scholarly journals Generalized λ-Array Type Polynomials with Exponential Riordan Array

2016 ◽  
Vol 06 (03) ◽  
pp. 288-298
Author(s):  
兰 青
Keyword(s):  
Array Type ◽  
Riordan Array

scholarly journals On identities involving generalized harmonic, hyperharmonic and special numbers with Riordan arrays

2021 ◽  
Vol 9 (1) ◽  
pp. 22-30
Author(s):  
Sibel Koparal ◽  
Neşe Ömür ◽  
Ömer Duran
Keyword(s):  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Riordan Arrays ◽  
Riordan Array

Abstract In this paper, by means of the summation property to the Riordan array, we derive some identities involving generalized harmonic, hyperharmonic and special numbers. For example, for n ≥ 0, ∑ k = 0 n B k k ! H ( n . k , α ) = α H ( n + 1 , 1 , α ) - H ( n , 1 , α ) , \sum\limits_{k = 0}^n {{{{B_k}} \over {k!}}H\left( {n.k,\alpha } \right) = \alpha H\left( {n + 1,1,\alpha } \right) - H\left( {n,1,\alpha } \right)} , and for n > r ≥ 0, ∑ k = r n - 1 ( - 1 ) k s ( k , r ) r ! α k k ! H n - k ( α ) = ( - 1 ) r H ( n , r , α ) , \sum\limits_{k = r}^{n - 1} {{{\left( { - 1} \right)}^k}{{s\left( {k,r} \right)r!} \over {{\alpha ^k}k!}}{H_{n - k}}\left( \alpha \right) = {{\left( { - 1} \right)}^r}H\left( {n,r,\alpha } \right)} , where Bernoulli numbers Bn and Stirling numbers of the first kind s (n, r).

scholarly journals Observational manifestations of ‘cosmological dinosaurs’ at redshifts z ∼ 20

2021 ◽  
Vol 503 (2) ◽  
pp. 3081-3088
Author(s):  
V K Dubrovich ◽  
Yu N Eroshenko ◽  
S I Grachev
Keyword(s):  
Black Hole ◽  
Atomic Hydrogen ◽  
Radiation Transfer ◽  
Ring Width ◽  
High Mass ◽  
Primordial Black Hole ◽  
Array Type ◽  
Local Sources ◽  
Order Of Magnitude ◽  
Very High

ABSTRACT We consider a primordial black hole of very high mass, $10^9\!-\!10^{10}\, \mathrm{M}_\odot$, surrounded by the dark matter and bayonic halo at redshifts z ∼ 20 without any local sources of energy release. Such heavy and concentrated objects in the early Universe were previously called ‘cosmological dinosaurs’. Spectral distribution and spatial variation of the brightness in the 21-cm line of atomic hydrogen are calculated with the theory of radiation transfer. It is shown that a narrow and deep absorption arises in the form of the spherical shell around the primordial black hole at the certain radius. The parameters of this shell depend almost exclusively on the mass of the black hole. The angular diameter 18 arcsec of the absorption ring at z ∼ 20 is well within the current technical possibilities of the Square Kilometre Array type telescopes. But the observation of the ring width itself requires an order of magnitude better resolution.

Numerically controlled sacrificial plasma oxidation using array-type electrode toward high-throughput deterministic machining

2011 ◽  
Vol 7 (3/4) ◽  
pp. 289
Author(s):  
Yasuhisa Sano ◽  
Keinosuke Yoshinaga ◽  
Shohei Kamisaka ◽  
Hidekazu Mimura ◽  
Satoshi Matsuyama ◽  
...  
Keyword(s):  
High Throughput ◽  
Plasma Oxidation ◽  
Array Type

Characterization of Maximum Current Capacity for Microprocessor Sockets

2005 ◽  
Author(s):  
David Song ◽  
Ashish Gupta ◽  
Chia-Pin Chiu
Keyword(s):  
Risk Assessment ◽  
Computational Modeling ◽  
Carrying Capacity ◽  
Infrared Camera ◽  
Experimental Results ◽  
Array Type ◽  
Maximum Current ◽  
Modeling And Experiments ◽  
Subsequent Risk

This paper presents the current-carrying-capacity (CCC) characterization of a land-grid-array type microprocessor socket. This CCC study has been performed using both computational modeling and experiments using infrared camera. A subsequent risk assessment was performed against the maximum allowed temperature at the point of pressure contact of socket pin for the use-condition socket pin current and motherboard temperature. The results from the modeling and the experimental results are compared.

scholarly journals Hi-Speed Tactile Sensing for Array-type Tactile Sensor and Object Manipulation based on Tactile Information

2012 ◽  
Vol 25 (5) ◽  
pp. 117-125
Author(s):  
Wataru Fukui ◽  
Futoshi Kobayashi ◽  
Fumio Kojima ◽  
Hiroyuki Nakamoto ◽  
Tadashi Maeda ◽  
...  
Keyword(s):  
Tactile Sensor ◽  
Object Manipulation ◽  
Tactile Sensing ◽  
Tactile Information ◽  
Array Type

Development of a micro array type electron multiplier

2002 ◽  
Author(s):  
J. Kawarabayashi ◽  
D. Fukuda ◽  
H. Takahashi ◽  
T. Iguchi ◽  
M. Nakazawa ◽  
...  
Keyword(s):  
Electron Multiplier ◽  
Array Type ◽  
Micro Array
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