Signalling over a Gaussian channel with feedback and autoregressive noise

1975 ◽  
Vol 12 (04) ◽  
pp. 713-723 ◽  
Author(s):  
J. Wolfowitz
Keyword(s):  
Regression Coefficient ◽  
Positive Root ◽  
Average Energy ◽  
Gaussian Channel ◽  
Straightforward Manner ◽  
First Order ◽  
Unique Positive Root ◽  
Equivalent Expression ◽  
Optimal Linear ◽  
General Regression

We study in detail the case of first-order regression, but our results can be extended to the general regression in a straightforward manner. An average energy constraint ((1.2) below) is imposed on each signal. In Section 2 we give an optimal linear signalling scheme (definition and proof in Section 4) for this channel. We conjecture that this scheme is optimal among all signalling schemes. Then the capacity C of the channel is (see Section 5) – log b, where b is the unique positive root (in x) of the equation x 2 = (1 + g 2(1 + |α|x)2)–1. Here a is the regression coefficient, and g 2 is the ratio of the average energy per signal to the variance of the noise. An equivalent expression is C = ½log(1 + g2(1 + |α| b)2).

Signalling over a Gaussian channel with feedback and autoregressive noise

1975 ◽  
Vol 12 (4) ◽  
pp. 713-723 ◽  
Author(s):  
J. Wolfowitz
Keyword(s):  
Regression Coefficient ◽  
Positive Root ◽  
Average Energy ◽  
Gaussian Channel ◽  
Straightforward Manner ◽  
First Order ◽  
Unique Positive Root ◽  
Equivalent Expression ◽  
Optimal Linear ◽  
General Regression

We study in detail the case of first-order regression, but our results can be extended to the general regression in a straightforward manner. An average energy constraint ((1.2) below) is imposed on each signal. In Section 2 we give an optimal linear signalling scheme (definition and proof in Section 4) for this channel. We conjecture that this scheme is optimal among all signalling schemes. Then the capacity C of the channel is (see Section 5) – log b, where b is the unique positive root (in x) of the equation x2 = (1 + g2(1 + |α|x)2)–1. Here a is the regression coefficient, and g2 is the ratio of the average energy per signal to the variance of the noise. An equivalent expression is C = ½log(1 + g2(1 + |α| b)2).

scholarly journals On the Roots of the Modified Orbit Polynomial of a Graph

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 972
Author(s):  
Modjtaba Ghorbani ◽  
Matthias Dehmer
Keyword(s):  
Positive Root ◽  
Current Work ◽  
Positive Zero ◽  
Unique Positive Root ◽  
Definition Of

The definition of orbit polynomial is based on the size of orbits of a graph which is OG(x)=∑ix|Oi|, where O1,…,Ok are all orbits of graph G. It is a well-known fact that according to Descartes’ rule of signs, the new polynomial 1−OG(x) has a positive root in (0,1), which is unique and it is a relevant measure of the symmetry of a graph. In the current work, several bounds for the unique and positive zero of modified orbit polynomial 1−OG(x) are investigated. Besides, the relation between the unique positive root of OG in terms of the structure of G is presented.

scholarly journals Kinetic Studies for the Biosorption of Chromium Using Cherry Leaves (Muntingia calabura L.)

2014 ◽  
Vol 25 ◽  
pp. 6-11 ◽  
Author(s):  
R. Aathithya ◽  
J. Rajani Sowparnika ◽  
V. Balakrishnan
Keyword(s):  
Regression Coefficient ◽  
Kinetic Studies ◽  
Order Reaction ◽  
First Order Reaction ◽  
Standard Errors ◽  
Second Order Reaction ◽  
Pseudo First Order Reaction ◽  
First Order ◽  
Pseudo First Order ◽  
Muntingia Calabura

Biosorption is an attractive technology which is used for the sorption of substances by a biomaterial. In this present work the heavy metal chromium was subjected to biosorption because of their non-degradability nature and causes water and land pollution. Cherry leaves were used as a biomaterial for the biosorption. Kinetic studies were performed for the biosorption experiment. From the experiment it was found that the reaction follows pseudo first order reaction because of the larger value of regression coefficient R2 and lower value of standard errors (χ2) for pseudo first order reaction than second order reaction.

A Consistent Hydrodynamic Theory for Moored and Positioned Vessels

1982 ◽  
Vol 26 (02) ◽  
pp. 97-105
Author(s):  
Michael S. Triantafyllou
Keyword(s):  
Slow Motion ◽  
Hydrodynamic Theory ◽  
Ship Motions ◽  
Multiple Time ◽  
Governing Equations ◽  
Straightforward Manner ◽  
Drift Motion ◽  
First Order ◽  
Slow Motions ◽  
Force Calculation

The motion of a moored, or positioned, vessel under the influence of waves can be decomposed into a large-amplitude, slowly varying part and a small-amplitude, fast varying part. A consistent theory can be formulated, therefore, based on a multiple time scale expansion, together with an amplitude expansion of the general governing equations. The existing theory of ship motions remains unchanged within the present approach, while the equations of drift motion can be obtained separately from the fast dynamics, in a straightforward manner. It is shown that if the slow motion flow is modeled as inviscid and irrotational, its potential is of first order and satisfies linear boundary conditions. Also, the second-order force calculation is not influenced by the slow motions. The rolling motion of a moored vessel is studied as an example of the concepts introduced.

Degradation Kinetic of Oxytetracycline Antibiotic inside UV Reactor in the Presence of H2O2

2014 ◽  
Vol 625 ◽  
pp. 901-906
Author(s):  
Anisa Ur Rahmah ◽  
Sabtanti Harimurti ◽  
Abdul Aziz Omar ◽  
Thanabalan Murugesan
Keyword(s):  
Experimental Data ◽  
Kinetic Study ◽  
Regression Coefficient ◽  
Kinetic Studies ◽  
Second Order ◽  
Degradation Kinetic ◽  
First Order ◽  
Uv Reactor ◽  
Pseudo First Order ◽  
Veterinary Antibiotic

–Oxytetracycline (OTC), a widely used of veterinary antibiotic, was degraded inside a UV/H2O2system. Kinetic study was conducted at 30°C of temperature and pH 6.37, as suggested by the previous optimization experiment. About 250, 375 and 500 ppm initial OTC concentration were used for the kinetic studies, at H2O2concentration of 0.116 M. The experimental data were plotted against the pseudo zero-th, first and second order of kinetic. Based on regression coefficient value, the data was well fitted with the pseudo first order of kinetic. The calculated value ofkobswas 0.181 min-1.

A new proof of Sahlqvist's theorem on modal definability and completeness

1989 ◽  
Vol 54 (3) ◽  
pp. 992-999 ◽  
Author(s):  
G. Sambin ◽  
V. Vaccaro
Keyword(s):  
Modal Logic ◽  
Personal Computer ◽  
Topological Spaces ◽  
Straightforward Manner ◽  
Original Proof ◽  
Complete Proof ◽  
Modal Formula ◽  
First Order ◽  
Modal Definability ◽  
General Frames

There are not many global results on modal logics. One of these is the following theorem by Sahlqvist on completeness and correspondence for a wide class of modal formulae (including many well known logics, e.g. D, T, B, S4, K4, S5, …) (see [S]).Sahlqvist's Theorem. Let A be any modal formula which is equivalent to a conjunction of formulae of the form □m(A1 → A2), where m ≥ 0, A2 is positive and A1 is obtained from propositional variables and their negations applying ∧, ∨, ♢, and □ in such a way that no positive occurrence of a variable is in a subformula of the form B1 ∨ B2 or ♢ B1 within the scope of some □. Then A corresponds effectively to a first order formula, and L + A is canonical whenever Lis a canonical logic.A formula A satisfying the above conditions is henceforth called a Sahlqvist formula. Unfortunately, till now, the only complete proof was the original proof of Sahlqvist (a proof of the correspondence half has also been given by van Benthem [vB]). It is so complicated and long that even in an advanced textbook of modal logic [HC] it has not found a place. Here, by considering general frames as topological spaces, an attitude which we developed in [TD], we give a proof of Sahlqvist's theorem simplified to such an extent that one can easily grasp the key idea on which it is based and apply the resulting algorithm to specific modal formulae in a straightforward manner, suitable even for implementation on a personal computer. This key idea also improves on previous preliminary work in the same direction (see [S1], [S2]).

Adsorption and Desorption Potential of Cadmium Using Green Algae: Equilibrium and Kinetic Studies

2015 ◽  
Vol 1130 ◽  
pp. 693-696 ◽  
Author(s):  
Z.S. Birungi ◽  
E.M.N. Chirwa
Keyword(s):  
Sorption Capacity ◽  
Regression Coefficient ◽  
Kinetic Studies ◽  
Adsorption And Desorption ◽  
First Order ◽  
Rate Of Reaction ◽  
Freshwater Bodies ◽  
Pseudo Second Order ◽  
Better Than ◽  
Stichococcus Bacillaris

Microalgae has a diversity of species found in freshwater bodies but only a few have been explored for their biosorption potential as compared to macro algae (sea weed). Equilibrium and kinetic experiments were used to estimate sorption capacity and rate of reaction respectively. Chloroidium saccharophilum had the highest sorption capacity (qmax) of 200 mg/g and lower affinity (b) of 0.0095 L/g for removal of Cd. However, Stichococcus bacillaris was the best adsorbent for Cd as it had both a higher qmaxand higher b of 125 and 0.049 L/g. The Langmuir and Pseudo-second order models performed better than the Freundlich and First-order models with a regression coefficient (R2) > 0.9. Adsorption and desorption efficiency was achieved highest for Stichococcus bacillaris at 95.8% and 73.49% respectively.

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