scholarly journals New Eulerian Numbers of Type $D$

10.37236/5514 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Anna Borowiec ◽  
Wojciech Młotkowski
Keyword(s):  
Recurrence Relation ◽  
Generating Function ◽  
Probability Distributions ◽  
Type A ◽  
Eulerian Numbers ◽  
Eulerian Polynomials ◽  
Type D

We introduce a new array of type $D$ Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation, Worpitzky formula and the generating function. We also find the probability distributions whose moments are Eulerian polynomials of type $A$, $B$ and $D$.

scholarly journals CTNI-03. IMAGING FEATURES OF LEPTOMENINGEAL METASTASES OF NON-SMALL CELL LUNG CANCER: A SINGLE-CENTER REAL-WORLD STUDY

2020 ◽  
Vol 22 (Supplement_2) ◽  
pp. ii41-ii41
Author(s):  
Junjie Zhen ◽  
Lei Wen ◽  
Shaoqun Li ◽  
Mingyao Lai ◽  
Changguo Shan ◽  
...  
Keyword(s):  
Spinal Cord ◽  
Type A ◽  
Brain Parenchyma ◽  
Imaging Features ◽  
Type B ◽  
Type D ◽  
Mri Examination ◽  
Mri Features ◽  
Brain And Spinal Cord ◽  
The Brain

Abstract BACKGROUND According to EANO-ESMO clinical practice guidelines, the MRI findings of LM are divided into 4 types, namely linear enhancement (type A), nodular enhancement (type B), linear combined with nodular enhancement (type C), and sign of hydrocephalus (type D). METHODS The MRI features of brain and spinal cord in patients diagnosed with NSCLC-LM in Guangdong Sanjiu Brain Hospital from 2010 until 2019 were investigated, and then were classified into 4 types. The imaging features were analyzed. RESULTS A total of 80 patients were enrolled in the study. The median age of the patients was 53.5 years old, and the median time from the initial diagnosis to the confirmed diagnosis of LM was 11.6 months. The results of enhanced MRI examination of the brain in 79 cases showed that the number of cases with enhancements of type A, B, C and D were 50 (63.3%), 0, 26 (32.9%) and 3 (3.8%), respectively, and that LM with metastases to the brain parenchyma was found in 42 cases (53.2%). The results of enhanced MRI examination of spinal cord in 59 cases showed that there were only enhancements of type A and C in 40 cases (67.8%) and 3 cases (5.0%), and no enhancement sign in the other 16 cases (27.2%). CONCLUSION MRI examination of brain and spinal cord will improve the detection rate of LM. The MRI features of NSCLC-LM in real world are mainly characterized by the linear enhancements of brain and spinal cord, followed by linear combined with nodular enhancement. The enhancements of type B and type D are rare in clinic. Almost half of the patients have LM and metastases to the brain parenchyma. Therefore, the differentiation of tumor metastases is needed to be paid attention to for the early diagnosis and the formulation of reasonable treatment plans.

MRI analysis and surgical treatment of Wassel Type IV duplicated thumbs

2021 ◽  
pp. 175319342098321
Author(s):  
Anyuan Wang ◽  
Jian Ding ◽  
Long Wang ◽  
Tinggang Chu ◽  
Zhipeng Wu ◽  
...  
Keyword(s):  
Type A ◽  
Surgical Reconstruction ◽  
Mri Findings ◽  
Level Of Evidence ◽  
Type D ◽  
Type Iv ◽  
Secondary Operations ◽  
Type C

We present the MRI findings for 39 Wassel Type IV duplicated thumbs in 38 patients. We found that MRI revealed the morphology of the cartilaginous connection between the thumb anlages and the location of the deviation corresponding to the classification of Horii, which allowed precise preoperative planning of corrective osteotomies. All 39 thumbs were available for follow-up after surgical reconstruction at a mean of 29 months (range 25 to 39). Four out of nine Horii Type A cases and all 12 Type B, as well as the six Type C and the six Type D cases, achieved good results according to the Tada scoring system. Five Type A cases achieved fair results with residual stiffness of the interphalangeal joint. No secondary operations were needed. We conclude that MRI proved useful in subclassifying Wassel Type IV duplicated thumbs and may aid in planning the osteotomies needed for their reconstruction. Level of evidence: IV

scholarly journals The effectiveness of TiO2 additions to mortar to maintain initial conditions in terms of its reflectance to solar radiation

2017 ◽  
Vol 17 (3) ◽  
pp. 39-56 ◽  
Author(s):  
Sérgio Roberto Andrade Dantas ◽  
Fulvio Vittorino ◽  
Kai Loh
Keyword(s):  
Solar Radiation ◽  
Ultraviolet Radiation ◽  
Initial Conditions ◽  
Type A ◽  
Just Noticeable Difference ◽  
Type B ◽  
Climate Conditions ◽  
Type D ◽  
Type C ◽  
Over Time

Abstract Contact of facades with degradation agents and direct incidence of ultraviolet radiation on external coatings make them more opaque over time, affecting their colour and reflectance characteristics. This study evaluated the effect of adding different TiO2 contents to mortars applied in concrete substrates in order to verify the reflectance maintenance on surfaces after exposure over time. Mortar with different concentrations of TiO2 (1%, 5%, 10%) were produced in relation to the total dry premix, added as a powder and compared to unpainted mortar without TiO2 (type "A") and painted mortar without TiO2 (type "B"), both used as a reference for colour and reflectance. Exposed over 16 months to climate conditions in São Paulo, regarding the maintenance of reflectance and solar radiation, the results showed that type "B" (0%TiO2) painted mortar presented the best performance. Type "C" (1%TiO2) and type "D" (5%TiO2) unpainted mortar remained more stable. Type "A" (0%TiO2) and type "E" (10%TiO2) unpainted mortar showed greater differences according to the Just Noticeable Difference (JND) range caused by dirt pick up.

scholarly journals Derangement Polynomials and Excedances of Type $B$

10.37236/81 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
William Y. C. Chen ◽  
Robert L. Tang ◽  
Alina F. Y. Zhao
Keyword(s):  
Normal Distribution ◽  
Generating Function ◽  
Type B ◽  
Eulerian Polynomials ◽  
Basic Properties ◽  
Asymptotic Normal Distribution ◽  
Asymptotic Normal

Based on the notion of excedances of type $B$ introduced by Brenti, we give a type $B$ analogue of the derangement polynomials. The connection between the derangement polynomials and Eulerian polynomials naturally extends to the type $B$ case. Using this relation, we derive some basic properties of the derangement polynomials of type $B$, including the generating function formula, the Sturm sequence property, and the asymptotic normal distribution. We also show that the derangement polynomials are almost symmetric in the sense that the coefficients possess the spiral property.

scholarly journals Gamma Positivity of the Descent Based Eulerian Polynomial in Positive Elements of Classical Weyl Groups

10.37236/9037 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Hiranya Kishore Dey ◽  
Sivaramakrishnan Sivasubramanian
Keyword(s):  
Coxeter Groups ◽  
Weyl Groups ◽  
Alternating Group ◽  
Type B ◽  
Eulerian Polynomial ◽  
Eulerian Polynomials ◽  
Type D ◽  
Positive Elements

The Eulerian polynomial $A_n(t)$ enumerating descents in $\mathfrak{S}_n$ is known to be gamma positive for all $n$. When enumeration is done over the type B and type D Coxeter groups, the type B and type D Eulerian polynomials are also known to be gamma positive for all $n$. We consider $A_n^+(t)$ and $A_n^-(t)$, the polynomials which enumerate descents in the alternating group $\mathcal{A}_n$ and in $\mathfrak{S}_n - \mathcal{A}_n$ respectively.  We show the following results about $A_n^+(t)$ and $A_n^-(t)$: both polynomials are gamma positive iff $n \equiv 0,1$ (mod 4). When $n \equiv 2,3$ (mod 4), both polynomials are not palindromic. When $n \equiv 2$ (mod 4), we show that {\sl two} gamma positive summands add up to give $A_n^+(t)$ and $A_n^-(t)$. When $n \equiv 3$ (mod 4), we show that {\sl three} gamma positive summands add up to give both $A_n^+(t)$ and $A_n^-(t)$.  We show similar gamma positivity results about the descent based type B and type D Eulerian polynomials when enumeration is done over the positive elements in the respective Coxeter groups. We also show that the polynomials considered in this work are unimodal.

On a Generating Function and its Probability Distributions. A Contribution to the Theory of Transition Rates I

2006 ◽  
Vol 61 (9) ◽  
pp. 457-468
Author(s):  
Hans Kupka
Keyword(s):  
Probability Distribution ◽  
Generating Function ◽  
Probability Distributions ◽  
Addition Theorem ◽  
Complex Variables ◽  
Transition Rates ◽  
Multidimensional Distribution ◽  
Multiple Peak ◽  
Integer Variables ◽  
A Value

A function of two complex variables with two real parameters a and b is described, which generates a sequence of probability distributions of two integer variables m ≥ 0 and n ≥ 0. Closed expressions for the special b = 0 and general case b≠ 0 and recurrence equations for calculating the probability distributions are derived. The probability distribution for m = 0 and a large enough is qualitatively bell-shaped, and that for m ≠ 0 has multiple peak structures. In both cases, the b parameter influences solely the skewness of the curves. For small a values, the distributions fall rapidly from a value of nearly one, decreasing by a factor of 1010 or more as n increases from zero to n = 10. The influence of the b parameter on their properties can be pronounced. Finally, we note an important property of the distributions when two or several of them are convoluted with one another. The result is expressed in terms of an addition theorem in respect to the parameter a and describes a multidimensional distribution.

Strong Converse Inequalities for Averages in Weighted Lp Spaces on [-1,1]

1999 ◽  
Vol 51 (3) ◽  
pp. 546-565
Author(s):  
M. Felten
Keyword(s):  
Type A ◽  
Weighted Spaces ◽  
Difference Operators ◽  
Lp Spaces ◽  
Type D ◽  
Strong Converse

AbstractAverages in weighted spaces defined by additions on [−1; 1] will be shown to satisfy strong converse inequalities of type A and B with appropriate K-functionals. Results for higher levels of smoothness are achieved by combinations of averages. This yields, in particular, strong converse inequalities of type D between K-functionals and suitable difference operators.

scholarly journals Postsurgical residual lung complications following left upper trisegmentectomy

2019 ◽  
Author(s):  
Yutaro Koike ◽  
Aritoshi Hattori ◽  
Takeshi Matsunaga ◽  
Kazuya Takamochi ◽  
Shiaki Oh ◽  
...  
Keyword(s):  
Surgical Intervention ◽  
Type A ◽  
X Rays ◽  
Limited Information ◽  
Type B ◽  
Type D ◽  
Thoracic Computed Tomography ◽  
Isolated Segment ◽  
Type C ◽  
Lung Torsion

AbstractOBJECTIVESSegmentectomy has become an increasingly popular surgical procedure for small-sized lung lesions. Left upper trisegmentectomy (LUTS) is one of the most common segmentectomies performed because of its relative ease and simplicity; however, limited information is currently available on the specific postoperative complications associated with this procedure.METHODSAmong 2060 surgically resected cases in our institute between 2009 and 2016, 129 (6.2%) underwent LUTS. Postoperative chest X-rays and/or thoracic computed tomography (CT) scans were retrospectively assessed for all cases to assess postsurgical residual lung complications following LUTS. We categorized cases into 4 groups: type A (atelectasis of the lingular segment), type B (lung torsion of the lingular segment), type C (necrosis of the ‘isolated segment’) and type D (haematoma along stapling lines).RESULTSPostsurgical lung complications following LUTS were observed in 17 (13.1%) patients (type A: n = 7, type B: n = 1, type C: n = 4 and type D: n = 5). Three patients (2.3%) required surgical intervention because of type B (n = 1) and type C (n = 2), namely, decreased permeability and remaining ground glass opacities in the residual lung, showing an exacerbated systemic inflammatory response. In contrast, type A and D cases were successfully observed by chest CT without any surgical intervention, and patients recovered within a few months of surgery.CONCLUSIONSWe identified several postoperative residual lung complications following LUTS. Lung torsion or necrosis of the residual segment may require intensive care, including reoperation. Potentially serious complications always need to be ruled out after LUTS when radiological consolidation is detected postoperatively.

Positivity and continued fractions from the binomial transformation

2019 ◽  
Vol 149 (03) ◽  
pp. 831-847 ◽  
Author(s):  
Bao-Xuan Zhu
Keyword(s):  
Generating Function ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Hankel Matrix ◽  
Eulerian Polynomials ◽  
Binomial Convolution ◽  
Image Position ◽  
Moment Property

AbstractGiven a sequence of polynomials$\{x_k(q)\}_{k \ges 0}$, define the transformation$$y_n(q) = a^n\sum\limits_{i = 0}^n {\left( \matrix{n \cr i} \right)} b^{n-i}x_i(q)$$for$n\ges 0$. In this paper, we obtain the relation between the Jacobi continued fraction of the ordinary generating function ofyn(q) and that ofxn(q). We also prove that the transformation preservesq-TPr+1(q-TP) property of the Hankel matrix$[x_{i+j}(q)]_{i,j \ges 0}$, in particular forr= 2,3, implying ther-q-log-convexity of the sequence$\{y_n(q)\}_{n\ges 0}$. As applications, we can give the continued fraction expressions of Eulerian polynomials of typesAandB, derangement polynomials typesAandB, general Eulerian polynomials, Dowling polynomials and Tanny-geometric polynomials. In addition, we also prove the strongq-log-convexity of derangement polynomials typeB, Dowling polynomials and Tanny-geometric polynomials and 3-q-log-convexity of general Eulerian polynomials, Dowling polynomials and Tanny-geometric polynomials. We also present a new proof of the result of Pólya and Szegö about the binomial convolution preserving the Stieltjes moment property and a new proof of the result of Zhu and Sun on the binomial transformation preserving strongq-log-convexity.

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