Cohen real model

2017 ◽  
pp. 46-56
Author(s):  
Arnold W. Miller
Keyword(s):  
Real Model ◽  
Cohen Real

scholarly journals Orthogonal families of real sequences

1998 ◽  
Vol 63 (1) ◽  
pp. 29-49
Author(s):  
Arnold W. Miller ◽  
Juris Steprans
Keyword(s):  
Hilbert Space ◽  
Inner Product ◽  
Partial Functions ◽  
Perfect Set ◽  
Mad Families ◽  
Real Model ◽  
Cohen Real ◽  
Image Position ◽  
Orthogonal Set ◽  
Orthogonal Sequences

For x, y ϵ ℝω define the inner productwhich may not be finite or even exist. We say that x and y are orthogonal if (x, y) converges and equals 0.Define lp to be the set of all x ϵ ℝω such thatFor Hilbert space, l2, any family of pairwise orthogonal sequences must be countable. For a good introduction to Hilbert space, see Retherford [4].Theorem 1. There exists a pairwise orthogonal family F of size continuum such that F is a subset of lp for every p > 2.It was already known that there exists a family of continuum many pairwise orthogonal elements of ℝω. A family F ⊆ ℝω∖0 of pairwise orthogonal sequences is orthogonally complete or a maximal orthogonal family iff the only element of ℝω orthogonal to every element of F is 0, the constant 0 sequence.It is somewhat surprising that Kunen's perfect set of orthogonal elements is maximal (a fact first asserted by Abian). MAD families, nonprincipal ultrafilters, and many other such maximal objects cannot be even Borel.Theorem 2. There exists a perfect maximal orthogonal family of elements of ℝω.Abian raised the question of what are the possible cardinalities of maximal orthogonal families.Theorem 3. In the Cohen real model there is a maximal orthogonal set in ℝω of cardinality ω1, but there is no maximal orthogonal set of cardinality κ with ω1 < κ < ϲ.By the Cohen real model we mean any model obtained by forcing with finite partial functions from γ to 2, where the ground model satisfies GCH and γω = γ.

Extending Baire property by uncountably many sets

2010 ◽  
Vol 75 (3) ◽  
pp. 896-904
Author(s):  
Paweł Kawa ◽  
Janusz Pawlikowski
Keyword(s):  
Lebesgue Measure ◽  
Baire Property ◽  
Borel Sets ◽  
Real Model ◽  
Cohen Real ◽  
Image Position ◽  
Random Reals ◽  
Meager Sets

AbstractWe show that for an uncountable κ in a suitable Cohen real model for any family {Av}v<κ of sets of reals there is a σ-homomorphism h from the σ-algebra generated by Borel sets and the sets Av, into the algebra of Baire subsets of 2κ modulo meager sets such that for all Borel B,The proof is uniform, works also for random reals and the Lebesgue measure, and in this way generalizes previous results of Carlson and Solovay for the Lebesgue measure and of Kamburelis and Zakrzewski for the Baire property.

scholarly journals Modeling in ADAMS of a 6R industrial robot

2018 ◽  
Vol 184 ◽  
pp. 02006
Author(s):  
Mariana Ratiu ◽  
Alexandru Rus ◽  
Monica Loredana Balas
Keyword(s):  
Dynamic Analysis ◽  
Industrial Robot ◽  
Kinematic Model ◽  
Future Research ◽  
Robot Motion ◽  
Cad Model ◽  
3D Cad ◽  
Revolute Joints ◽  
Real Model ◽  
Articulated Robot

In this paper, we present the first steps in the process of the modeling in ADAMS MBS of MSC software of the mechanical system of an articulated robot, with six revolute joints. The geometric 3D CAD model of the robot, identical to the real model, in the PARASOLID format, is imported into ADAMS/View and then are presented the necessary steps for building the kinematic model of the robot. We conducted this work, in order to help us in our future research, which will consist of kinematic and dynamic analysis and optimization of the robot motion.

Unknown Parameter Excitation and Estimation for Complex Systems With Dynamic Performances

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Yi-Ping Chen ◽  
Kuei-Yuan Chan
Keyword(s):  
Complex Systems ◽  
Simulation Models ◽  
Credible Interval ◽  
Specific Model ◽  
Model Parameters ◽  
Real Model ◽  
Dynamic Case ◽  
Dynamic Performances ◽  
Validation Stage ◽  
Setting Parameters

Abstract Simulation models play crucial roles in efficient product development cycles, therefore many studies aim to improve the confidence of a model during the validation stage. In this research, we proposed a dynamic model validation to provide accurate parameter settings for minimal output errors between simulation models and real model experiments. The optimal operations for setting parameters are developed to maximize the effects by specific model parameters while minimizing interactions. To manage the excessive costs associated with simulations of complex systems, we propose a procedure with three main features: the optimal excitation based on global sensitivity analysis (GSA) is done via metamodel techniques, for estimating parameters with the polynomial chaos-based Kalman filter, and validating the updated model based on hypothesis testing. An illustrative mathematical model was used to demonstrate the detail processes in our proposed method. We also apply our method on a vehicle dynamic case with a composite maneuver for exciting unknown model parameters such as inertial and coefficients of the tire model; the unknown model parameters were successfully estimated within a 95% credible interval. The contributions of this research are also underscored through multiple cases.

scholarly journals THE IMPACT OF THERMAL PERFORMANCE ON THE ROOF SURFACE TO ENERGY EFFICIENT OF HIGH-RISE BUILDING IN THE TROPICAL REGION

Arsitektura ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 129
Author(s):  
Sri Yuliani ◽  
Wiwik Setyaningsih
Keyword(s):  
Thermal Performance ◽  
Energy Efficient ◽  
Heat Load ◽  
Building Envelope ◽  
Tropical Region ◽  
High Rise ◽  
High Rise Building ◽  
Real Model ◽  
Urban Heat ◽  
The Impact

<p class="Abstract"><em>The surface temperature of the building material may release a heat load in the micro-environment. The largest building envelope receives the heat load of solar radiation is the roof. The strategic roof position at the top of the building has the opportunity to radiate heat received into the environment. Heat emissions lead to rising temperatures, so it is necessary to lower the temperature in micro-environment. When the heat of the building is not lowered will lead to an increase in the urban heat island (UHI). The objective of the study was to find the relationship between the thermal performance of the roof of the building and the energy efficiency in the high-rise building, in order to establish efficient thermal comfort. The research method uses experimental way in real model which is in Surakarta City, as humid tropical climate area. The result of the study is a comparison of the heat performance of three roofing materials which would later recommend the criteria of energy efficient roof for high buildings.</em><em></em></p>

Secure Deployment with Optimal Connectivity in Wireless Sensor Networks

2020 ◽  
pp. 147-168
Author(s):  
Anju Sangwan ◽  
Rishipal Singh
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Performance Metrics ◽  
Network Size ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Security Level ◽  
Real Model ◽  
Homogeneous Network ◽  
Basic Issue

In the hostile areas, deployment of the sensor nodes in wireless sensor networks is one of the basic issue to be addressed. The node deployment method has great impact on the performance metrics like connectivity, security and resilience. In this paper, a technique based on strong keying mechanism is proposed which will enhance the security of a non-homogeneous network using the random deployment of the nodes. For this, the q-composite key pre-distribution technique is presented with new flavor that will enhance the network size as well as the security level in comparison to the existing techniques. The technique ensures the k-connectivity among the nodes with a redundant method to provide backup for failed nodes. In the simulation section, the performance of the proposed scheme is evaluated using NS-2 based upon the real model MICAz. A discussion based on various obtained results is also given in the paper.

THE SOLIDITY AND NONSOLIDITY OF INITIAL SEGMENTS OF THE CORE MODEL

2018 ◽  
Vol 83 (3) ◽  
pp. 920-938
Author(s):  
GUNTER FUCHS ◽  
RALF SCHINDLER
Keyword(s):  
Core Model ◽  
Solid Core ◽  
The Core ◽  
Inner Model ◽  
Cohen Real ◽  
Image Position ◽  
Woodin Cardinal

AbstractIt is shown that $K|{\omega _1}$ need not be solid in the sense previously introduced by the authors: it is consistent that there is no inner model with a Woodin cardinal yet there is an inner model W and a Cohen real x over W such that $K|{\omega _1}\,\, \in \,\,W[x] \setminus W$. However, if ${0^{\rm{\P}}}$ does not exist and $\kappa \ge {\omega _2}$ is a cardinal, then $K|\kappa$ is solid. We draw the conclusion that solidity is not forcing absolute in general, and that under the assumption of $\neg {0^{\rm{\P}}}$, the core model is contained in the solid core, previously introduced by the authors.It is also shown, assuming ${0^{\rm{\P}}}$ does not exist, that if there is a forcing that preserves ${\omega _1}$, forces that every real has a sharp, and increases $\delta _2^1$, then ${\omega _1}$ is measurable in K.

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