthant dependent random variables , the conditions for strong law of large number of are given. Both cases are treated.

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

It is known that if C is an [24m + 2l, 12m + l, d] selfdual binary linear code with $0{\leq}l<11,\;then\;d{\leq}4m+4$. We present a sufficient condition for the nonexistence of extremal selfdual binary linear codes with d=4m+4,l=1,2,3,5. From the sufficient condition, we calculate m's which correspond to the nonexistence of some extremal self-dual binary linear codes. In particular, we prove that there are infinitely many such m's. We also give similar results for additive self-dual codes over GF(4) of length n=6m+1.☊ᔀЀ㘴〻᠀䡯浥‭⁦慭楬礠浡湡来浥湴