Double-root inversion for complex malposition of the great arteries with tricuspid valve straddling

Dextro-transposition of the great vessels associated with pulmonary stenosis, double-outlet right ventricle, and straddling of the tricuspid valve is an uncommon condition. Several treatment options are available for this malformation, but most of them are not optimal. For patients with transposition of the great vessels, the gold standard procedure, which is an arterial switch procedure, would usually be performed, whereas for patients with pulmonary stenosis, a Rastelli operation or a Nikaidoh procedure would be proposed. Both of these methods have several advantages and disadvantages. Selected patients can qualify for the double-root rotation procedure, which is limited by the function of the pulmonary and aortic valves, the position of the coronary arteries, and the skill of the surgeon[1]. After a thorough analysis of all the preoperative test results, our patient qualified for a surgical correction of the malformation. Due to preexisting pulmonary regurgitation and severe dilation of the pulmonary root, the patient was not considered a good candidate for the arterial switch operation. Therefore, it was decided that the double-root inversion was the best option. Introduction The double-root inversion gives the patient the possibility of avoiding a reoperation. If the patient were to have the Nikaidoh or the Rastelli procedure, we know that the pulmonary graft would eventually have to be replaced. For this reason, we would like to share our experience with the double-root inversion method.

Extremal p-Adic L-Functions

In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations to automorphic forms on arbitrary groups. In the classical setting of GL2 over Q, this allows for us to construct the p-adic L-function in the so far uncovered extremal case, which arises under the unlikely hypothesis that p-th Hecke polynomial has a double root. Although Tate’s conjecture implies that this case should never take place for GL2/Q, the obvious generalization does exist in nature for Hilbert cusp forms over totally real number fields of even degree, and this article proposes a method that should adapt to this setting. We further study the admissibility and the interpolation properties of these extremal p-adic L-functionsLpext(f,s), and relate Lpext(f,s) to the two-variable p-adic L-function interpolating cyclotomic p-adic L-functions along a Coleman family.

Flow Field, Spray Distribution and Pilot Flame Stabilization in a Centrally Staged Combustor

Centrally staged lean premixed prevaporized low emission combustor has achieved great commercial success in the past decade. Pilot flame characteristics is with key importance to centrally staged combustor, which is considered not entirely up to the design of pilot stage, but also influenced by the flow field and fuel distribution of the combustor. The flow field and fuel distribution behaviors in centrally staged combustor are not very clear since the role of LRZ is unknown, as well as the pilot flame stabilization mechanism. The goal of this paper is to study the flow field, spray distribution and pilot flame stabilization in centrally staged combustor. This paper designs a comparison scheme of the dome lip for study. Particle image velocimetry, Planar Mie scattering measurements and high-speed camera experiments are conducted to get an in depth understanding on the flow field, spray distribution characteristics and pilot flame stabilization in a centrally staged combustor. The flow field with a 3.0 mm lip incline is quite different. Two PRZs forms, one connected with the LRZ and the other at the outlet of pilot stage. Pilot flow no longer joins to the main flow but flows alone in the center. It seems like it is the decoupling pilot stage air cutting PRZ into two PRZs. The pilot spray has a conical boundary and it is probably formed by the high velocity main air flow. A considerable number of fuel droplets are involved in LRZ with the lip incline. Two shapes of pilot flame are observed, the V-shaped flame and double root flame. High-speed camera has captured the flame stabilization process close to LBO. As for the V-shaped pilot flame, the central flame root performs an extinction/relight cycle close to LBO. The cycle duration time is much longer than the critical time of swirl cup methane flame previously reported. As for the double root pilot flame, the central flame root is lighted before the lip flame root and it is the central flame that plays the leading role in stabilizing the whole flame. The lip flame root can weaken the quench effect of main air and broaden the flame stability boundary. A relatively large lip height is recommended for the consideration of the LBO performance.

PREVALENCE OF SUPERNUMERARY ROOTS OF PERMANENT MANDIBULAR TEETH ACCODING TO CONE-BEAM COMPUTED TOMOGRAPHY STUDY

1800 pre-made cone beam computed tomograms (CBCT) were examined, of which 202 CBCT were selected. It was revealed that a prevalence of three-rooted mandibular first molar was 2,5 %, second molars – 4,5 %. First molar supernumerary root was always distolingual root (radix entomolaris). Second molar supernumerary root was distolingual root in 2,5 % (radix entomolaris), in 2 % mesialbuccal root (radix paramolaris)., The prevalence of double-root in the mandibular first premolar was 2 %, in the second premolar was 1 %, in the mandibular canines was 5 %, the bifurcation was located in the apical and middle third root canals of canine and premolar, which makes endodontic treatment of such teeth as difficult as possible.

Responsibility – an Anthropological Outline

In the article, I try to present an outline of the theory of responsibility. Its double root – based on the logical distinction between criterion and testimony – is derived from Abelard’s anthropology of action and the theory of personhood developed by Timothy Chappell. Initially, I discuss the metaphysical difficulties related to the problem of freedom (especially linked with determinism). Afterwards, following Abelard, I try to indicate an anthropological justification of punishment based on guilt. The last part of the paper is devoted to the attempt to enter the free will into a broader view of Chappell’s theory. The aim of the work is to prepare the ground for future studies on the proleptic notion of personhood and its further application within the philosophy of law.

Some representations of the general solution to a difference equation of additive type

The general solution to the difference equation $$x_{n+1}=\frac {ax_{n}x_{n-1}x_{n-2}+bx_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n}x_{n-1}x_{n-2}},\quad n\in\mathbb{N}_{0}, $$ x n + 1 = a x n x n − 1 x n − 2 + b x n − 1 x n − 2 + c x n − 2 + d x n x n − 1 x n − 2 , n ∈ N 0 , where $a, b, c\in\mathbb{C}$ a , b , c ∈ C , $d\in\mathbb{C}\setminus\{0\}$ d ∈ C ∖ { 0 } , is presented by using the coefficients, the initial values $x_{-j}$ x − j , $j=\overline{0,2}$ j = 0 , 2 ‾ , and the solution to the difference equation $$y_{n+1}=ay_{n}+by_{n-1}+cy_{n-2}+dy_{n-3}, \quad n\in\mathbb{N}_{0}, $$ y n + 1 = a y n + b y n − 1 + c y n − 2 + d y n − 3 , n ∈ N 0 , satisfying the initial conditions $y_{-3}=y_{-2}=y_{-1}=0$ y − 3 = y − 2 = y − 1 = 0 , $y_{0}=1$ y 0 = 1 . The representation complements known ones of the general solutions to the corresponding difference equations of the first and second order. Besides, the general representation formula is investigated in detail and refined by using the roots of the characteristic polynomial $$P_{4}(\lambda )=\lambda ^{4}-a\lambda ^{3}-b\lambda ^{2}-c\lambda -d $$ P 4 ( λ ) = λ 4 − a λ 3 − b λ 2 − c λ − d of the linear equation. The following cases are considered separately: (1) all the roots of the polynomial are distinct; (2) there is a unique double root of the polynomial; (3) there is a triple root of the polynomial and one simple; (4) there is a quadruple root of the polynomial; (5) there are two distinct double roots of the polynomial.

General rogue wave solutions of the coupled Fokas–Lenells equations and non-recursive Darboux transformation

We formulate a non-recursive Darboux transformation technique to obtain the general n th-order rational rogue wave solutions to the coupled Fokas–Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.