Abstract: Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2, and let n > 2 be a fixed even integer. Consider a sequence {Fk}k>1 of square integrable random variables, belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k → ∞, we prove that Fk converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k )− 12E(F 3 k ) → 12ν...

Th is project gives the study of the principles of Adaptive Noise Cancellation (ANC) and its Applications. Adaptive noise Cancellat ion is an alternative technique of estimat ing signals corrupted by additive noise or interference. In signal processing methods of removing noise, levels of noise rejection are not attainable without prior knowledge about speech signal and noise. But in this metho...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

6. Spectral Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random vectors . . . . . . . . . . ....

Let [W(s, t): (s, t) E R+7, R+2 = [0, co) x [0, co), be the standard twoparameter Wiener process defined on a complete probability space (Q, F, P), i.e., a Gaussian stochastic process with EW(s, t) = 0 and EW(s, t) W(s’, t’) = Min(s, s’) Min(t, t’). We shall also assume, as we may do without restricting the generality, that W(s, t; UJ) is sample path continuous, i.e., for each w, W(.; U) is a c...

In this paper, stochastic Volterra equations driven by cylindrical and genuine Wiener process in Hilbert space are investigated. Sufficient conditions for existence of strong solutions are given. The key role is played by convergence of α-times resolvent families.

motivated by the terminal wiener index‎, ‎we define the ashwini index $mathcal{a}$ of trees as‎ begin{eqnarray*}‎ % ‎nonumber to remove numbering (before each equation)‎ ‎mathcal{a}(t) &=& sumlimits_{1leq i‎&+& deg_{_{t}}(n(v_{j}))],‎ ‎end{eqnarray*}‎ ‎where $d_{t}(v_{i}‎, ‎v_{j})$ is the distance between the vertices $v_{i}‎, ‎v_{j} in v(t)$‎, ‎is equal to the length of the shortest path start...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

In this paper novel compression techniques are developed for portable heart-monitoring equipment that could also form the basis for more intelligent diagnostic systems thanks to the way the compression algorithms depend on signal classification. There are two main categories of compression which are employed for electrocardiogram signals: lossless and lossy. Design of an optimal Wiener filter i...

We analyze a modified version of the Coleman-Hepp model, that is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-1/2 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such a limit and in a restricted portion of the total Hilbert space, the particle u...