Mass Dimension for Infinite Networks

2018 ◽  
pp. 45-50
Author(s):  
Eric Rosenberg
Keyword(s):  
Mass Dimension ◽  
Infinite Networks

Synthesis of symmetrical cables for infocommunication systems with improved noise immunity characteristics

2018 ◽  
pp. 99-108
Author(s):  
А. B. Semenov ◽  
T. S. Abbasova
Keyword(s):  
Noise Immunity ◽  
Mass Dimension ◽  
Dimensional Parameters ◽  
Improved Characteristics

A synthesis of construction of cables of category 6a for infocommunication systems with improved characteristics of noise immunity is carried out. The parameters of transient pickups and total transient pickups for the proposed cable design are calculated, and the cable diameter of the initial and proposed designs is estimated. The estimation of improvement of mass-dimension parameters of a cable of a proposed design is carried out. It is shown that due to chamber (group) unearthed screening, it is possible to significantly reduce the influence characteristics and the mass-dimensional parameters of the cable.

scholarly journals Quasiharmonic classification of infinite networks

1980 ◽  
Vol 2 (4) ◽  
pp. 339-344 ◽  
Author(s):  
Maretsugu Yamasaki
Keyword(s):  
Infinite Networks

scholarly journals Effective operator bases for beyond Standard Model scenarios: an EFT compendium for discoveries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Upalaparna Banerjee ◽  
Joydeep Chakrabortty ◽  
Suraj Prakash ◽  
Shakeel Ur Rahaman ◽  
Michael Spannowsky
Keyword(s):  
Standard Model ◽  
High Energy ◽  
Beyond The Standard Model ◽  
Minimal Extension ◽  
Effective Operator ◽  
Abelian Gauge ◽  
Gauge Symmetries ◽  
Higher Dimensional ◽  
The Standard Model ◽  
Mass Dimension

Abstract It is not only conceivable but likely that the spectrum of physics beyond the Standard Model (SM) is non-degenerate. The lightest non-SM particle may reside close enough to the electroweak scale that it can be kinematically probed at high-energy experiments and on account of this, it must be included as an infrared (IR) degree of freedom (DOF) along with the SM ones. The rest of the non-SM particles are heavy enough to be directly experimentally inaccessible and can be integrated out. Now, to capture the effects of the complete theory, one must take into account the higher dimensional operators constituted of the SM DOFs and the minimal extension. This construction, BSMEFT, is in the same spirit as SMEFT but now with extra IR DOFs. Constructing a BSMEFT is in general the first step after establishing experimental evidence for a new particle. We have investigated three different scenarios where the SM is extended by additional (i) uncolored, (ii) colored particles, and (iii) abelian gauge symmetries. For each such scenario, we have included the most-anticipated and phenomenologically motivated models to demonstrate the concept of BSMEFT. In this paper, we have provided the full EFT Lagrangian for each such model up to mass dimension 6. We have also identified the CP, baryon (B), and lepton (L) number violating effective operators.

scholarly journals Stability and moment bounds under utility-maximising service allocations: Finite and infinite networks

2020 ◽  
Vol 52 (2) ◽  
pp. 463-490
Author(s):  
Seva Shneer ◽  
Alexander Stolyar
Keyword(s):  
Steady State ◽  
Wide Class ◽  
Continuous Time ◽  
Service Rate ◽  
Fluid Limit ◽  
Natural Conditions ◽  
Infinite Systems ◽  
Moment Bounds ◽  
Infinite Networks ◽  
State Moment

AbstractWe study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.

scholarly journals Causality, unitarity and symmetry in effective field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Timothy Trott
Keyword(s):  
Effective Field ◽  
Tree Level ◽  
Global Symmetry ◽  
Fundamental Limits ◽  
Effective Interactions ◽  
Effective Contact ◽  
Higher Dimensional ◽  
Forward Limit ◽  
Mass Dimension ◽  
Flavour Violation

Abstract Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the S-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension 8 operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in SU(2) and SU(3) global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension 6 operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension 8 and 4 legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.

scholarly journals A spectral small-gain condition for input-to-state stability of infinite networks

2020 ◽  
Vol 53 (2) ◽  
pp. 5303-5308
Author(s):  
Christoph Kawan ◽  
Andrii Mironchenko ◽  
Abdalla Swikir ◽  
Navid Noroozi ◽  
Majid Zamani
Keyword(s):  
Small Gain ◽  
Infinite Networks

Study on the Aging Rules of Rigid Polyurethane Foams at Indoor Storage and Different Hygrothermal Conditions

2005 ◽  
Vol 24 (4) ◽  
pp. 197-208 ◽  
Author(s):  
Yuan-Jun Liu ◽  
Wen Zhai ◽  
Chuan-Lan He ◽  
Jian-Guo Deng ◽  
Ke-Jian Ji ◽  
...  
Keyword(s):  
Compressive Strength ◽  
Aging Time ◽  
Fire Retardant ◽  
Ester Group ◽  
Polyurethane Foams ◽  
Compressive Modulus ◽  
Glass Beads ◽  
Hygrothermal Aging ◽  
Aging Properties ◽  
Mass Dimension

The aging rules of rigid polyurethane foam (PUR) at indoor storage and different hygrothermal conditions have been studied. Four parameters, which are mass, dimension, compressive strength and compressive modulus were tested. At indoor storage, mass, dimension and compressive strength vary slowly with an increase in aging time, while compressive modulus decreases quickly. PUR is sensitive to relative humidity (RH) verified by accelerated hygrothermal aging, and hydrolysis of ester group is the main reason resulting in the decrease of compressive properties. The filling with fire retardant and glass beads had some effect on hygrothermal aging properties of PUR. The addition of fire retardant increased compressive strength with aging time in the total trend, but it made dimension stability worse. The addition of glass beads slightly improved hygrothermal aging properties.

scholarly journals Characters and group invariant polynomials of (super)fields: road to “Lagrangian”

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Upalaparna Banerjee ◽  
Joydeep Chakrabortty ◽  
Suraj Prakash ◽  
Shakeel Ur Rahaman
Keyword(s):  
Standard Model ◽  
Explicit Construction ◽  
Effective Field ◽  
Compact Groups ◽  
Group Invariant ◽  
Fundamental Particles ◽  
Quantum Numbers ◽  
The Standard Model ◽  
Mass Dimension ◽  
Complete Set

AbstractThe dynamics of the subatomic fundamental particles, represented by quantum fields, and their interactions are determined uniquely by the assigned transformation properties, i.e., the quantum numbers associated with the underlying symmetry of the model under consideration. These fields constitute a finite number of group invariant operators which are assembled to build a polynomial, known as the Lagrangian of that particular model. The order of the polynomial is determined by the mass dimension. In this paper, we have introduced an automated $${\texttt {Mathematica}}^{\tiny \textregistered }$$ Mathematica ® package, GrIP, that computes the complete set of operators that form a basis at each such order for a model containing any number of fields transforming under connected compact groups. The spacetime symmetry is restricted to the Lorentz group. The first part of the paper is dedicated to formulating the algorithm of GrIP. In this context, the detailed and explicit construction of the characters of different representations corresponding to connected compact groups and respective Haar measures have been discussed in terms of the coordinates of their respective maximal torus. In the second part, we have documented the user manual of GrIP that captures the generic features of the main program and guides to prepare the input file. We have attached a sub-program CHaar to compute characters and Haar measures for $$SU(N), SO(2N), SO(2N+1), Sp(2N)$$ S U ( N ) , S O ( 2 N ) , S O ( 2 N + 1 ) , S p ( 2 N ) . This program works very efficiently to find out the higher mass (non-supersymmetric) and canonical (supersymmetric) dimensional operators relevant to the effective field theory (EFT). We have demonstrated the working principles with two examples: the standard model (SM) and the minimal supersymmetric standard model (MSSM). We have further highlighted important features of GrIP, e.g., identification of effective operators leading to specific rare processes linked with the violation of baryon and lepton numbers, using several beyond standard model (BSM) scenarios. We have also tabulated a complete set of dimension-6 operators for each such model. Some of the operators possess rich flavour structures which are discussed in detail. This work paves the way towards BSM-EFT.

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