blackboard framing

What is the framing of a knot?

In my understanding, framing of a knot is not something you can calculate from the knot, but rather an additional piece of information. It is defined as follows. On the boundary of a tubular neighborhood of the knot there is a unique nontrivial simple closed curve which bounds a disc in the tubular neighbourhood. We call such a curve the meridian. Then there are infinitely many curves on the boundary of the tubular neighbourhood, which intersect the meridian once. They are called longitudes. Now a choice of a longitude is the framing of our knot. It is naturally in bijection with integers: all longitudes differ by some number of twists around the meridian (the sign of the difference is pinned down by orientation) and there is a unique longitude that is homologically zero in the complement of the knot, which is mapped to zero in our correspondence between integers and longitudes

Is a longitude a bijection?

Now a choice of a longitude is the framing of our knot. It is naturally in bijection with integers: all longitudes differ by some number of twists around the meridian (the sign of the difference is pinned down by orientation) and there is a unique longitude that is homologically zero in the complement of the knot, ...

How wide is an exit door?

When installed in exit doorways, exit doors shall be capable of opening at least 90 degrees and shall be mounted so that the clear width of the exitway is no less than 32 inches. In computing the exit width required, the net dimension of the exitway shall be used. Exception: Existing buildings may be less than 3 feet in width if the clear width ...

How wide is a landing?

Where a door opens over a landing, the landing shall be at least as wide as the door, and at least 5 feet long. (Title 24, Part 2, Section 2-3303 (i) (1) and (i) (2).)

Is a turntile considered an exit?

Turnstiles shall not be considered as providing any exit width. (Title 24, Part 2, Section 2-3303 (n) (1).) (k) Doors in Folding Partitions. When permanently-mounted folding or movable partitions are used to divide a room into smaller spaces, exits from these enclosures shall be provided as required under Section 3228.

Can you use edge bolts on exit doors?

Manually- operated edge bolts or surface-mounted flush bolts and surface bolts are prohibited on required exit doors. When exit doors are installed in pairs and automatic flush bolts are used, the door leaf with these bolts shall have no door knob or surface-mounted hardware.

How many rads are in a 90 degree cleanout extension?

Each cleanout extension shall be considered as drainage piping and each 90 degree (1.57 rad) cleanout extension shall be extended from a wye-type fitting or other approved fitting of equivalent sweep.

What temperature should brazed joints be?

Brazed joints between copper or copper alloy pipe and fittings shall be made with brazing alloys having a liquid temperature above 1000°F (538°C). The joint surfaces to be brazed shall be cleaned bright by either manual or mechanical means. Piping shall be cut square and reamed to full inside diameter. Brazing flux shall be applied to the joint surfaces where required by manufacturer's recommendation. Brazing filler metal in accordance with AWS A5.8 shall be applied at the point where the pipe or tubing enters the socket of the fitting.

What bends are required for drainage piping?

Changes in direction of drainage piping shall be made by the appropriate use of approved fittings and shall be of the angles presented by a one-sixteenth bend, one-eighth bend, or one-sixth bend, or other approved fittings of equivalent sweep.

Where to place a cleanout?

Cleanouts shall be placed inside the building near the connection between the building drain and the building sewer or installed outside the building at the lower end of the building drain and extended to grade.

What is drainage and plumbing?

The drainage and plumbing systems must permit the quick runoff of all water from plant buildings, and of surface water around the plant buildings, and of surface water around the plant and on the premises; and all such water shall be disposed of in such a manner as to prevent a nuisance or health hazard.

How thick is a pan?

For safe pans - not less than 4 pounds per square foot (lb/ft 2 (19 kg/m 2) or 1 / 16 of an inch (1.6 mm) thick. For flashings or vent terminals - not less than 3 lb/ft 2 (15 kg/m 2) or 0.0472 of an inch (1.1989 mm) thick. Lead bends and lead traps shall be not less than 1 / 8 of an inch (3.2 mm) in wall thickness.

Where are expansion joints permitted?

Expansion joints shall be accessible, except where in vent piping or drainage stacks , and shall be permitted to be used where necessary to provide for expansion and contraction of the pipes.

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