Couple stresses are moments per unit area applied on a surface.

The tensor's components, in a three-dimensional Cartesian coordinate system, form the matrix: whose columns are the stresses ( forces per unit area ) acting on the e < sub > 1 </ sub >, e < sub > 2 </ sub >, and e < sub > 3 </ sub > faces of the cube.

The UHI decreases air quality by increasing the production of pollutants such as ozone, and decreases water quality as warmer waters flow into area streams, which stresses their ecosystems.

The metal in this area is often weaker than both the base material and the fusion zone, and is also where residual stresses are found.

Present day scientists still explore the viability of such a project, as a key to resolving economic, population, and ecological stresses in the area.

Practically every formal introduction to cognitive science stresses that it is a highly interdisciplinary research area in which psychology, neuroscience, linguistics, philosophy, computer science, anthropology, and biology are its principal specialized or applied branches.

The area experiences regular seismic activity, mostly of low intensity, which is believed mostly from small ancient faults reactivated by regional stresses, or by the sinking of the Valley of Mexico.

The complete clearcut of this ecologically fragile area, followed by extensive wildfires and overgrazing, exacerbated by the ecological stresses of the elevation, have prevented quick regeneration of the forest which has taken decades to recover.

After the flows ceased, tectonic stresses fractured the area into many separate fault blocks.

The bolts and the area of rail around the drilled holes endure huge stresses as train wheels pass over the joint.

The area inside the curve, accordingly, represents a safe combination of stresses for this material. The yield curve determines how much a material is elongating after yield point of the material.

Thomas Jordan, director of the Southern California Earthquake Center, stated that the slip likely stopped in the area near Cajon Pass, perhaps because the tectonic stresses on that part of the fault had been released several decades earlier during the 1812 Wrightwood earthquake.

The bileaflet models have high stresses during forward and leakage flows as well as adjacent stagnant flow in the hinge area.

The student of ideas and their place in history will always be concerned with the patterns of transition, which are at the same time patterns of transformation, whereby ideas pass from one area of activity to another.

The meat cutters' union, which has a history of being one of the fairest and least corrupt in our area, represents the little corner markets as well as the large supermarkets.

The name " Queen's College " was denied to the Baptist school, so it was renamed " Acadia College " in 1841, in reference to the history of the area as an Acadian settlement.

It is an area of rich history from Pictish times onwards.

The demographic history of Croatia is marked by significant migrations, including the arrival of the Croats in the area growth of Hungarian and German speaking population since the personal union of Croatia and Hungary, and joining of the Habsburg Empire, migrations set off by Ottoman conquests and growth of Italian speaking population in Istria and in Dalmatia during Venetian rule there.

Approximately 75 % of the island's population is located in the Cape Breton Regional Municipality ( CBRM ) which includes all of Cape Breton County and is often referred to as Industrial Cape Breton, given the history of coal mining and steel manufacturing in this area.

The leading hypothesis is that Anyang, ruled by the same Shang in the official history, coexisted and traded with numerous other culturally diverse settlements in the area that is now referred to as China proper.

By area of extent, it was one of the largest empires ever in history.

Located in the Arno valley near the town of Pontassieve, the Rufina region includes much area in the Pomino region, an area that has a long history of wine production.

During its history the area has also been known as Congo, Congo Free State, Belgian Congo and Zaire.

The débâcle of the Afghan civil war left a vacuum in the Hindu Kush area that concerned the British, who were well aware of the many times in history it had been employed as the invasion route to South Asia.

In history of art and other fields, the adjectives Flemish and Netherlandish are commonly used to designate all the artistic production in this area before about 1580, after which it refers specifically to the southern Netherlands.

This area is one of the region ’ s oldest milk producers ; it has chalky soil, marked by history and human activity, and is favourable for the raising of goats.

There is little written history of Gabon prior to European contact, but various Bantu peoples are known to have immigrated to the area beginning in the 14th century.

The modern state of Guinea did not come into existence until 1958, but the history of the area stretches back well before European intervention.

Although any amount of rock emplacement and rock deformation can occur, and they can occur any number of times, these concepts provide a guide to understanding the geological history of an area.

They also plot and combine measurements of geological structures in order to better understand the orientations of faults and folds in order to reconstruct the history of rock deformation in the area.

The area of the later city of Gdynia shared its history with Pomerelia ( Eastern Pomerania ); in prehistoric times it was the center of Oksywie culture ; it was later populated by Slavs with some Baltic Prussian influences.

The written history of Afghanistan can be traced back to around 500 BC when the area was under the Achaemenid Empire, although evidence indicates that an advanced degree of urbanized culture has existed in the land since between 3000 and 2000 BC.

There are several folks museums around the area that keeps trace of its history.

Several decisive battles were fought in the area, which shaped much of the history of India.

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.

Ireland has, throughout most of its history, had a relatively small population ; until the 19th century this was comparable to other regions of similar area in Europe.

Eschatology, generally is the area of theology and philosophy concerned with the final events in the history of the world, the ultimate destiny of humanity, and related concepts.

Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level when proving null and alternative hypotheses.

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

C *- algebras ( pronounced " C-star ") are an important area of research in functional analysis, a branch of mathematics.

In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

As he began to understand physics and how physicists were using mathematics, he developed a coherent mathematical theory for what he found, most importantly in the area of integral equations.

The occurrence of the triples in the Sulvasutras is comparable to mathematics that one may encounter in an introductory book on architecture or another similar applied area, and

Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as TextGraphs, as well as various ' Net ' projects, such as WordNet, VerbNet, and others.

In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

In mathematics, Archimedes used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi.

* Integration, in mathematics, a fundamental concept of calculus — the operation of calculating the area between the curve of a function on the x-axis or y-axis

Knots have been the subject of interest for their ancient origins, their common uses, and the area of mathematics known as knot theory.

Many mathematicians feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts ; others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics.

Furthermore, a mathematician is not someone who merely manipulates formulas, numbers or equations — the diversity of mathematics allows for research concerning how concepts in one area of mathematics can be used in other areas too.

The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint, without making what was correctly proved before in any way incorrect ; of course mathematical progress clarifies gaps in previous proofs, often by exposing hidden assumptions, which progress has revealed worth conceptualizing.

# proof theory and constructive mathematics ( considered as parts of a single area ).

In a similar way to proof theory, model theory is situated in an area of interdisciplinarity between mathematics, philosophy, and computer science.

Many of these structures are drawn from functional analysis, a research area within pure mathematics that was influenced in part by the needs of quantum mechanics.