Hence, there is an isomorphism between the category of groups and the category of discrete groups.

Hence, the political programs of the Sudetenland and the Austrian national socialist parties addressed their particular discontents with the Habsburg monarchic society ; thus the development of ideologically discrete German Worker parties in Vienna, Aussig, and Eger.

Hence the value of a physical quantity q is expressed as the product of a numerical value N < sub > q </ sub > and a unit of measurement u < sub > q </ sub >;

Hence, the intensity of radiation passing through any unit area ( directly facing the point source ) is inversely proportional to the square of the distance from the point source.

Hence, frequency no longer measures the number of cycles per unit time, but is still closely related.

Hence the relative amount of labour embodied in deer production coincides with the competitive relative price of deer in units of beavers, which can be written as ( where the stands for absolute competitive prices in some arbitrary unit of account, and are defined as ).

Hence one must say " 兩頭牛 / 两头牛 two head of cattle ", not two cows, with " 頭 / 头 head " being the unit of measurement, or measure word.

Hence different forms of a morpheme ( minimum meaningful unit of language ) are often spelt identically or similarly in spite of differences in their pronunciation.

Hence both the Macau pataca and the Straits dollar were launched at a sterling value of 2 shillings and 4 pence, but where the Straits dollar remained at that value until the 1960s, the Macau pataca fluctuated with the value of silver, just like the Hong Kong unit.

Hence the mass per unit volume of the gas ( its density ) decreases.

Hence, the term name-bearing type or onomatophore is sometimes used, to denote the fact that biological types do not define " typical " individuals or taxa, but rather fix a scientific name to a specific operational taxonomic unit.

Hence, it is risky to buy wood sold in this manner, as the transaction is not based on a legally enforceable unit of measure.

Hence each repeating unit of PCTFE have a chlorine atom in place of a fluorine atom.

Hence we draw the unique line between the poles of the two given lines, and intersect it with the unit disk ; the chord of intersection will be the desired common perpendicular of the ultraparallel lines.

Hence the only equilibrium in the Bertrand model occurs when both firms set price equal to unit cost ( the competitive price ).

Hence, given the radius, r, center, P < sub > c </ sub >, a point on the circle, P < sub > 0 </ sub > and a unit normal of the plane containing the circle,, one parametric equation of the circle starting from the point P < sub > 0 </ sub > and proceeding in a positively oriented ( i. e., right-handed ) sense about is the following:

Hence this device serves in an essential role as the junction element of the outdoor, unit ( ODU ) of a VSAT modem.

Hence, correlation does not imply causation ; in example, Gould said that the measures of the changes, over time, in " my age, the population of México, the price of Swiss cheese, my pet turtle ’ s weight, and the average distance between galaxies " have a high, positive correlation — yet that correlation does not indicate that Gould ’ s age increased because the Mexican population increased.

Hence my headache afterwards.

Hence, Tsubasa Ozora's motto of " The ball is my friend ".

Hence, I endured the humiliation to preserve my life for making great achievements in future.

Hence my dissent.

Once in an interview she stated " My grandfather was my angel in a household from hell " Hence she wears his name on her back ( Ethello )

Hence the prefix and the suffix combine to indicate someone who has wrought words, themes, and other elements into a dramatic form, someone who crafts plays.

Hence, technological progress plays a key role in the economic growth of nations, or the lack of it.

Hence in electromagnetism, the vortex plays the role of ' effect ' whereas in aerodynamics, the vortex plays the role of ' cause '.

Hence, if you play Rummikub, simply take all the tiles that anyone plays and you have the distinct advantage of being able to use those tiles, while everyone else does not.

Hence, the substructure has been removed, and the bellows moved to the back of the instrument, where they are operated with one hand while the other plays the keyboard.

Hence, God's middle knowledge plays an important role in the actualization of the world.

Hence, the institute plays an influential role in the Eastern, Central & Southern African Federation of Accountants ( ECSAFA ).

Hence docking plays an important role in the rational design of drugs.

Hence, there are two different conceptions of art in aesthetics: art as knowledge or art as action, but aesthetics is neither epistemology nor ethics.

Hence for both logic and mathematics, the different formal categories are the objects of study, not the sensible objects themselves.

Hence GSSPs are usually described in terms of transitions between different faunal stages, though far more faunal stages have been described than GSSPs.

Hence, there are censoring mosaics in Japan, and scene removals and different ages of characters in America.

Hence, by combining several different types of gauge, it is possible to measure system pressure continuously from 10 mbar down to 10 < sup >− 11 </ sup > mbar.

Hence, it can be arranged into a word square that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left.

Hence the Internet's core is owned and managed by a number of different network service providers, not a single entity.

Hence a tumour cell line might show a different genetic fingerprint from that of the host tissue.

Hence, sweeps should never be limited solely to the above pattern ; one can choose to construct completely new and different patterns just as chords can be modified into endless combinations.

Hence the easy alteration of existing laws in favor of new and different ones weakens the power of law itself.

Hence, there are different ways to present them and to rank the departments.

Hence, the different senders can have a possible cross-talk or co-channel interference on the signal of each other.

Hence, it is studied by researchers from a variety of different backgrounds, such as psychology, cognitive science, linguistics, and speech and language pathology.

Hence the main difference between Software analysis and design is that the output of the analysis of a software problem will be smaller problems to solve and it should not deviate so much even if it is conducted by different team members or even by entirely different groups.

Network elements belonging to the same Operator but located in different areas ( a typical situation where assignment of local licenses is a common practice ) pair depends on the switch and its location. Hence, software changes and a greater processing capability are required, but furthermore this situation could introduce the fairly new concept of roaming on a per MSC basis instead of per Operator basis.

Hence taking infinite-dilution behavior to be the standard state allows corrections for non-ideality to be made consistently for all the different solutes.

Hence when the executable is loaded in the memory, different parts of the executable are placed in different pages ( which might not be contiguous ).

Hence, the same hangul letter may be represented by different Roman letters, depending on its pronunciation in context.

Hence Ω ( X ) is not an arbitrary complete lattice but a complete Heyting algebra ( also called frame or locale-the various names are primarily used to distinguish several categories that have the same class of objects but different morphisms: frame morphisms, locale morphisms and homomorphisms of complete Heyting algebras ).

Hence, the ashoka tree is often mentioned in classical Indian religious and amorous poetry, having at least 16 different names in Sanskrit referring to the tree or its flowers.

Hence, in order to move notation between different scorewriters ( or to / from other kinds of music software such as sequencers ), most scorewriters can also import or export one or more standard interchange file formats, such as:

Hence, there are censoring mosaics in Japan and scene removals and different ages of characters in America.