A formula is given for the Seiberg–Witten invariants of a 4–manifold that is cut along certain kinds of 3–dimensional tori. The formula involves a Seiberg– Witten invariant for each of the resulting pieces. AMS Classification numbers Primary: 57R57 Secondary: 57M25, 57N13

The nesting problem is a two-dimensional cutting and packing problem where the small pieces to cut have irregular shapes. The variant of the problem that we are going to deal with, which naturally arises in several industrial production processes (textile, garment, metalware, etc), considers only one big rectangular piece, the plate, with fixed width and infinite length. The objective will be t...

This paper addresses interesting interface design issues in the designing of 3D clothes and 3D garments for synthetic actors. A complete methodology is presented for realizing what tailors and dress designers have done for centuries: cut flat pieces of cloth according to patterns and pin them around mannequins to see how they fit.

We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces. 2000 Mathematics Subject Classification. Primary 53A10; Secondary 49Q05, 53C42.

Let us imagine that red candles and blue candles are placed on the top of a cake. We want to cut it with a knife into two pieces in such a way that all the red candles are on one of the two pieces and all the blue candles are on the other piece. A question is when we can cut it successfully. The following Kirchberger’s theorem [5] answers this question in a general setting. Let X be a finite su...

The problem addressed in this paper is the decision problem of determining if a set of multi-dimensional rectangular boxes can be orthogonally packed into a rectangular bin while satisfying the requirement that the packing should be guillotine cuttable. That is, there should exist a series of face parallel straight cuts that can recursively cut the bin into pieces so that each piece contains a ...

Due to the increasing interest for healthy foods, the feasibility of using fresh-cut fruits to vehicle probiotic microorganisms is arising scientific interest. With this aim, the survival of probiotic lactic acid bacteria, belonging to Lactobacillus plantarum and Lactobacillus fermentum species, was monitored on artificially inoculated pineapple pieces throughout storage. The main nutritional, ...

Insects and mammals cut their food up into small pieces to facilitate ingestion and chemical digestion. Teeth and jaws act as cutting tools, but, unlike engineering tools designed for a specific purpose, must generally cope with substantial variation in food properties and work at many scales. Knowing how teeth and jaws work effectively requires an understanding of the cutting on the edges and ...

What is beta-amyloid? Beta-amyloid is a small piece of a larger protein called “amyloid precursor protein” (APP). Although scientists have not yet determined APP’s normal function, they have learned a great deal about how it appears to work. In its complete form, APP extends from the inside to the outside of brain cells by passing through a fatty membrane around the cell. When APP is “activated...