Deligne's regularity criterion for an integrable connection ∇ on a smooth complex algebraic variety X says that ∇ is regular along the irreducible divisors at infinity in some fixed normal compactification of X if and only if the restriction of ∇ to every smooth curve on X is regular (i. e. has only regular singularities at infinity). The " only if " part is the difficult implication. Deligne's...

The real algebraic set we obtain will in general be singular. The homeomorphism will be piecewise differentiable. Total algebraicity is a very useful concept since it eiliminates many obstructions to making a topological situation algebraic, c.f. [AK1], [AK2], [AK5]. At first glance our result does not seem to be very useful since current algebraic approximation lemmas require nonsingularity. T...

Let φ : V 99K W be a birational map between smooth algebraic varieties which does not change the canonical class (in the sense of Batyrev, [Bat99]). We prove that the total homology Chern classes of V and W are push-forwards of the same class from a resolution of indeterminacies of φ. For example, it follows that the push-forward of the total Chern class of a crepant resolution of a singular va...

A PDAE model of a multicomponent gas pipeline has been formulated and solved using the ode15s solver of Matlab. The model with boundary conditions allows for reactions and di usion. Also, general cubic equations of state for pressure and enthalpy are described. To simplify the implementation at this stage, a non-reactive, non-di usional model with fixed feed composition is considered, and multi...

We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and pro...

The state-covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter, and also imposes a generalized interpolation constraint on the power spectrum of the input process. This algebraic property and the relationship between state-covariance and the power spectrum of the input allow the use of matrix pencils and analytic interp...

Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionali...

In this paper, we introduce a method of generating the dual graph of the minimal normal resolution of the algebraic curve singularities. Using factorization of polynomials over algebraic extension field, we can calculate the dual graph from the coefficients of the given polynomial exactly. The computing process includes no approximation. We constructed the system to generate the dual graph on R...

In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...