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

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.

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C-Band and X-Band Switchable Frequency-Selective Surface

Electronics ◽

10.3390/electronics10040476 ◽

2021 ◽

Vol 10 (4) ◽

pp. 476

Author(s):

Umer Farooq ◽

Adnan Iftikhar ◽

Muhammad Farhan Shafique ◽

Muhammad Saeed Khan ◽

Adnan Fida ◽

...

Keyword(s):

Bottom Layer ◽

Frequency Selective Surface ◽

Transverse Magnetic ◽

Unit Element ◽

Angular Stability ◽

Band Spectrum ◽

Pin Diode ◽

Pin Diodes ◽

X Band ◽

Frequency Selective

This paper presents a highly compact frequency-selective surface (FSS) that has the potential to switch between the X-band (8 GHz–12 GHz) and C-band (4 GHz–8 GHz) for RF shielding applications. The proposed FSS is composed of a square conducting loop with inward-extended arms loaded with curved extensions. The symmetric geometry allows the RF shield to perform equally for transverse electric (TE), transverse magnetic (TM), and 45° polarizations. The unit cell has a dimension of 0.176 λ0 and has excellent angular stability up to 60°. The resonance mechanism was investigated using equivalent circuit models of the shield. The design of the unit element allowed incorporation of PIN diodes between adjacent elements for switching to a lower C-band spectrum at 6.6 GHz. The biasing network is on the bottom layer of the substrate to avoid effects on the shielding performance. A PIN diode configuration for the switching operation was also proposed. In simulations, the PIN diode model was incorporated to observe the switchable operation. Two prototypes were fabricated, and the switchable operation was demonstrated by etching copper strips on one fabricated prototype between adjacent unit cells (in lieu of PIN diodes) as a proof of the design prototypes. Comparisons among the results confirmed that the design offers high angular stability and excellent performance in both bands.

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Computation of several Hessenberg determinants

Mathematica Slovaca ◽

10.1515/ms-2017-0445 ◽

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.

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SIMPLE FORMULA FOR CALCULATION OF THE PÆDIATRIC DOSE

The Lancet ◽

10.1016/s0140-6736(62)90752-3 ◽

1962 ◽

Vol 280 (7263) ◽

pp. 990

Author(s):

J.E. Cullis

Keyword(s):

Simple Formula ◽

Paediatric Dose

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A new risk-adjusted Bernoulli cumulative sum chart for monitoring binary health data

Statistical Methods in Medical Research ◽

10.1177/0962280214530883 ◽

2016 ◽

Vol 25 (6) ◽

pp. 2704-2713 ◽

Cited By ~ 5

Author(s):

Giuseppe Rossi ◽

Simone Del Sarto ◽

Marco Marchi

Keyword(s):

Simple Formula ◽

Efficient Solution ◽

Real Data ◽

Health Data ◽

Data Sets ◽

Cumulative Sum ◽

Baseline Incidence ◽

Health Event ◽

Control Limits ◽

Underlying Risk

To monitor a health event in patients with a specific risk of developing the event, a risk-adjusted cumulative sum chart is needed. The risk-adjusted cumulative sum chart proposed in the literature has some limitations. Setting appropriate control limits is not straightforward, there is no simple formula for constructing them, and they remain sensitive to changes in the underlying risk distribution and the baseline incidence rate. To overcome these limits, we propose a new risk-adjusted Bernoulli cumulative sum chart as a simple and efficient solution. Analyses of simulated and real data sets illustrate the performance and usefulness of the proposed procedure.

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