1.1 Research Statement and Scope The main goal of this research is to prove that the efficiency and cost of symbolic execution of evolving state machines can be measurably improved using incremental analysis. Since we aim to use IBM Rhapsody Statecharts as the input state-based models to build ...
is globally attractive. so in order to prove theorem 6.3 , we only need to show that it is asymptotically stable. to do this, by using lemma a.1 we denote \(bx(t)-px(t)y(t)\doteq p(x,y)\) and \(\frac{cx(t)y(t)}{1+\omega x(t)}-qx(t)y(t)-\delta y(t)...
Arbitrary quantum states cannot be copied, a property known as the no-cloning theorem. It is essential to the security of quantum cryptography but also prevents signal amplification to bridge long distances. To overcome this problem, quantum repeaters have been proposed (Briegel et al., 1998; ...
Thirdly, most DL models use the recurrent DL architecture which may prove to work well with sequence data such as the SOC but are hard and slow to train41. Recurrent models also do not leverage on the parallel GPU computation that could significantly improve training time25. Lastly, even ...
This study established a general steady-state solution in the z-convex domain (the domain boundary must have at most two points of intersection with any straight line parallel to the z -axis) for thermo-poroelastic materials. Two displacement functions to simplify the equations governing elasticity...
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Theorem 1 The equilibrium of the LPV system in (10) is globally asymptotically stable if there exists a common positive-definite matrix P such that(12)Ai⊤P+PAi≺0,i∈IN. Note that condition (12) is represented in the form of linear matrix inequalities (LMIs). Hence, the stability an...
B Proofs of Theorems 1 and 2 In this section we will prove Theorem 1 and Theorem 2 in details, using the notion of dual regions, as in Fig. 7, to test if there exists a crossing map between two strata, see Defini- tion 1. For any crossing map H , the configurations H (0) and...
Theorem 2.1 Let P:K→Sn+ and vd:K→R, 1≤d≤n, be C1-functions and let λ1(x)≥…≥λn(x) denote the solutions of the algebraic equation(2)det[Df(x)⊤P(x)+P(x)Df(x)+P˙(x)−λP(x)]=0. Let Λd≥0, 1≤d≤n, be constants so that(3)∑i=1dλi(x)+v˙...
Finally, when a proposition evaluates to true or false, it can prove or disprove other propositions or instantiations according to Table 1 (not included in the example figure). We refer to such a network as a Spatial Pattern Network (SPatterNet). We use a representation based on bit arrays...