ABOUT THE MEAN KING'S PROBLEM AND DISCRETE WIGNER DISTRIBUTIONS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1742-1760 ◽  
Author(s):  
THOMAS DURT
Keyword(s):  
Weyl Function ◽  
Galois Field ◽  
Bell States ◽  
Quadratic Extensions ◽  
System A ◽  
Wigner Distributions ◽  
Particular Solution ◽  
The Mean ◽  
One To One ◽  
Adjoint Operators

When the state of a quantum system belongs to a N-dimensional Hilbert space, with N the power of a prime number, it is possible to associate to the system a finite field (Galois field) with N elements. In this paper, we introduce generalized Bell states that can be intrinsically expressed in terms of the field operations. These Bell states are in one to one correspondence with the N2elements of the generalised Pauli group or Heisenberg-Weyl group. This group consists of discrete displacement operators and provides a discrete realisation of the Weyl function. Thanks to the properties of generalised Bell states and of quadratic extensions of finite fields, we derive a particular solution for the Mean King's problem. This solution is in turn shown to be in one to one correspondence with a set of N2self-adjoint operators that provides a discrete realisation of the Wigner quasi-distribution.

scholarly journals How to Distinguish Languages and Dialects

2020 ◽  
Vol 45 (4) ◽  
pp. 823-831 ◽  
Author(s):  
Søren Wichmann
Keyword(s):  
Temporal Distance ◽  
Strong Tendency ◽  
Data Sets ◽  
Language Group ◽  
Lexical Information ◽  
Normal Distributions ◽  
Mixture Of Normal Distributions ◽  
The Mean ◽  
One To One

The terms “language” and “dialect” are ingrained, but linguists nevertheless tend to agree that it is impossible to apply a non-arbitrary distinction such that two speech varieties can be identified as either distinct languages or two dialects of one and the same language. A database of lexical information for more than 7,500 speech varieties, however, unveils a strong tendency for linguistic distances to be bimodally distributed. For a given language group the linguistic distances pertaining to either cluster can be teased apart, identifying a mixture of normal distributions within the data and then separating them fitting curves and finding the point where they cross. The thresholds identified are remarkably consistent across data sets, qualifying their mean as a universal criterion for distinguishing between language and dialect pairs. The mean of the thresholds identified translates into a temporal distance of around one to one-and-a-half millennia (1,075–1,635 years).

Multiple channel queues in heavy traffic. I

1970 ◽  
Vol 2 (01) ◽  
pp. 150-177 ◽  
Author(s):  
Donald L. Iglehart ◽  
Ward Whitt
Keyword(s):  
Heavy Traffic ◽  
Arrival Rate ◽  
Standard System ◽  
Interarrival Time ◽  
Service Rate ◽  
Service Channel ◽  
Multiple Channel ◽  
System A ◽  
The Mean ◽  
Service Channels

The queueing systems considered in this paper consist of r independent arrival channels and s independent service channels, where as usual the arrival and service channels are independent. Arriving customers form a single queue and are served in the order of their arrival without defections. We shall treat two distinct modes of operation for the service channels. In the standard system a waiting customer is assigned to the first available service channel and the servers (servers ≡ service channels) are shut off when they are idle. Thus the classical GI/G/s system is a special case of our standard system. In the modified system a waiting customer is assigned to the service channel that can complete his service first and the servers are not shut off when they are idle. While the modified system is of some interest in its own right, we introduce it primarily as an analytical tool. Let λ i denote the arrival rate (reciprocal of the mean interarrival time) in the ith arrival channel and μ j the service rate (reciprocal of the mean service time) in the jth service channel. Then is the total arrival rate to the system and is the maximum service rate of the system. As a measure of congestion we define the traffic intensity ρ = λ/μ.

An Approximate Method for the Dynamic Analysis of Elastic Linkages

1977 ◽  
Vol 99 (2) ◽  
pp. 449-455 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Exact Analytical Solution ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Degree Of Freedom ◽  
Suggested Approach ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
System A ◽  
Suggested Technique ◽  
Particular Solution

A new numerical procedure based on an iterative technique is progressively developed in this paper for obtaining an approximate particular solution from the equations of motion of an elastic linkage with small damping and at subresonant speeds. The method is introduced by employing a simple vibrating system, a single degree-of-freedom mass-dashpot-spring model under both harmonic forcing and periodic forcing. A harmonically excited two degree-of-freedom model is also solved by the suggested approach. Error functions are developed for each case to give an estimation of the order of error between the exact analytical solution and the approximate technique. The suggested technique is then extended to solve an elastic linkage problem where the uncoupled equations of motion are treated as a series of single degree-of-freedom problems and solved. These are retransformed into the physical coordinate system to obtain the particular solution. The first and second derivatives of the forcing functions (involving rigid-body inertia) are approximated utilizing the finite difference method.

scholarly journals A Flow-Calibrated Method to Project Groundwater Infiltration into Coastal Sewers Affected by Sea Level Rise

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1934
Author(s):  
Adrienne Fung ◽  
Roger Babcock
Keyword(s):  
Sea Level Rise ◽  
Sea Level ◽  
Monitoring Data ◽  
Groundwater Levels ◽  
Flow Monitoring ◽  
System A ◽  
Coastal Cities ◽  
The Mean ◽  
Groundwater Infiltration

Collection systems in coastal cities are often below the groundwater table, leading to groundwater infiltration (GWI) through defects such as cracks and poor lateral connections. Climate-change-induced sea level rise (SLR) will raise groundwater levels, increasing the head and thus the inflow. A method has been developed to predict GWI when groundwater levels change using calibration with sewershed flow monitoring data. The calibration results in a parameter that characterizes the porosity of the collection system. A case study is presented for a coastal city with reliable flow monitoring data for eight days that resulted in a large range of effective defect sizes (minimum 0.0044 to maximum 0.338 radians), however, the range of predicted future GWI in currently submerged pipes varied by only 12% from the mean. The mean effective defect predicts 70 to 200% increases in GWI due to SLR of 0.3 to 0.9 m (1 to 3 ft), respectively, for currently submerged pipes. Predicted additional GWI for pipes that will become submerged due to SLR will increase GWI to values that approach or exceed the current average dry weather flow. This methodology can be used for planning of infrastructure improvements to enhance resiliency in coastal communities.

Analysis of an Artificial Ventricle and Mock Circulatory System

1977 ◽  
Vol 99 (4) ◽  
pp. 184-188 ◽  
Author(s):  
K. M. High ◽  
J. A. Brighton ◽  
A. D. Brickman ◽  
W. S. Pierce
Keyword(s):  
Artificial Heart ◽  
Circulatory System ◽  
Experimental Tests ◽  
Mean Flow ◽  
Actual System ◽  
Mock Circulatory System ◽  
System A ◽  
The Mean ◽  
Artificial Ventricle ◽  
Good Agreement

A mathematical model is developed for calculating the pressures and flows in an artificial heart, its pneumatic drive unit, and a mock circulatory system. The system is divided into convenient subsystems to facilitate the analysis, and each subsystem is then analyzed separately. The set of independent equations developed is solved on a computer and corresponding experimental tests are made on the actual system. A comparison of the experimental and computer results shows good agreement for the mean flow rate through the pump and also for several instantaneous pressures and flow rates in the system.

Multiple channel queues in heavy traffic. I

1970 ◽  
Vol 2 (1) ◽  
pp. 150-177 ◽  
Author(s):  
Donald L. Iglehart ◽  
Ward Whitt
Keyword(s):  
Heavy Traffic ◽  
Arrival Rate ◽  
Standard System ◽  
Interarrival Time ◽  
Service Rate ◽  
Service Channel ◽  
Multiple Channel ◽  
System A ◽  
The Mean ◽  
Service Channels

The queueing systems considered in this paper consist of r independent arrival channels and s independent service channels, where as usual the arrival and service channels are independent. Arriving customers form a single queue and are served in the order of their arrival without defections. We shall treat two distinct modes of operation for the service channels. In the standard system a waiting customer is assigned to the first available service channel and the servers (servers ≡ service channels) are shut off when they are idle. Thus the classical GI/G/s system is a special case of our standard system. In the modified system a waiting customer is assigned to the service channel that can complete his service first and the servers are not shut off when they are idle. While the modified system is of some interest in its own right, we introduce it primarily as an analytical tool. Let λi denote the arrival rate (reciprocal of the mean interarrival time) in the ith arrival channel and μj the service rate (reciprocal of the mean service time) in the jth service channel. Then is the total arrival rate to the system and is the maximum service rate of the system. As a measure of congestion we define the traffic intensity ρ = λ/μ.

scholarly journals Non-weak compactness of the integration map for vector measures

1993 ◽  
Vol 54 (3) ◽  
pp. 287-303 ◽  
Author(s):  
S. Okada ◽  
W. J. Ricker
Keyword(s):  
Banach Space ◽  
Volterra Operator ◽  
Continuous Operator ◽  
Weakly Compact ◽  
Vector Measures ◽  
Mean Convergence ◽  
Integrable Functions ◽  
The Mean ◽  
The Fourier Transform ◽  
Adjoint Operators

AbstractLet m be a vector measure with values in a Banach space X. If L1(m) denotes the space of all m integrable functions then, with respect to the mean convergence topology, L1(m) is a Banach space. A natural operator associated with m is its integration map Im which sends each f of L1(m) to the element ∫fdm (of X). Many properties of the (continuous) operator Im are closely related to the nature of the space L1(m). In general, it is difficult to identify L1(m). We aim to exhibit non-trivial examples of measures m in (non-reflexive) spaces X for which L1(m) can be explicitly computed and such that Im is not weakly compact. The examples include some well known operators from analysis (the Fourier transform on L1 ([−π, π]), the Volterra operator on L1 ([0, 1]), compact self-adjoint operators in a Hilbert space); such operators can be identified with integration maps Im (or their restrictions) for suitable measures m.

scholarly journals The receptor subunit Tom20 is dynamically associated with the TOM complex in mitochondria of human cells

2021 ◽  
pp. mbc.E21-01-0042
Author(s):  
Maniraj Bhagawati ◽  
Tasnim Arroum ◽  
Niklas Webeling ◽  
Ayelén González Montoro ◽  
Henning D. Mootz ◽  
...  
Keyword(s):  
Single Particle Tracking ◽  
Human Cells ◽  
Receptor Subunit ◽  
Core Complex ◽  
Tom Complex ◽  
System A ◽  
Precursor Proteins ◽  
The Mean ◽  
Reduced Mobility ◽  
Peripheral Receptor

The outer membrane translocase (TOM) is the import channel for nuclear-encoded mitochondrial proteins. The general import pore contains Tom40, Tom22, Tom5, Tom6 and Tom7. Precursor proteins are bound by the peripheral receptor proteins Tom20, Tom22 and Tom70 before being imported by the TOM complex. Here we investigated the association of the receptor Tom20 with the TOM complex. Tom20 was found in the TOM complex, but not in a smaller subcomplex. In addition, a subcomplex was found without Tom40 and Tom7 but with Tom20. Using single particle tracking of labeled Tom20 in overexpressing human cells, we show that Tom20 has, on average, higher lateral mobility in the membrane than Tom7/TOM. After ligation of Tom20 with the TOM complex by post-tranlational protein trans-splicing using the trackless, ultra-fast cleaved Gp41-1 integrin system, a significant decrease in the mean diffusion coefficient of Tom20 was observed in the resulting Tom20-Tom7 fusion protein. Exposure of Tom20 to high substrate loading also resulted in reduced mobility. Taken together, our data show that the receptor subunit Tom20 interacts dynamically with the TOM core complex. We suggest that the TOM complex containing Tom20 is the active import pore and that Tom20 is associated when substrate is available.

scholarly journals MSE Minimized Joint Transmission in Coordinated MultiPoint Systems with Sparse Feedback and Constrained Backhaul Requirements

2020 ◽  
Author(s):  
Mohammad Bagher Nezafati ◽  
Mehrdad Taki ◽  
Tommy Svensson
Keyword(s):  
Base Stations ◽  
Channel State ◽  
Coordinated Multipoint ◽  
System A ◽  
Backhaul Link ◽  
Central Coordination ◽  
The Mean ◽  
Value Decomposition ◽  
The Cost ◽  
Joint Transmission

Abstract In a joint transmission coordinated multipoint (JT-CoMP) system, a shared spectrum is utilized by all neighbor cells. In the downlink, a group of base stations (BSs) coordinately transmit the users’ data to avoid serious interference at the users in the boundary of the cells, thus substantially improving area fairness. However, this comes at the cost of high feedback and backhaul load; In a frequency division duplex (FDD) system, all users at the cell boundaries have to collect and send feedback of the downlink channel state information (CSI). In centralized JT-CoMP, although with capabilities for perfect coordination, a central coordination node (CCN) have to send the computed precoding weights and corresponding data to all cells which can overwhelm the backhaul resources. In this paper, we design a JT-CoMP scheme, by which the sum of the mean square error (MSE) at the boundary users is minimized, while feedback and backhaul loads are constrained and the load is balanced between BSs. Our design is based on the singular value decomposition (SVD) of CSI matrix and optimization of a binary link selection matrix to provide sparse feedback - constrained backhaul link. For comparison, we adopt the previously presented schemes for feedback and backhaul reduction in the physical layer. Extensive numerical evaluations show that the proposed scheme can reduce the MSE with at least 25% , compared to the adopted and existing schemes.

scholarly journals Determinants of financial euroisation in a small open economy: The case of Serbia

2018 ◽  
Vol 63 (218) ◽  
pp. 9-21
Author(s):  
Mile Bosnjak ◽  
Gordana Kordic ◽  
Vlatka Bilas
Keyword(s):  
Time Series ◽  
Open Economy ◽  
Small Open Economy ◽  
Banking System ◽  
Behaviour Pattern ◽  
Monthly Data ◽  
System A ◽  
The Mean ◽  
The Interest Rate ◽  
Clustering Pattern

This paper examines the phenomenon of financial euroisation in Serbia, focusing on the liability side of the banking system. A time series model is estimated and evaluated using a monthly data sample from January 2007 to January 2016 for Serbia. The results of this paper show that the mean pattern of financial euroisation in Serbia is determined by the exchange rate, inflation, and the interest rate differential. Financial euroisation in Serbia is found to be volatile and to exhibit a clustering pattern. Of the estimated and tested models the ARCH (1) model is found to be best suited to explain the volatile behaviour pattern of financial euroisation in Serbia.

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