Thus the Dirac Hamiltonian is fundamentally distinguished from its classical counterpart, and we must take great care to correctly identify what is an observable in this theory.

Jeff Snyder is a spokesman for the view that gun possession is a civil right, and that therefore arguments about whether gun restrictions reduce or increase violent crime are beside the point: " I am not here engaged in ... recommending ... policy prescriptions on the basis of the promised or probable results crime ... Thus these essays are not fundamentally about guns at all.

Thus Norman came into use as a language of polite discourse and literature, and this fundamentally altered the role of Old English in education and administration, even though many Normans of the early period were illiterate and depended on the clergy for written communication and record-keeping.

Thus the flow characteristics is not an inherent property of the material alone, but a relative property that depends on two fundamentally different characteristic times.

I listen and I make from it a present that is rich of memory. Thus these archives are fundamentally and even perhaps genetically modified.

Thus, the RF allocations fundamentally differ between continents.

Thus Paul Cartledge claims that " the history of Sparta (…) is fundamentally the history of the class struggle between the Spartans and the Helots ".

Thus: hylostatism ( universe is deterministic, thus “ static ” in a four-dimensional sense ); hylostochastism ( universe contains a fundamentally random or stochastic component ); hylozoism ( universe contains a fundamentally alive aspect ).

Thus, the nature of noble status was fundamentally changed.

Thus, fundamentally, critical criminologists are critical of state definitions of crime, choosing instead to focus upon notions of social harm or human rights.

Thus, Conservative Judaism rejects patrilineal descent and would hold that a child of a non-Jewish mother who was raised as a Reform or Reconstructionist Jew is not legally Jewish and would have to undergo conversion to become a Jew.

Thus, Judaism has also been characterized as a culture or as a civilization.

Thus, as an ethnic religion, Judaism holds that others may have their own, different, paths to God ( or holiness, or " salvation "), as long as they are consistent with the Seven Laws of Noah.

Thus, Judaism rejects the notion that anyone can or should die for anyone else's sin.

Thus, Christianity acquired an identity distinct from Rabbinic Judaism, but this distinction was not recognised all at once by the Roman Empire, see Split of early Christianity and Judaism for details.

Thus, although there is an esoteric tradition in Judaism ( Kabbalah ), Rabbinic scholar Max Kadushin has characterized normative Judaism as " normal mysticism ", because it involves everyday personal experiences of God through ways or modes that are common to all Jews.

Thus a Jew who claims to be an atheist or converts to another religion is still considered by traditional Judaism to be Jewish.

Thus, Judaism views Muslims as righteous people of God.

Thus, although Modern Orthodox Jews find all non-Orthodox forms of Judaism to be wrong, the non-Orthodox movements are not considered to be inherent antagonists ; rather they are perceived to be competitors offering a faulty product, so to speak.

Thus Orthodoxy should work together on some issues with non-Orthodox Judaism, and it is far better for Jews to be members of non-Orthodox Judaism than to assimilate and not be religious Jews at all.

Thus, for example, the Conservative movement typically does not accept Reform converts to Judaism whose conversions did not meet the requirements of Jewish law as being Jews.

Thus, in Judaism, the " Written Instruction " ( Torah she-bi-khtav תורה שבכתב ) comprises the Torah and the rest of the Tanakh ; the " Oral Instruction " ( Torah she-be ' al peh תורה שבעל פה ) was ultimately recorded in the Talmud ( lit.

Thus in all forms of Judaism following the Oral Law, women are allowed to marry whom they wish, including exogamously, whether they have gained an inheritance or not.

" Thus, in debating and disagreeing over the meaning of the Torah or how best to put it into practice, no rabbi felt that he ( or his opponent ) were in some way rejecting God or threatening Judaism ; on the contrary, it was precisely through such arguments that the rabbis imitated and honored God.

Thus, while early Jewish literature has few historical works, many notes on the history of Judaism have been introduced into the responsa.

Thus, in Europe of the early 19th century, all of Judaism that differed from the strictest forms present at the time was called " Reform ".

Thus, the martyrdom may have occurred in the aftermath of Septimus Severus ’ s decrees of 202 that forbade conversion to Judaism and Christianity .< ref > Brent Shaw, “ The Passion of Perpetua ,” Past and Present 139, ( May 1993 ), JSTOR 30 < http :// www. jstor. org / stable / 651089 >, 10-11.

Thus, he combined central figures in the founding of Judaism and Christianity.

Thus, any divergence from the tenets of Biblical Judaism espoused by Jesus would disqualify him from being considered a prophet in Judaism.

Thus Jews who had converted to Christianity could be regarded as especially deceitful and subversive, while Gentiles who had converted to Judaism were perceived as traitors to the " Aryan race " and were among the first to be persecuted and killed.

Thus, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

Thus, on the highroad, a troop of soldiers `` marched in their own dust and sang '', while on the footpath one man walks alone.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus in Prokofieff the Union of Soviet Socialist Republics produced one of the great composers of the Twentieth Century.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

Thus, a low intensity of hypothalamic-cortical discharges prevails in sleep and a high one during wakefulness, resulting in synchronous EEG potentials in the former and asynchrony in the latter condition.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus, the writer decided to hold one experimental section of the functional preparation for marriage course in the spring semester of 1960 exclusively for persons already married -- that is, prerequisite: `` marriage ''.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus, one can think of a dictionary entry as a word rather than a form.

Thus the first lines of one of Charles Wesley's hymns are as follows.

Thus, in the aggregate, the odd-lot trader is one who buys at the tops and sells at the bottoms, notwithstanding occasional individual exceptions.

Thus one line in five from The Iliad and The Odyssey is to be found somewhere else in the two poems.

Thus, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.

Thus, if one accelerometer is properly aligned, the other is also.

Thus a man who is butting a stone wall at the office may become unusually aggressive in bed -- the one place he can still be champion.

Thus there was really an excess of eighteenth-century charm as one of these light-weight pieces followed another on Saturday night.

Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

Thus, according to the character Pausanias in Plato's Symposium, Aphrodite is two goddesses, one older while the other younger.

Thus arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

Thus, an analog signal is one represented by a continuous stream of data, in this case along an electrical circuit in the form of voltage, current or charge changes ( compare with digital signals below ).