ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES

For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers $j\geq 1$ and $k\geq 0$. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators $\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to obtain other sums.Comment: LaTeX, 8 page

Contact systems and corank one involutive subdistributions

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistributions. We also distinguish regular points, at which the system is equivalent to the canonical contact system, and singular points, at which we propose a new normal form that generalizes the canonical contact system on Jn(R,Rm) in a way analogous to that how Kumpera-Ruiz normal form generalizes the canonical contact system on Jn(R,R), which is also called Goursat normal form.Comment: LaTeX2e, 29 pages, submitted to Acta applicandae mathematica

Back to the future of soil metagenomics

JN was funded by a fellowship from the French MENESR.Peer reviewedPeer Reviewe

We would see Jesus

Historical series, 10. Jn 12:20-33. Preached during Lent, 1997, Hodgeville Lutheran parish

Solvability of eigenvalues in jn configurations

Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the interaction and are rational non-negative num- bers. It is shown here that a state which is an eigenstate of any two-body interaction has this solvability property. This includes, in particular, any state with spin J if there are no other states with this J in the jn configuration. It is also shown that eigenstates with solvable eigenvalues have definite seniority v and thus, exhibit partial dynamical symmetry

Lazarus laughed

Sermon preached on All Saints Sunday at the Mount Zion Lutheran Church, Waterloo, Ontario, 5 N 2006. Jn 11:32-44

Freedom from death\u27s thrall

Sermons, edt E R Riegert. Jn 11:32-44. Preached at St Mark\u27s Lutheran Church, Kitchener, Ont on the Festival of All Saints, 5 N 2006

Social engagement: risk and love

Sermon preached at the KAIROS Prairie Regional Meeting, Alberta, 17 S 2006. 2 Kgs 5:1-15; Jn 13:13:1, 3-5, 12-15

Le prologue du quatrième évangile, clé de voûte de la littérature johannique

Like its last verse (Jn 1.18), the Prologue of the Johannine Gospel has a double meaning: christological and soteriological. The christological one is mainly connected with John 1-20, the soteriological with John 21, and both are linked to 1 John. Indeed, while the Prologue interacts with the Gospel narrative and with the Epilogue (Jn 21), it works also as a ‘relecture' (re-reading) of 1 John. It recapitulates the promise by Jesus to lead the believers ‘where he is'—i.e. ‘in(to) the bosom of the Father' (Jn 1.18//Jn 12.26; 14.2-3, 6; 17.24)—as well as the assertion of the Letter regarding the children of God (Jn 1.12//1 Jn 3.1-2). In adding a Prologue and an Epilogue, the last redactor of Jn created a huge meta-historical arch evoking the whole Divine design, from the Alpha before the Creation (ἐν ἀρχῇ, Jn 1.1-2) to the Omega of the eschatological coming of the Risen One (ἕως ἔρχομαι, Jn 21.22, 23; cf. the παρουσία of 1 Jn 2.28). The Prologue is then the keystone and the reading key of the Johannine literatur