Thus, given a linear filter evaluated through, for example, reverse correlation, one can rearrange the two spatial dimensions into one dimension, thus yielding a two dimensional filter ( space, time ) which can be decomposed through SVD.

Thus, in quantitative or spatial terms, God is simple as opposed to being made up of pieces, present in entirety everywhere, if in fact present anywhere.

Thus the basic spatial structure of the Southwest can be seen as focused on the largest metropolitan areas in each state such as Phoenix, Albuquerque, Denver, Salt Lake City, Las Vegas, and El Paso.

Thus, unique combinations of pair-rule gene expression create spatial domains along the anterior-posterior axis to set up each of the 14 individual segments.

Thus, corrections for curvature of the earth exist at two separate spatial scales — a smaller scale within townships, and a larger scale between multiple townships and within standard parallels.

Thus quaternions are a preferred method for representing spatial rotations – see quaternions and spatial rotation.

Thus, Flamm's paraboloid is useful for visualizing the spatial curvature of the Schwarzschild metric.

Thus here it is possible to analyze their spatial

Thus, the positions of the end-effector of a robot can be identified with the group of spatial rigid transformations, often denoted SE ( 3 ).

Thus the optotype can only be recognized if the person viewing it can discriminate a spatial pattern separated by a visual angle of 1 minute of arc.

Thus, two spatial features are prominent in navigating a path: general layout and landmark orienting ( Kahana et al., 2006 ).

Thus, the evidence for the spatial memory of some species of animals, such as rats, indicates that they do use spatial memory to locate and retrieve hidden food stores.

Thus the spatial location of each single flash of fluorescence is reflected as a pattern of voltages within the interconnecting circuit array.

Thus, a spatial displacement defines a transformation for Plücker coordinates of lines given by

Thus ACS can study objects outside the field of view of the other instruments, with surprising spatial and energy resolution.

Thus it makes sense to state the precise spectral distribution and spatial, especially altitudinal, distribution of locations of absorption of non-window radiation in the atmosphere.

Thus we are led to two equations: the first in the spatial variables

Thus, conservation of this species requires a landscape ( multiple habitats at appropriate spatial scales ) perspective.

Thus, in order to establish the convergence of the finite-difference approximation, it is necessary to use other methods, which in turn could imply further limitations on the length of the time step and / or the lengths of the spatial intervals.

Thus, the proairetic code pictures the text as a location with spatial and temporal dimensions through which the reader moves.

Thus, for example, the funerary god Anubis was portrayed as a jackal, a creature whose scavenging habits threatened the preservation of the body, in an effort to counter this threat and employ it for protection.

Thus Osiris was identified explicitly with Apis, really an aspect of Ptah, who had already been identified as Osiris by this point, and a syncretism of the two was created, known as Serapis, and depicted as a standard Greek god.

Thus am I, and everyone else here not the  conscious representations of god, or GOD himself?

" Thus the meaning of the word in Greek was " rule by god ( s )" or human incarnation ( s ) of god ( s ).

Thus, the Athenians sent a religious mission to the island of Delos ( one of Apollo's most sacred sanctuaries ) on the Athenian state galley — the ship itself — to pay their fealty to the god.

Thus, the god of kingship becomes the embodiment of his kingdom.

Thus, the meaning of the Greek word, under the influence of the Hebrew word, was eventually taken as meaning " set apart ", ( like herem ) rather than " offering to god ", and eventually the word came to be seen as meaning " banished " and to be considered beyond the judgment and help of the community.

Thus, the Greek god of interpretive communication was combined with the Egyptian god of wisdom as a patron of astrology and alchemy.

Thus, in later versions of the story, the ram is said to have been the offspring of the sea god Poseidon and Themisto ( less often, Nephele or Theophane ).

Thus the Rhodians traced their mythic descent from Rhode and the Sun god Helios.

Thus he became the patron god of cattle, fruit trees, hunting, husbandry and bee-keeping.

Thus Virpiranta sees Efnisien as a Sun god and therefore the Welsh equivalent to Esus.

Thus, Nephthys was also seen in the Pyramid Texts as a supportive cosmic force occupying the night-bark on the journey of Ra, the majestic sun god, particularly when he entered Duat at the transitional time of dusk, or twilight.

Thus this deity is also known as the " god of millions of years ".

Thus later she was sometimes said to be paired with Shai, who became a god of destiny after the deity evolved out of an abstract concept.

Thus, seen as a symbol of the later sun god, Ra, the Mnevis was often depicted, in art, with the solar disc of their mother, Hathor between its horns.

Thus Indra, the chief of the devas, was regarded as the regent of the east ; Agni, the fire, was in the same way associated with the southeast ; Yama, lord of death and justice with the south ; Surya, the sun, with the southwest ; Varuna, originally the representative of the all-embracing heaven ( atmosphere ), now the god of the ocean, with the west ; Vayu ( or Pavana ), the wind, with the northwest ; Kubera, the god of wealth, with the north ; and Soma with the northeast.

Thus, Mahishi began performing a fearsome set of austerities, and pleased the creator god Brahma.

Thus the god of beginning is not structurally reducible to a sovereign god, nor the goddess of ending to any of the three categories on to which the goddesses are distributed.

Thus there is a reciprocal link between the god of beginnings and unending motion, who bestows life to the beings of this world ( Cerus Manus ) as well as presiding over its end, and the goddess of the hearth of man, which symbolises through fire the presence of life.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus, the Dhrystone score counts only the number of program iteration completions per second, allowing individual machines to perform this calculation in a machine-specific way.

Thus, interlaced video captures samples the scene motion twice as often as progressive video does, for the same number of frames per second.

Thus it is 1 volt ( 1 joule per coulomb, 1 J / C ) multiplied by the electron charge ( 1 e, or ).

In a digital implementation, the number of computations performed per sample is proportional to N. Thus the mathematical problem is to obtain the best approximation ( in some sense ) to the desired response using a smaller N, as we shall now illustrate.

Thus, although Scots were only 10 per cent of the British population, they made up 15 per cent of the national armed forces and eventually accounted for 20 per cent of the dead.

) Thus lighting energy accounts for about four or five million barrels of oil ( equivalent ) per day.

Thus commercial lighting alone consumes about four to five million barrels per day ( equivalent ) of petroleum, in line with the alternate rationale above to estimate U. S. lighting energy consumption.

Thus under optimum conditions, the preparation of only one atom of element 101 per experiment could be expected.

Thus, while the probability might be extremely small that any particular universe would have the requisite conditions for life ( as we understand life ) to emerge and evolve, this does not require intelligent design per the teleological argument as the only explanation for the conditions in the Universe that promote our existence in it.

Thus, " iambic pentameter " is a meter comprising five feet per line, in which the predominant kind of foot is the " iamb ".

"< ref name = Stoner > < nowiki > < http :// www. allacademic. com / meta / p245585_index. html ></ nowiki >.</ ref > Thus, in some American colleges where there is no separate School or College of Arts and Sciences per se, political science may be a separate department housed as part of a division or school of Humanities or Liberal Arts.

Thus, sunlight's composition at ground level, per square meter, with the sun at the zenith, is about 527 watts of infrared radiation, 445 watts of visible light, and 32 watts of ultraviolet radiation.

Thus to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction.

Thus, all parts share the same rate of rotation, or the same number of rotations or revolutions per unit of time.

Thus, as per Draper's argument above, the theory that there is an omniscient and omnipotent being who is indifferent requires no hidden reasons in order to explain evil.

Two computers P and Q are called Turing equivalent if P can simulate Q and Q can simulate P. Thus, a Turing-complete system is one that can simulate a Turing machine ; and, per the Church-Turing thesis, that any real-world computer can be simulated by a Turing machine, it is Turing equivalent to a Turing machine.

Thus there are 3 cavities per housing, all repeating the same cycle.

Thus, it is the proportionality factor that relates the molar mass of an entity, i. e., the mass per amount of substance, to the mass of said entity.

Thus, if a person owns 100 shares and the cash dividend is USD $ 0. 50 per share, the holder of the stock will be paid USD $ 50.

Thus it is seen that a polyp is an animal of very simple structure, a living fossil that has not changed significantly for about half a billion years ( per generally accepted dating of Cambrian sedimentary rock ).