We consider the Schrödinger operator −∆ − V (x) on R, but with the difference from the usual case that V is a Hermitian matrix-valued potential. In other words, the Hilbert space is not L(R) but L(R;C). The values of functions in this space, ψ(x), are N−dimensional vectors. (What we say here easily generalizes to ‘operatorvalued’ potentials, i.e., C is replaced by a Hilbert space such as L(R), ...

A standard rule of thumb about whether a quantum Hamiltonian H = -A + V(x) has purely discrete spectrum or some continuous spectrum is the following. Look at the volume {(p, q) Ip* + V(q) <E} in R*“. If this volume is finite for all E, the standard wisdom is that H has only discrete spectrum. This standard wisdom also says that if this volume is infinite for some E < oo, then the spectrum is no...

"!$# !%#& '( )+* # -, /. 0 12 ) 3546 ",27 '( 8* & 79 / '( 0 & #: #;'(#2, ? 0 & 19 # @* #: , @ !%# 'A B #: C -, 0 1D &E; E8'( '(# 7F 3G H 0 2 G < + # -, # 9 #:'( E >I #? JK + < 9 & + JK 0 E JK 7F !$ E & 0 & . / LM < ; #& 1 ; N < D #:)& 0 '( N M < D D 7O #:)& 0 '('( ) E & ): ) :> ,P < 9 ? 9 #F #:'( E 9 #& ?>5 #F #2, Q . #:'( E & # I> #R #: S #2, :> & -,6 #R T &E; ? & '( 2...

In this paper we develop a framework for computing upper and lower bounds of an exponential form for a class of single server queueing systems with non-renewal inputs. These bounds generalize Kingman's bounds for queues with renewal inputs.

E. Mossel and J. Neeman recently provided a heat flow monotonicity proof of Borell’s noise stability theorem. In this note, we develop the argument to include in a common framework noise stability, Brascamp-Lieb inequalities (including hypercontractivity), and even a weak form of Slepian inequalities. The scheme applies furthermore to families of measures with are more log-concave than the Gaus...

In the context of the ring Q[x,y], of polynomials in 2n variables x = x1, . . . , xn and y = y1, . . . , yn, we introduce the notion of diagonally quasisymmetric polynomials. These, also called diagonal Temperley-Lieb invariants, make possible the further introduction of the space of diagonal Temperley-Lieb harmonics and diagonal Temperley-Lieb coinvariant space. We present new results and conj...

We generalize the theorems of Stein–Tomas and Strichartz about surface restrictions of Fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions. We deduce the corresponding Strichartz bounds for solutions to Schrödinger equations up to the endpoint, thereby solving an open problem of Frank, Lewin, Lieb and Seiringer. We also prove uniform Sobo...

Abstract Research background Every country attempts to improve its balance of payments (BOP) position enhance macroeconomic policy. Algeria, like many developing countries, is experiencing a BOP deficit. This raises concerns about the reasons for this deficit and prioritizes quest potential answers. Purpose In context Monetary Approach (MABP), paper investigates long-run relationship between do...