(a) [Problem 2.2 in DFT] For u 1 : For u 2 : For u 3 : Note that u 1 = u 2 2 = ∞ 0 1 · dt = ∞, while u ∞ = 1 and P ow(u) = lim T →∞ 1 2T T 0 1 · dt = 1 2. T −T u 2 (t)dt = T 0 u 2 (t)dt = T 0 |u(t)|dt = k−1 i=0 2 2i for 2 2k−1 ≤ T ≤ 2 2k , k ≥ 1. Hence, u 1 = u 2 = ∞ while u ∞ = 1. Finally: P ow(u) = lim T →∞ 1 2T T −T u 2 (t)dt =    lim k→∞ 1 2 2k k−1 i=0 2 2i = 1 4 when T = 2 2k−1 , k ≥ 1 ...

Radiative corrections to the 2E1 decay width of the 2s1/2-state in the low-Z hydrogen-like system are examined within logarithmic approximation. The correction is found to be 2.025(1)α(Zα)/π log(Zα) in units of the non-relativistic rate.

We present mixed gauge R-matrix Floquet calculations of multiphoton ionization of Li within a single active electron local model potential. The laser frequency ranges from 15 000 to 15 800 cm, and at least three photons are needed to ionize the electron in the 2s ground state. We found that the measured ionization rate as a function of photon frequency results from ionization processes in diffe...

We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to efficiently enumerate connected quandles of small orders, and present new proofs concerning connected quandles of order p and 2p. We also present a new characterization of connected quandles that are affine.

Osteochondroma is the most common benign neoplasm of the skeleton commonly affecting the long bones due to endochondral growth. In the craniofacial region this tumour is very rare. The sites of predilection are the coronoid process and the mandibular condyle. Here, we report an exceptional case of osteochondroma originating from the maxillary posterior region in a 26-year-old male patient, mimi...

BACKGROUND Current technological advances have allowed application of different study designs and techniques for investigation of dental anatomy. Some clinical studies have provided evidence that Cone Beam computed tomography (CBCT) scanning is an important resource in assessment of root canal systems notably to identify MB2 canals in maxillary molars as CBCT scans allow in vivo dental investig...

OBJECTIVE The aim of the study was to analyze the prevalence and distribution of ectopic eruption of the permanent maxillary first molar (EEM) in individuals scheduled for orthodontic treatment and to investigate the association of EEM with dental characteristics, maxillary skeletal features, crowding, and other dental anomalies. METHODS A total of 1,317 individuals were included and randomly...

Removal of a maxillary third molar is a common dental procedure, and oral surgeons rarely experience accidental displacement of a maxillary impacted third molar into the maxillary sinus as a complication of this procedure. In the case in which such displacement occurs, the molar is removed via a transantral (Caldwell-Luc) approach through bone removal or window osteotomy of the anterior wall of...

We studied the effect of stimulus quality on the basic physiological response characteristics of oxygenation-sensitive MRI signals. Paradigms comprised a contrast-reversing checkerboard vs. darkness or vs. gray light as well as gray light vs. darkness in a 2 s/52 s protocol (nine subjects). MRI was performed at 2.0 T using single-shot gradient-echo EPI (TR/TE = 500/54 ms, flip angle 30 degrees)...

In this article, we generalize results about binary sequences of length 2p and evaluate the linear complexity and autocorrelation properties of generalized cyclotomic binary sequences of length 2p. We show that in most cases these sequences have high linear complexity and poor autocorrelation performance.