scholarly journals Kazhdan-Lusztig Polynomials of Matroids Under Deletion

10.37236/9026 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Tom Braden ◽  
Artem Vysogorets
Keyword(s):  
Simple Formula ◽  
Parallel Connection ◽  
Connection Graph ◽  
Lusztig Polynomials

We present a formula which relates the Kazhdan–Lusztig polynomial of a matroid $M$, as defined by Elias, Proudfoot and Wakefield, to the Kazhdan–Lusztig polynomials of the matroid  obtained by deleting an element, and various contractions and localizations of $M$.   We give a number of applications of our formula to Kazhdan–Lusztig polynomials of graphic matroids, including a simple formula for the Kazhdan–Lusztig polynomial of a parallel connection graph.

A Parallel Connection Graph Proof Procedure

1981 ◽  
pp. 160-167 ◽  
Author(s):  
Günter Hornung ◽  
Anfried Knapp ◽  
Ulrike Knapp
Keyword(s):  
Parallel Connection ◽  
Connection Graph ◽  
Proof Procedure

Dynamics of Electrodiffusion Friction Probes. I. Shape-Dependent Potentiostatic Transient

1997 ◽  
Vol 62 (3) ◽  
pp. 397-419 ◽  
Author(s):  
Ondřej Wein ◽  
Václav Sobolík
Keyword(s):  
Simple Formula ◽  
Flow Direction ◽  
Voltage Step ◽  
Convex Shape ◽  
Exact Theory ◽  
Working Electrode ◽  
Arbitrary Convex

An exact theory is given of the voltage-step transient under limiting diffusion conditions for an electrodiffusion friction probe of arbitrary convex shape. The actual transient courses are given for the strip, circular, elliptic, triangular, and rectangular probes of any orientation with respect to the flow direction. A simple formula for any probe with a single working electrode of convex shape is suggested to facilitate the calibration of electrodiffusion probes based on the voltage-step transient.

scholarly journals Base graph–connection graph: Dissection and construction

2021 ◽  
Vol 291 ◽  
pp. 116-128
Author(s):  
Primož Potočnik ◽  
Gabriel Verret ◽  
Stephen Wilson
Keyword(s):  
Base Graph ◽  
Connection Graph

Wideband piezoelectric energy harvester design using parallel connection of multiple beams

2020 ◽  
Vol 12 (3) ◽  
pp. 206
Author(s):  
Sourav Naval ◽  
Prasun Kumar Sinha ◽  
Nikhil Kumar Das ◽  
Ashutosh Anand ◽  
Sudip Kundu
Keyword(s):  
Energy Harvester ◽  
Parallel Connection ◽  
Piezoelectric Energy ◽  
Multiple Beams

scholarly journals Design and Analysis of a Novel Piezoceramic Stack-based Smart Aggregate

Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6438
Author(s):  
Guangtao Lu ◽  
Xin Zhu ◽  
Tao Wang ◽  
Zhiqiang Hao ◽  
Bohai Tan
Keyword(s):  
Resonance Frequency ◽  
Electromechanical Coupling ◽  
Structural Parameters ◽  
Electromechanical Coupling Factor ◽  
Coupling Factor ◽  
Stress Waves ◽  
Parallel Connection ◽  
Smart Aggregate ◽  
In Series ◽  
Piezoelectric Wafers

A novel piezoceramic stack-based smart aggregate (PiSSA) with piezoceramic wafers in series or parallel connection is developed to increase the efficiency and output performance over the conventional smart aggregate with only one piezoelectric patch. Due to the improvement, PiSSA is suitable for situations where the stress waves easily attenuate. In PiSSA, the piezoelectric wafers are electrically connected in series or parallel, and three types of piezoelectric wafers with different electrode patterns are designed for easy connection. Based on the theory of piezo-elasticity, a simplified one-dimensional model is derived to study the electromechanical, transmitting and sensing performance of PiSSAs with the wafers in series and parallel connection, and the model was verified by experiments. The theoretical results reveal that the first resonance frequency of PiSSAs in series and parallel decreases as the number or thickness of the PZT wafers increases, and the first electromechanical coupling factor increases firstly and then decrease gradually as the number or thickness increases. The results also show that both the first resonance frequency and the first electromechanical coupling factor of PiSSA in series and parallel change no more than 0.87% as the Young’s modulus of the epoxy increases from 0.5 to 1.5 times 3.2 GPa, which is helpful for the fabrication of PiSSAs. In addition, the displacement output of PiSSAs in parallel is about 2.18–22.49 times that in series at 1–50 kHz, while the voltage output of PiSSAs in parallel is much less than that in parallel, which indicates that PiSSA in parallel is much more suitable for working as an actuator to excite stress waves and PiSSA in series is suitable for working as a sensor to detect the waves. All the results demonstrate that the connecting type, number and thickness of the PZT wafers should be carefully selected to increase the efficiency and output of PiSSA actuators and sensors. This study contributes to providing a method to investigate the characteristics and optimize the structural parameters of the proposed PiSSAs.

scholarly journals Computation of several Hessenberg determinants

2020 ◽  
Vol 70 (6) ◽  
pp. 1521-1537
Author(s):  
Feng Qi ◽  
Omran Kouba ◽  
Issam Kaddoura
Keyword(s):  
Linear Algebra ◽  
Simple Formula ◽  
Binomial Coefficients ◽  
Explicit Formulas ◽  
Methods And Techniques

AbstractIn the paper, employing methods and techniques in analysis and linear algebra, the authors find a simple formula for computing an interesting Hessenberg determinant whose elements are products of binomial coefficients and falling factorials, derive explicit formulas for computing some special Hessenberg and tridiagonal determinants, and alternatively and simply recover some known results.

Simple formula for the ground band spectrum of even-mass rotational nuclei

1982 ◽  
Vol 25 (5) ◽  
pp. 2837-2840 ◽  
Author(s):  
A. Partensky ◽  
C. Quesne
Keyword(s):  
Simple Formula ◽  
Band Spectrum ◽  
Ground Band
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