The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Deterministic Division Algorithm in a Negative Base

Described here is a deterministic division algorithm in a negative-base number system; here, the divisor is mapped into a suitable range by premultiplication, so that the choice of the quotient digit is deterministic.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.

New flame-retardant poly(pyromellitic imide aryl phosphoramide-ester)s

Flame-retardant poly(pyromellitic imide aryl phosphoramide-ester)s were synthesized by interfacial polycondensation of N,N?-bis(p-hydroxyphenyl)pyromellitic diimide with aryl phosphoramidic dichlorides. The polymers were characterized by IR and 1H-NMR spectroscopy. The molecular composition was confirmed by elemental analysis. The thermal stability and flammability of the polymers were studied by thermogravimetry and limiting oxygen index, respectively. Durch Grenzflächen-Polykondensation von N,N?-bis(4-hydroxyphenyl)pyromellitsäurediimid mit Dichloriden verschiedener Phosphoramide wurden flammhemmende Polymere erhalten. Diese wurden mittels IR- und 1H-NMR-Spektroskopie und Elementaranalyse charakterisiert. Thermische Stabilität und Entflammbarkeit wurden thermogravimetrisch bzw. durch Bestimmung des Sauerstoff-Indexes untersucht.

On Training and Training Voids for Receive Antenna Subset Selection in Time-Varying Channels

Antenna selection (AS) provides most of the benefits of multiple-antenna systems at drastically reduced hardware costs. In receive AS, the receiver connects a dynamically selected subset of N available antennas to the L available RF chains. The "best" subset to be used for data reception is determined by means of channel estimates acquired using training sequences. Due to the nature of AS, the channel estimates at different antennas are obtained from different transmissions of the pilot sequence, and are, thus, outdated by different amounts in a time-varying channel. We show that a linear weighting of the estimates is optimum for the subset selection process, where the weights are related to the temporal correlation of the channel variations. When L is not an integer divisor of N, we highlight a new issue of "training voids", in which the last pilot transmission is not fully exploited by the receiver. We present a "void-filling" method for fully exploiting these voids, which essentially provides more accurate training for some antennas, and derive the optimal subset selection rule for any void-filling method. We also derive new closed-form equations for the performance of receive AS with optimal subset selection.

Training and Voids in Receive Antenna Subset Selection in Time-Varying Channels

Receive antenna selection (AS) provides many benefits of multiple-antenna systems at drastically reduced hardware costs. In it, the receiver connects a dynamically selected subset of N available antennas to the L available RF chains. Due to the nature of AS, the channel estimates at different antennas, which are required to determine the best subset for data reception, are obtained from different transmissions of the pilot sequence. Consequently, they are outdated by different amounts in a time-varying channel. We show that a linear weighting of the estimates is necessary and optimum for the subset selection process, where the weights are related to the temporal correlation of the channel variations. When L is not an integer divisor of N , we highlight a new issue of ``training voids'', in which the last pilot transmission is not fully exploited by the receiver. We then present new ``void-filling'' methods that exploit these voids and greatly improve the performance of AS. The optimal subset selection rules with void-filling, in which different antennas turn out to have different numbers of estimates, are also explicitly characterized. Closed-form equations for the symbol error probability with and without void-filling are also developed.