Algebraically, a map is anticonformal if at every point the Jacobian is a scalar times an orthogonal matrix with negative determinant: in two dimensions the Jacobian must be a scalar times a reflection at every point.

Algebraically, let a + b be the circumference of a circle, divided into a longer arc of length a and a smaller arc of length b such that

Algebraically, a lattice is a set with two associative, commutative idempotent binary operations linked by corresponding absorption laws.

; Algebraically closed field: A field F is algebraically closed if every polynomial in F has a root in F ; equivalently: every polynomial in F is a product of linear factors.

; Algebraically independent elements: Elements of an extension field of F are algebraically independent over F if they don't satisfy any non-zero polynomial equation with coefficients in F.

Algebraically compact modules share many other properties with injective objects because of the following: there exists an embedding of R-Mod into a Grothendieck category G under which the algebraically compact R-modules precisely correspond to the injective objects in G.

Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions.

Algebraically, this means that the standard MV-algebra generates the variety of all MV-algebras.

Suvorov saw in these scimitar-wielding skirmishers not demographic units but military men of a high potential.

It is not an exaggeration to say that the state government has little or no fiscal control over these units of government.

In total, these increases in operating costs outweigh the savings that result from declining programs and from economy measures, such as reduced numbers of units and installations, smaller inventories of major equipment, and improvements in the supply and distribution systems of the Armed Forces.

Of these, 376 said they make no extra charge for strapping in standard units, because they save enough on mechanized carloading to offset their strapping cost.

Sample units ( villages in rural areas, houses in cities ) were drawn systematically within these strata.

and these costs must somehow be apportioned among the various classes and then must somehow be reapportioned among the units of service in order to report unit costs that can serve as tentative measures of reasonable rates.

The general basis on which these common costs are assigned to differently measured units of service will be illustrated by the following highly simplified problem of an electric-utility cost analysis.

The epic poems, the consolidation of the Greek pantheon, the rise of firm political units, the self-awareness which could permit painted and sculptured representations of men -- all these had to await the progress of following decades.

The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny quantities has been around for millennia, but these ideas were founded in abstract, philosophical reasoning rather than experimentation and empirical observation.

The reliability of the system was limited to about 1 error in 100, 000 calculations by these units, primarily attributed to lack of control of the sheets ' material characteristics.

In some armies only designated artillery HQs have the tactical fire control authority to order fire units to engage a target, all ' calls for fire ' being requests to these HQs.

* Meteorological data: historically these were usually divisional level specialist teams but advances in technology mean they are now increasingly part of artillery units.

Most armies now place these services in specialist branches with specialist repair elements in batteries and units.

In addition to these troops Belarus was the area of deployment for units subordinated directly to the USSR Defence Ministry and chiefs of different Soviet Armed Forces services, namely the 103rd Guards Airborne Division, the 38th Guards Airborne Brigade, the 11th corps of the 2nd Separate Air Defence Army, the 26th Air Army and also units and formations of the Strategic Rocket Forces, Long Range Aviation, the Navy and special forces.

The exact chemical composition and the sequence in which these units are arranged is called the primary structure, in the case of proteins.

Many cover versions are in different languages rewritten to reference local units ; these include:

The strengths of the bellingerent forces are unknown, but we know that Cniva divided his forces into three units, with one of these parts concealed behind a swamp.

While these included elite Bersaglieri, Alpini and Cacciatori units, a large proportion of the troops were inexperienced conscripts recently drafted from metropolitan regiments in Italy into newly formed " di formazione " battalions for service in Africa.

Instead, these substances are discussed in terms of formula units or unit cells as the smallest repeating structure within the substance.

Through further insertion of non-day units of time, the calendar year can be further synchronized ; however, these extra units of time are not considered part of the calendar.

An essential property of these block structures is that logical units never overlap.

And no messages can be transmitted on these circuits until senders and receivers authenticate in advance, by special codes, that the messages actually come from their purported sources.

We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.

Underlying these conceptions of mimesis are certain presuppositions concerning the nature of primary human experience which require some exposition before the main argument can proceed.

We feel uncomfortable at being bossed by a corporation or a union or a television set, but until we have some knowledge about these phenomena and what they are doing to us, we can hardly learn to control them.

The men who speculate on these institutions have, for the most part, come to at least one common conclusion: that many of the great enterprises and associations around which our democracy is formed are in themselves autocratic in nature, and possessed of power which can be used to frustrate the citizen who is trying to assert his individuality in the modern world ''.

The Axioms required to make the theoretical machinery operate are set out tersely and powerfully, so that all permissible operations within the theory can be traced rigorously back to these axioms, rules, and primitive notions.

But when these expectations are once too often ground into the dust, innocence can falter, since its strength is according to the strength of him who possesses it.

As a nation we can successfully pursue these objectives only from a position of broadly based strength.

A contrast of the scripture reading of, let us say, St. Augustine, John Bunyan, and Thomas Jefferson, all three of whom found in such study a real source of enlightenment, can tell us a great deal about these three men and the age that each represented and helped bring to conscious expression.

Within the fixed frame of these aspirations, they can afford to place a high value on the expressive and people-oriented aspects of occupation and to minimize the instrumental-reward values of power, prestige, and wealth.

How effectively these warnings can be presented is seen in Pohl and Kornbluth's The Space Merchants, Vonnegut's Player Piano and Wyndham's Re-Birth.

Perhaps the moralities of world law are not advanced by stealing American diplomatic papers and planes, but the Kennedy administration can always file a demurrer to the effect that, but for its own incompetence in protecting American interests, these things would not happen.

After all, where else can the public see a wagon these days??

The demand for these lots can be met for some time to come.

Visitors are welcome to come see what these dedicated mothers can do.

On these they feel they can rely.

He merely said, `` Any good decorator these days can make you a tasteful home ''.

You can do anything with these dumb fucks if you know how.

`` See, Argiento, if you control the way these folds are bunched, like this, or made to flow, you can enrich the body attitudes.

It all began on an autumn afternoon -- and who, after all these centuries, can describe the fineness of an autumn day??

In several significant cases, such as India, a decade of concentrated effort can launch these countries into a stage in which they can carry forward their own economic and social progress with little or no government-to-government assistance.

and now, therefore, do I, John A. Notte, Jr., governor of the State of Rhode Island and Providence Plantations, proclaim the week of april 29th to may 7th, 1961, as Rhode Island Heritage Week, advising our citizens that throughout this week many historic houses and beautiful gardens will be open to visitors as well as industrial plants, craft shops, museums and libraries and I earnestly urge all to take advantage of these opportunities to see as many of these places as they can during this outstanding week.

A study of the hydrogen line profiles indicates that a measurement of these profiles can be used to calculate a temperature for the arc plasma that is reliable to about Af percent.