Affine maps of state spaces and state spaces of K 0 groups

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Xiaosheng Zhu
Keyword(s):  
Abelian Group ◽  
State Space ◽  
Quotient Ring ◽  
The State ◽  
Noetherian Rings ◽  
Group Rings ◽  
State Spaces ◽  
Affine Map ◽  
Finite Algebras ◽  
Partially Ordered

AbstractLet φ be a homomorphism from the partially ordered abelian group (S, v) to the partially ordered abelian group (G, u) with φ(v) = u, where v and u are order units of S and G respectively. Then φ induces an affine map φ* from the state space St(G, u) to the state space St(S, v). Firstly, in this paper, we give some suitable conditions under which φ* is injective, surjective or bijective. Let R be a semilocal ring with the Jacobson radical J(R) and let π: R → R/J(R) be a canonical map. We discuss the affine map (K 0 π)*. Secondly, for a semiprime right Goldie ring R with the maximal right quotient ring Q, we consider the relations between St(R) and St(Q). Some results from [ALFARO, R.: State spaces, finite algebras, and skew group rings, J. Algebra 139 (1991), 134–154] and [GOODEARL, K. R.-WARFIELD, R. B., Jr.: State spaces of K 0 of noetherian rings, J. Algebra 71 (1981), 322–378] are extended.

Bounds for the Reliability of Multistate Systems with Partially Ordered State Spaces and Stochastically Monotone Markov Transitions

2003 ◽  
Vol 10 (03) ◽  
pp. 235-248
Author(s):  
Bo Henry Lindqvist
Keyword(s):  
Markov Chain ◽  
System Performance ◽  
Failure Time ◽  
The State ◽  
Upper And Lower Bounds ◽  
State Spaces ◽  
Partially Ordered ◽  
Perfect System ◽  
Multistate System ◽  
Ordered State

Consider a multistate system with partially ordered state space E, which is divided into a set C of working states and a set D of failure states. Let X(t) be the state of the system at time t and suppose {X(t)} is a stochastically monotone Markov chain on E. Let T be the failure time, i.e., the hitting time of the set D. We derive upper and lower bounds for the reliability of the system, defined as Pm(T > t) where m is the state of perfect system performance.

On the Construction of Relativistic Representation Spaces in Functional Quantum Theory of the Nonlinear Spinor Field

1975 ◽  
Vol 30 (11) ◽  
pp. 1361-1371 ◽  
Author(s):  
H. Stumpf ◽  
K. Scheerer
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Functional State ◽  
Spinor Field ◽  
Function Spaces ◽  
The State ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
State Spaces ◽  
Representation Spaces

Functional quantum theory is defined by an isomorphism of the state space H of a conventional quantum theory into an appropriate functional state space D It is a constructive approach to quantum theory in those cases where the state spaces H of physical eigenstates cannot be calculated explicitly like in nonlinear spinor field quantum theory. For the foundation of functional quantum theory appropriate functional state spaces have to be constructed which have to be representation spaces of the corresponding invariance groups. In this paper, this problem is treated for the spinor field. Using anticommuting source operator, it is shown that the construction problem of these spaces is tightly connected with the construction of appropriate relativistic function spaces. This is discussed in detail and explicit representations of the function spaces are given. Imposing no artificial restrictions it follows that the resulting functional spaces are indefinite. Physically the indefiniteness results from the inclusion of tachyon states. It is reasonable to assume a tight connection of these tachyon states with the ghost states introduced by Heisenberg for the regularization of the nonrenormalizable spinor theory

scholarly journals Modular State Space Analysis of Coloured Petri Nets

1997 ◽  
Vol 26 (524) ◽  
Author(s):  
Søren Christensen ◽  
Laure Petrucci
Keyword(s):  
Petri Nets ◽  
State Space ◽  
The State ◽  
Total System ◽  
Entire System ◽  
State Spaces ◽  
Space Analysis ◽  
State Space Analysis ◽  
Full State ◽  
Local Properties

<p>State Space Analysis is one of the most developed analysis methods for Petri Nets. The main problem of state space analysis is the size of the state spaces. Several ways to reduce it have been proposed but cannot yet handle industrial size systems.</p><p>Large models often consist of a set of modules. Local properties of each module can be checked separately, before checking the validity of the entire system. We want to avoid the construction of a single state space of the entire system.</p><p>When considering transition sharing, the behaviour of the total system can be capture by the state spaces of modules combined with a Synchronisation Graph. To verify that we do not lose information we show how the full state space can be conctructed.</p><p>We show how it is possible to determine usual Petri Nets properites, without unfolding to the ordinary state space.</p>

scholarly journals Graph Inclusion and Matching Algorithms for Programs Manipulating Singly linked Heaps

2021 ◽  
Vol 9 (1) ◽  
pp. 30-37
Author(s):  
Muhsin H. Atto
Keyword(s):  
State Space ◽  
Data Structures ◽  
Graph Matching ◽  
The State ◽  
Memory Cells ◽  
Dynamic Data Structures ◽  
Dynamic Data ◽  
State Spaces ◽  
As Graph

Programs that manipulate heaps  such  as  singlylinked  lists,  doublylinked  lists,  skiplists,  and  treesare  ubiquitous,  and  hence ensuring their correctness is of utmost importance. Analysing correctness properties for such programs is not trivial since they induce dynamic data structures, leading to unbounded state spaces with intricate patterns. One approach that has been adopted to tackle this problem  is  the  use  of  symbolic  searching  techniques.  The  state  space  is  encoded  using  graphs  where  the  nodes represent memory cells, and the edges represent pointers between the cells. It is necessary to prune the search to avoid generating massive numbers of graphs, thus making the procedure unpractical. Pruning strategies are defined based on operations such as graph matching and inclusion. In this paper, a set of algorithms for performing these operations are presented. It is demonstrated that the proposed algorithms can handle typical graphs that arise in the verification of heap manipulating programs.

scholarly journals Distances between convex subsets of state spaces

1985 ◽  
Vol 32 (1) ◽  
pp. 109-117
Author(s):  
A.J. Ellis
Keyword(s):  
State Space ◽  
Hausdorff Space ◽  
Compact Convex ◽  
The State ◽  
Facial Structure ◽  
State Spaces ◽  
New Criteria ◽  
Uniformly Closed ◽  
Geometric Nature ◽  
Convex Subsets

Let L be a closed linear space of continuous real-valued functions, containing constants, on a compact Hausdorff space Ω. This paper gives some new criteria for a closed subset E of Ω to be an L-interpolation set, or more generally for L|E to be uniformly closed or simplicial, in terms of distances between certain compact convex subsets of the state space of L. These criteria involve the facial structure of the state space and hence are of a geometric nature. The results sharpen some standard results of Glicksberg.

scholarly journals Partitioning Techniques in LTLf Synthesis

2019 ◽  
Author(s):  
Lucas Martinelli Tabajara ◽  
Moshe Y. Vardi
Keyword(s):  
Model Checking ◽  
State Space ◽  
Reactive Systems ◽  
Computational Thinking ◽  
Standard Technique ◽  
The State ◽  
Problem Instance ◽  
State Spaces ◽  
Fundamental Limitations ◽  
Depth Analysis

Decomposition is a general principle in computational thinking, aiming at decomposing a problem instance into easier subproblems. Indeed, decomposing a transition system into a partitioned transition relation was critical to scaling BDD-based model checking to large state spaces. Since then, it has become a standard technique for dealing with related problems, such as Boolean synthesis. More recently, partitioning has begun to be explored in the synthesis of reactive systems. LTLf synthesis, a finite-horizon version of reactive synthesis with applications in areas such as robotics, seems like a promising candidate for partitioning techniques. After all, the state of the art is based on a BDD-based symbolic algorithm similar to those from model checking, and partitioning could be a potential solution to the current bottleneck of this approach, which is the construction of the state space. In this work, however, we expose fundamental limitations of partitioning that hinder its effective application to symbolic LTLf synthesis. We not only provide evidence for this fact through an extensive experimental evaluation, but also perform an in-depth analysis to identify the reason for these results. We trace the issue to an overall increase in the size of the explored state space, caused by an inability of partitioning to fully exploit state-space minimization, which has a crucial effect on performance. We conclude that more specialized decomposition techniques are needed for LTLf synthesis which take into account the effects of minimization.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

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