The article constructs a complete uniform asymptotic expansion in small parameter of the solution first boundary value problem. problem is posed for singularly perturbed linear inhomogeneous second-order partial differential equation with two independent variables parabolic type. investigated on rectangle. peculiarities are presence front heat conduction operator, existence corner layers at low...

Existence and boundedness is proved for the solutions of a boundary value problem two-dimensional Broadwell model in rectangle. The influence orientation relation to sides rectangle on form analysed. Exact are found use determine accommodation coefficients at boundaries fluid flow rectangular box.

A common method for constructing blending Dupin cyclides for two cones having a common inscribed sphere of radius r > 0 involves three steps: (1) computing the (?r)-oosets of the cones so that they share a common vertex, (2) constructing a blending cyclide for the ooset cones, and (3) computing the r-ooset of the cyclide. Unfortunately , this process does not always work properly. Worse, for so...

Abstract Invisibility, robustness and blindness are three difficult points for 3D model information hiding. In this paper, a new robust and blind information hiding algorithm for 3D models is proposed. Skeleton of 3D models is extracted, and skeleton points are obtained inside the objects at the same time. Taking skeleton points as centers, EMIS are obtained according to Euclidean Maximum Inscr...

Don't be square! A rare S(4) (2-) rectangle bridging two M(2)Cp(2)(mu(2)-CH(2))(2) (M=Rh, Ir) fragments is found to contain two "half-bonds" with S-S distances of 2.70 or 2.90 A. Computational studies explore the connection between these "half-bonds" and a Jahn-Teller distortion, as well as possible intermediates that form M(4)S(4) (2+) clusters having the S(4) (2-) rectangle rotated by 90 degr...

We examine a variant of the maximum empty square (or rectangle) problem: Find an axis-aligned square (or rectangle) that contains as many blue points as possible without containing any red points. Let n be the total number of red and blue points. We solve the bichromatic square problem in O(n log n) time and O(n) space. We also solve the bichromatic rectangle problem in O(n log n) time and O(n ...

We consider approximations of a smooth convex body by inscribed and circumscribed convex polytopes as the number of vertices, resp. facets tends to innnity. The measure of deviation used is the diierence of the mean width of the convex body and the approximating polytopes. The following results are obtained. (i) An asymptotic formula for best approximation. (ii) Upper and lower estimates for st...

Abstract. This paper deals with the rectangle packing problem, of filling a big rectangle with smaller rectangles, while the rectangle dimensions are real numbers. A new nonlinear programming formulation is presented and the validity of the formulation is proved. In addition, two cases of the problem are presented, with and without rotation of smaller rectangles by 90. The mixed integer piecewi...