Thus, if the size of the quantum dot is small enough that the quantum confinement effects dominate ( typically less than 10 nm ), the electronic and optical properties change, and the fluorescent wavelength is determined by the size.

Thus by varying the size of the quantum dot, the confinement energy of the exciton can be controlled.

Thus the triple product is only a weak function of density and temperature and therefore a good measure of the efficiency of the confinement scheme.

Thus the optimum temperature for inertial confinement fusion is that which maximizes < σv >/ T < sup > 3 / 2 </ sup >, which is slightly higher than the optimum temperature for magnetic confinement.

Thus confinement is incorporated naturally into the model.

Thus it is important that PS is maintained only in the inner leaflet of the bilayer to ensure normal blood flow in microcirculation.

Thus the term asteroid has come increasingly to refer specifically to the small bodies of the inner Solar System out to the orbit of Jupiter, which are usually rocky or metallic.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus, from the human body, the usual form assigned to the Deity, forasmuch as it is written that God created man in his own image, issue the two supporters, Nous and Logos, symbols of the inner sense and the quickening understanding, as typified by the serpents, for the same reason that had induced the old Greeks to assign this reptile for an attribute to Pallas.

Thus, in Steiner's view, we can overcome the subject-object divide through inner activity, even though all human experience begins by being conditioned by it.

Thus, while Pierre and the robot are both doing the same thing, only Pierre has the inner conscious experience.

Thus objective spiritual knowledge always entails creative inner activity.

Thus some of the suburbs of most of the developed world are comparable to several inner cities of the U. S. and Canada.

Thus, the inner product of two matrices has the same rank as the outer product ( or tensor product ) of two vectors.

Thus, he argued, leaders need to work on their inner psychology.

Thus the Christian individualism of the Quakers, that each person shares the " inner light " and the Arminianism of the Evangelicals were both differently based from the Lockean or Kantian individualism of a Philosophe or a Utilitarian, but all recognized the equal moral significance of the human person and that the disregard of it was wrong.

Thus the presence of an orthonormal basis reduces the study of a finite-dimensional inner product space to the study of R < sup > n </ sup > under dot product.

Thus, the lower jaw gradually became just one large bone, with several of the smaller jaw bones migrating into the inner ear and allowing sophisticated hearing.

Thus, unitary operators are just automorphisms of Hilbert spaces, i. e., they preserve the structure ( in this case, the linear space structure, the inner product, and hence the topology ) of the space on which they act.

Thus the outermost quadrant would comprise 90 ° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on.

Thus, roughly, two functions are orthogonal if their approximating vectors are perpendicular ( under this common inner product ).

The electron to be removed is shielded from the nucleus by the electrons present in the inner shell. Thus the electrons in the valence shell experience less attraction force from the inner shell. Asa result, these electrons can be removed from the shells easily.

Thus the inner development of Jewish apocalyptic was conditioned by the historical experiences of the nation.

Thus, the first inner tantra, Maha Yoga, is sub-divided into Maha-Maha, Maha-Anu, and Maha-Ati, thus making Maha-Ati the third sub-division of nine.

Thus, it was over 400 feet down the left field line ( east ) to the bleachers ( though this distance was shortened in later years by the construction of an inner fence ).

Thus Q defines an inner product on dom T. Let H < sub > 1 </ sub > be the completion of dom T with respect to Q. H < sub > 1 </ sub > is an abstractly defined space ; for instance its elements can be represented as equivalence classes of Cauchy sequences of elements of dom T. It is not obvious that all elements in H < sub > 1 </ sub > can identified with elements of H. However, the following can be proved:

Thus, radiation dominates in the inner portion of solar mass stars.

Thus the passing lane is called the inner lane ( belső sáv in Hungarian ).

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

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

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

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

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

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 Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.