AbstructWe develop a procedure for the order selection of damped sinusoidal models based on the maximum U posterion’ (MAP) criterion. The proposed method merges the concept of predictive densities with Bayesian inference to arrive at a complex multidimensional integral whose solution is achieved by way of the efficient Monte Carlo importance sampling technique. The importance function, a multiv...

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from R into S.

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from R into S.

We study the Cauchy problem for the dissipative Benjamin-Ono equations ut +Huxx + |D| αu+ uux = 0 with 0 ≤ α ≤ 2. When 0 ≤ α < 1, we show the ill-posedness in Hs(R), s ∈ R, in the sense that the flow map u0 7→ u (if it exists) fails to be C 2 at the origin. For 1 < α ≤ 2, we prove the global well-posedness in Hs(R), s > −α/4. It turns out that this index is optimal.

Soft-Output Viterbi Algorithm (SOVA) is one type of recovery memory-less Markov Chain and is used widely to decode convolutional codes. Fundamentally, conventional SOVA is designed on the basis of Maximum A-Posteriori Probability (APP) with the assumption of normal distribution. Therefore, conventional SOVA fails miserably in the presence of symmetric alpha stable noise S S α which is one form ...

Applying (enriched) categorical structures we define the notion of ordered sheaf on a quantaloid Q, which we call ‘Q-order’. This requires a theory of semicategories enriched in the quantaloid Q, that admit a suitable Cauchy completion. There is a quantaloid Idl(Q) of Q-orders and ideal relations, and a locally ordered category Ord(Q) of Q-orders and monotone maps; actually, Ord(Q) = Map(Idl(Q)...

We prove existence of a countable family of spherically symmetric self-similar wave maps from the Minkowski spacetime into the 3-sphere. These maps can be viewed as excitations of the ground state wave map found previously by Shatah. The first excitation is particularly interesting in the context of the Cauchy problem since it plays the role of a critical solution sitting at the threshold of si...

This paper presents the regularity of a split-quaternionic function and corresponding split- Cauchy-Riemann system split quaternion. The properties an inverse implicit mapping theory for map are investigated. In addition, proposes definition expression biregular in open set C2. obtained results illustrated with some examples.

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

Let lK be a commutative field and (P, +) be a uniquely 2-divisible group (not necessarily abelian). We characterize all functions T: IK -+ P such that the Cauchy difference T(s+ t) T(t) T(s) depends only on the product st for all s, t E ~{. Further, we apply this result to describe solutions of the functional equation F(s + t) = K(st) 0 H(s) 0 G(t), where the unknown functions F, K, H, G map th...