scholarly journals Permutations of Type $B$ with Fixed Number of Descents and Minus Signs

10.37236/7306 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Katarzyna Kril ◽  
Wojciech Młotkowski
Keyword(s):  
Three Dimensional ◽  
Fixed Number ◽  
Type B ◽  
Dimensional Array ◽  
Combinatorial Interpretations

We study three dimensional array of numbers $B(n,k,j)$, $0\le j,k\le n$, where $B(n,k,j)$ is the number of type $B$ permutations of order $n$ with $k$ descents and $j$ minus signs. We prove in particular, that $b(n,k,j):=B(n,k,j)/\binom{n}{j}$ is an integer and provide two combinatorial interpretations for these numbers.

scholarly journals Controlling dipolar exchange interactions in a dense three-dimensional array of large-spin fermions

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
A. Patscheider ◽  
B. Zhu ◽  
L. Chomaz ◽  
D. Petter ◽  
S. Baier ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Exchange Interactions ◽  
Dimensional Array ◽  
Large Spin

scholarly journals The $1/k$-Eulerian Polynomials of Type $B$

10.37236/9313 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Shi-Mei Ma ◽  
Jun Ma ◽  
Jean Yeh ◽  
Yeong-Nan Yeh
Keyword(s):  
Recurrence Relations ◽  
Type B ◽  
Eulerian Polynomials ◽  
Combinatorial Interpretations ◽  
Symmetric Decomposition

In this paper, we define the $1/k$-Eulerian polynomials of type $B$. Properties of these polynomials, including combinatorial interpretations, recurrence relations and $\gamma$-positivity are studied. In particular, we show that the $1/k$-Eulerian polynomials of type $B$ are $\gamma$-positive when $k>0$. Moreover, we define the $1/k$-derangement polynomials of type $B$, denoted $d_n^B(x;k)$. We show that the polynomials $d_n^B(x;k)$ are bi-$\gamma$-positive when $k\geq 1/2$. In particular, we get a symmetric decomposition of the polynomials $d_n^B(x;1/2)$ in terms of the classical derangement polynomials.

Local Heat Transfer Characteristics in Simulated Electronic Modules

2003 ◽  
Vol 125 (3) ◽  
pp. 362-368 ◽  
Author(s):  
Seong-Yeon Yoo ◽  
Jong-Hark Park ◽  
Min-Ho Chung
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Three Dimensional ◽  
Vortex Generator ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Two Dimensional ◽  
Heat Transfer Characteristics ◽  
Dimensional Array ◽  
Transfer Characteristics

When heat is released by forced convection from electronic modules in a narrow printed circuit board channel, complex flow phenomena—such as stagnation and acceleration on the front surface, separation and reattachment on the top surface, wake or cavity flow near the rear surface—affect the heat transfer characteristics. The purpose of this study is to investigate how these flow conditions influence the local heat transfer from electronic modules. Experiments are performed on a three-dimensional array of hexahedral elements as well as on a two-dimensional array of rectangular elements. Naphthalene sublimation technique is employed to measure three-dimensional local mass transfer, and the mass transfer data are converted to their counterparts of the heat transfer process using the analogy equation between heat and mass transfer. Module location and streamwise module spacing are varied, and the effect of vortex generators on heat transfer enhancement is also examined. Dramatic change of local heat transfer coefficients is found on each surface of the module, and three-dimensional modules have a little higher heat transfer value than two-dimensional modules because of bypass flow. Longitudinal vortices formed by vortex generator enhance the mixing of fluids and thereby heat transfer, and the rectangular wing type vortex generator is found to be more effective than the delta wing type vortex generator.

Investigation of three-dimensional printing materials for printing aorta model replicating Type B aortic dissection

2021 ◽  
Vol 17 ◽  
Author(s):  
Chia-An Wu ◽  
Andrew Squelch ◽  
Zhonghua Sun
Keyword(s):  
3D Printing ◽  
Aortic Dissection ◽  
Three Dimensional ◽  
Ct Images ◽  
Patient Specific ◽  
Type B ◽  
Type B Aortic Dissection ◽  
Ct Attenuation ◽  
Significant Difference ◽  
3D Printed

Aim: To determine a printing material that has both elastic property and radiology equivalence close to real aorta for simulation of endovascular stent graft repair of aortic dissection. Background: With the rapid development of three-dimensional (3D) printing technology, a patient-specific 3D printed model is able to help surgeons to make better treatment plan for Type B aortic dissection patients. However, the radiological properties of most 3D printing materials have not been well characterized. This study aims to investigate the appropriate materials for printing human aorta with mechanical and radiological properties similar to the real aortic computed tomography (CT) attenuation. Objective: Quantitative assessment of CT attenuation of different materials used in 3D printed models of aortic dissection for developing patient-specific 3D printed aorta models to simulate type B aortic dissection. Method: A 25-mm length of aorta model was segmented from a patient’s image dataset with diagnosis of type B aortic dissection. Four different elastic commercial 3D printing materials, namely Agilus A40 and A50, Visijet CE-NT A30 and A70 were selected and printed with different hardness. Totally four models were printed out and conducted CT scanned twice on a 192-slice CT scanner using the standard aortic CT angiography protocol, with and without contrast inside the lumen.Five reference points with region of interest (ROI) of 1.77 mm2 were selected at the aortic wall and intimal flap and their Hounsfield units (HU) were measured and compared with the CT attenuation of original CT images. The comparison between the patient’s aorta and models was performed through a paired-sample t-test to determine if there is any significant difference. Result: The mean CT attenuation of aortic wall of the original CT images was 80.7 HU. Analysis of images without using contrast medium showed that the material of Agilus A50 produced the mean CT attenuation of 82.6 HU, which is similar to that of original CT images. The CT attenuation measured at images acquired with other three materials was significantly lower than that of original images (p<0.05). After adding contrast medium, Visijet CE-NT A30 had an average CT attenuation of 90.6 HU, which is close to that of the original images with statistically significant difference (p>0.05). In contrast, the CT attenuation measured at images acquired with other three materials (Agilus A40, A50 and Visiject CE-NT A70) was 129 HU, 135 HU and 129.6 HU, respectively, which is significantly higher than that of original CT images (p<0.05). Conclusion: Both Visijet CE-NT and Agilus have tensile strength and elongation close to real patient’s tissue properties producing similar CT attenuation. Visijet CE-NT A30 is considered the appropriate material for printing aorta to simulate contrast-enhanced CT imaging of type B aortic dissection. Due to lack of body phantom in the experiments, further research with simulation of realistic anatomical body environment should be conducted.

scholarly journals A Three‐Dimensional Array for the Study of Infrasound Propagation Through the Atmospheric Boundary Layer

2019 ◽  
Vol 124 (16) ◽  
pp. 9299-9313 ◽  
Author(s):  
Madelon M. E. Smink ◽  
Jelle D. Assink ◽  
Fred C. Bosveld ◽  
Pieter S. M. Smets ◽  
Läslo G. Evers
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Three Dimensional ◽  
Dimensional Array

scholarly journals Purification, Characterization, and Gene Sequence of Michiganin A, an Actagardine-Like Lantibiotic Produced by the Tomato Pathogen Clavibacter michiganensis subsp. michiganensis

2006 ◽  
Vol 72 (9) ◽  
pp. 5814-5821 ◽  
Author(s):  
I. Holtsmark ◽  
D. Mantzilas ◽  
V. G. H. Eijsink ◽  
M. B. Brurberg
Keyword(s):  
Amino Acids ◽  
Three Dimensional ◽  
Reversed Phase ◽  
Dimensional Structure ◽  
Sequence Information ◽  
Type B ◽  
Clavibacter Michiganensis ◽  
Ring Rot ◽  
A Genome ◽  
Tomato Pathogen

ABSTRACT Members of the actinomycete genus Clavibacter are known to produce antimicrobial compounds, but so far none of these compounds has been purified and characterized. We have isolated an antimicrobial peptide, michiganin A, from the tomato pathogen Clavibacter michiganensis subsp. michiganensis, using ammonium sulfate precipitation followed by cation-exchange and reversed-phase chromatography steps. Upon chemical derivatization of putative dehydrated amino acids and lanthionine bridges by alkaline ethanethiol, Edman degradation yielded sequence information that proved to be sufficient for cloning of the gene by a genome-walking strategy. The mature unmodified peptide consists of 21 amino acids, SSSGWLCTLTIECGTIICACR. All of the threonine residues undergo dehydration, and three of them interact with cysteines via thioether bonds to form methyllanthionine bridges. Michiganin A resembles actagardine, a type B lantibiotic with a known three-dimensional structure, produced by Actinoplanes liguriae, which is a filamentous actinomycete. The DNA sequence of the gene showed that the michiganin A precursor contains an unusual putative signal peptide with no similarity to well-known secretion signals and only very limited similarity to the (only two) available leader peptides of other type B lantibiotics. Michiganin A inhibits the growth of Clavibacter michiganensis subsp. sepedonicus, the causal agent of ring rot of potatoes, with MICs in the low nanomolar range. Thus, michiganin A may have some potential in biological control of potato ring rot.

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