For example, the " standard " braid corresponding to the Borromean rings gives rise to the Hopf fibration S < sup > 3 </ sup > → S < sup > 2 </ sup >, and iterations of this ( as in everyday braiding ) is likewise Brunnian.

X + sY / ( 1 − exp (− s )), which then leads to braiding identities such as

This reorganization did not affect their role or equipment, although the traditional orange uniform braiding of the dragoons was replaced by the standard yellow of the Cavalry branch.

By the Greco-Roman era, many of them were considered healers, and were said to have other special powers, including dream interpretation and the ability to control the weather, which they did by braiding or not combing their hair.

In both Russian and German armies the grenadier regiments were considered a historic elite, distinguished by distinctions such as plumed helmets in full dress or special braiding.

Braided rugs are made by using three or more strips of fabric, usually wool, folding the raw edges to the middle and braiding them together.

The braiding is given on simple tensors of homogeneous elements by

Bobbin lace is a lace textile made by braiding and twisting lengths of thread, which are wound on bobbins to manage them.

Hair braiding is an ancient art, practiced by the Ancient Egyptians as long ago as 4000 BC.

It is traditionally made by hand-pulling steamed sheep's cheese into strings and braiding them.

It is likely that the earliest " ropes " were naturally occurring lengths of plant fibre, such as vines, followed soon by the first attempts at twisting and braiding these strands together to form the first proper ropes in the modern sense of the word.

Plaited rope is made by braiding twisted strands, and is also called square braid.

Both elaborate laundry and elaborate braiding demonstrated status, in that such grooming was being performed by others.

In film, the effect is achieved by braiding the whip over a steel or kevlar support cable and anchoring the tip permanently to a support such as a crane or scaffolding.

The khaki uniforms worn by the Chasseurs d ' Afrique from 1915 onwards were distinguished by dark blue collar patches with yellow braiding and regimental numbers.

Officers ' ranks were shown by gold or silver braiding on the kepi.

A method of making a lei by using a base material, such as softened tree bark or long leaves, and braiding it while adding the decorative plant material into each wrap of the braid.

Some whip-crackers doing target work prefer a whip made of kangaroo skin and kangaroo hide is preferred by whip makers because it is many times stronger than cow hide and can be cut into fine, strong laces allowing for more intricate braiding patterns that in the past only could only be done with rawhide, which is much harder to work with.

By exponentiating these operators, however, that is, by going to the continuous Heisenberg group, H < sub > 3 </ sub >( ℝ ), he showed that he could obtain ( his now eponymous ) braiding relations for the exponential operators U and V, ( which, incidentally, may also be effectively realized on finite-dimensional spaces, through Sylvester's celebrated clock and shift matrices in the finite Heisenberg group, as discussed below ).

Finger Weaving: Indian braiding, by Sterling Publishing, New York N. Y. ( ISBN 0-8069-5264-4 ).

Within each army different regiments were usually distinguished by " facings "-linings, turnbacks and braiding on coats in colours that were distinctive to one or several regiments.

Diplomatic uniforms worn on such occasions as the presentation of credentials by ambassadors normally included bicornes worn with feathers and gold or silver braiding.

In general, the braiding maps are in one-to-one correspondence with elements of the symmetric group, acting by permuting the tensor factors.

kity ) is a somewhat obsolete word for " plait " or " thing made by braiding " – for example, a 17th-century Russian source informed readers that U shapok janychary imeli kity, meaning " The Janissaries had braids hanging from their caps.

This is usually achieved by treating the hair with heat from a crimping iron ( also referred to as hair crimper ) or by braiding the hair, often in multiple strands, then undoing the braids.

River control has prevented the Sacramento from its natural flooding, braiding and course-changing patterns, which are important for the maintenance of existing wetlands and the creation of new ones.

As a result, the trail has a clumping, a braiding or a tangling of crescents, of each individual release of material.

Hair braiding, as we know it today has its origins in West Africa.

The difference between ancient and modern braiding: Nowadays, as well as the colorful beads and intricate designs of our ancestors, hair weaving has become part of the traditional braiding technique.

The Hip Hop industry has taken hair braiding and weaving to a whole new level of popularity and style, allowing people from all walks of life to enjoy creating a fashion statement with hair braids and weaves.

Plaiting ( or braiding ) with kangaroo leather has been a widely practised tradition in rural Australia since pioneering times.

Since the Victorian era, the modern dress coat for evening wear has been worn with matching trousers of the same cloth with two stripes of braiding down the side.

This frame has a number of parallel braiding tracks around the circumference of the cylinder but the mechanism allows the transfer of yarn carriers between adjacent tracks forming a multilayer braided fabric with yarns interlocking to adjacent layers.

Netting is a technique which involves braiding natural tresses under a thin, breathable net that serves as a flat surface onto which stylists can weave extensions. This method requires the use of hair net or cap to be placed over the person's hair that has been braided.

While France used smaller bearskins, Spain preferred towering ones with long flowing bags, and while Britain had its tall cloth mitres with lacing and braiding, Russia would sport equally tall leather helmets with brass front-plates.

Carbon fiber filament yarns are used in several processing techniques: the direct uses are for prepregging, filament winding, pultrusion, weaving, braiding, etc.

Similar braiding is used on pressurized rubber hoses, such as in plumbing and hydraulic brake systems in automobiles.

A lucet is a tool used in cordmaking or braiding which is believed to date back to the Viking and Medieval periods, when it was utilized to create cords that were used on clothing, or to hang useful items from the belt.

This knotting or braiding technique is also used with leather or paracord to create a decorative lanyard strapping for knife handles or other gear.

Further production processes include weaving or braiding into carbon fabrics, cloths and mats analogous to those described for glass that can then be used in actual reinforcement processes.

Commonly used reinforcement methods are braiding, spiralling, knitting and wrapping of fabric plies.

Horsehair is used for the crafts of horsehair hitching, horsehair braiding, pottery, and in making jewelry items such as bracelets, necklaces, earrings and barrettes.