[William Byam], An Exact Relation of the Most Execrable Attempts of John Allin … (1665)

2021 ◽  
pp. 343-349
Author(s):  
Carla Gardina Pestana ◽  
Sharon V. Salinger
Keyword(s):  
Exact Relation

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

FokI polymorphism of the vitamin D receptor (VDR) gene and susceptibility to tuberculosis: evidence through a meta-analysis

2021 ◽  
Author(s):  
Upendra Yadav ◽  
Pradeep Kumar ◽  
Vandana Rai
Keyword(s):  
Vitamin D ◽  
Vitamin D Receptor ◽  
Meta Analysis ◽  
Receptor Gene ◽  
Asian Population ◽  
Recessive Model ◽  
Dominant Model ◽  
Vdr Gene ◽  
Exact Relation ◽  
Significance Level

Abstract Background: Tuberculosis is one of the top ten causes of deaths worldwide. The deficiency of vitamin D was reported to be associated with the increased susceptibility of tuberculosis. Various previous reports were published to check the association of FokI polymorphism of the vitamin D receptor gene with tuberculosis risk. But their results were inconsistent so, we performed a meta-analysis to know the exact relation of the two.Methods: Different databases were screened up to November, 2020 with the keywords “Vitamin D receptor”, “VDR”, and “FokI”, along with “Tuberculosis” and “TB” to find the suitable articles. All the statistical analyses were performed by the Open Meta-Analyst program and all p-values were two-tailed with a significance level of 0.05.Results: No statistically significant association was observed in the allele contrast model (ORfvs.F= 1.11, 95%CI= 0.99-1.24, p= 0.05, I2= 73.46%), in the dominant model (ORff+Ffvs.FF= 1.11, 95%CI= 0.96-1.28, p= 0.14, I2= 71.39%), and in the co-dominant model (ORFfvs.FF= 1.05, 95%CI= 0.92-1.21, p= 0.41, I2= 65.97%). However, a significant association was found in the homozygote model (ORffvs.FF= 1.32, 95%CI= 1.03-1.69, p= 0.02, I2= 67.02%) and in the recessive model (ORFF+Ff vs.ff= 1.26, 95%CI= 1.03-1.54, p= 0.02, I2= 58.01%). Further analysis was performed on the bases of the ethnicity. In Asian population a significant association was found in the homozygote model (ORffvs.FF= 1.57, 95%CI= 1.12-2.21, p= 0.008, I2= 70.37%) and in the recessive model (ORFF+Ff vs.ff= 1.43, 95%CI= 1.08-1.89, p= 0.01, I2= 63.13%).Conclusion: In conclusion, a significant association of FokI with tuberculosis susceptibility was found in the overall analysis and in the Asian population.

scholarly journals The influence of pressure on the boiling points of metals

1910 ◽  
Vol 83 (565) ◽  
pp. 483-491 ◽  
Keyword(s):  
Atmospheric Pressure ◽  
Boiling Point ◽  
High Vacuum ◽  
Similar Type ◽  
Exact Relation ◽  
Reduced Pressure ◽  
Boiling Points ◽  
Experimental Values ◽  
Low Pressures ◽  
Very High

Part I. — Pressures below 760 mm . In a previous communication (‘Proc.’, A, vol. 82, 1909, p. 396) the approximate boiling points of a number of metals were determined at atmospheric pressure. Apart from the question of finding the exact relation between the boiling point and pressure, it is an important criterion of any method for fixing the temperatures of ebullition to demonstrate that the experimental values obtained are dependent on the pressure. It is specially desirable when dealing with substances boiling at temperatures above 2000° to have some evidence that the points indicated are true boiling points. Previous work on the vaporisation of metals at different pressures has been confined to experiments in a very high vacuum except for metals like bismuth, cadmium, and zinc, which boil at relatively low temperatures under atmospheric pressure. The observations were limited to very low pressures on account of the difficulty of obtaining any material capable of withstanding a vacuum at temperatures over 1400° and the consequent necessity for keeping the boiling point below this limit by using very low pressures. Moreover in the case of the majority of the metals, e. g. , copper, tin, ebullition under reduced pressure has never been observed. The difficulties indicated above were avoided by using a similar type of apparatus to that previously described, and arranging the whole furnace inside a vacuum enclosure, thus permitting of the use of graphite crucibles to contain the metal.

scholarly journals The Food of Birds

1903 ◽  
Vol 1 (3) ◽  
pp. 86-161
Author(s):  
Stephen A. Forbes
Keyword(s):  
Exact Relation ◽  
The Relationship

The primary purpose of this investigation is the determination of the exact relation of the different species of birds, and of the class in general, to agriculture and horticulture, but includes also birds whose interest is strictly scientific rather than practical, and takes into consideration injuries and benefits of birds. Emphasizes the relationship between birds and insects.

ENERGY DEPOSITION OF RELATIVISTIC ELECTRONS IN SUPER-HOT PLASMA

2007 ◽  
Vol 21 (27) ◽  
pp. 1855-1862 ◽  
Author(s):  
TONG-CHENG WU ◽  
XUAN ZHANG ◽  
WEI-KE AN
Keyword(s):  
Electron Beam ◽  
Energy Loss ◽  
Energy Deposition ◽  
Plasma Oscillation ◽  
Lorentz Factor ◽  
Relativistic Electrons ◽  
Exact Relation ◽  
Loss Mechanism ◽  
Electron Collisions ◽  
Thermonuclear Fuel

The intense ultrashort laser interacting with the thermonuclear fuel may produce a relativistic plasma and MeV electron beam, how to fix the Lorentz factors of the particles in the plasma and model the energy deposition of MeV electron beams are important subjects. In this letter, we demonstrate the exact relation between the average Lorentz factor and the temperature of the system; and then obtained the relativistic modified formula for the energy loss of the relativistic electron-beam due to binary electron-electron collisions. Another important energy loss mechanism, the excitation of Langmuir collective plasma oscillation, is also treated within the relativistic framework. Hence, we re-examine theoretically the possibility of igniting hot spots in the super-compressed DT target and the answer is that the fast ignitor scenario is able to yield thermonuclear ignition in the target.

scholarly journals COMMUTING POLYNOMIALS AND POLYNOMIALS WITH SAME JULIA SET

1996 ◽  
Vol 06 (12a) ◽  
pp. 2427-2432 ◽  
Author(s):  
PAU ATELA ◽  
JUN HU
Keyword(s):  
Julia Set ◽  
Exact Relation ◽  
Complete Answer ◽  
Commuting Pairs

It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fernández, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two problems of polynomials with the same Julia set and commuting pairs.

An exact relation for the chemical potential of a quasi-classical system

2015 ◽  
Vol 53 (4) ◽  
pp. 599-600 ◽  
Author(s):  
V. B. Bobrov ◽  
V. Ya. Mendeleev ◽  
S. A. Triger
Keyword(s):  
Chemical Potential ◽  
Classical System ◽  
Exact Relation

scholarly journals Bulk scaling in wall-bounded and homogeneous vertical natural convection

2018 ◽  
Vol 841 ◽  
pp. 825-850 ◽  
Author(s):  
Chong Shen Ng ◽  
Andrew Ooi ◽  
Detlef Lohse ◽  
Daniel Chung
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Power Law ◽  
Exact Relation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Previous numerical studies on homogeneous Rayleigh–Bénard convection, which is Rayleigh–Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($\mathit{Nu}$) and the Reynolds number ($\mathit{Re}$) vary with the Rayleigh number ($\mathit{Ra}$) according to $\mathit{Nu}\sim \mathit{Ra}^{1/2}$ and $\mathit{Re}\sim \mathit{Ra}^{1/2}$ at small Prandtl numbers ($\mathit{Pr}$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel to it; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $\mathit{Nu}$, $\mathit{Re}$ and $\mathit{Ra}$ and to find physical arguments for closure, rather than making use of the exact relation between $\mathit{Nu}$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous set-up, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focusing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $\mathit{Ra}$, $\mathit{Re}$ and $\mathit{Nu}$. From a stability perspective, at low- to moderate-$\mathit{Ra}$, we find that the time evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.

Sign in / Sign up

Export Citation Format

Share Document