Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination

We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case that the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison to the minimum failure probability.Comment: Replaced by final version, accepted for publication in Phys. Rev. A. Revtex4, 6 pages, 3 figure

Development and fabrication of bismaleimide-graphite composites

The successful fabrication of high temperature resistant composites depends mainly on the processability of the resin binder matrix. For two new bismaleimide type resins the processing of graphite fabric prepregs to composites is described. One resin coded M 751 has to be processed from N-Methylpyrrolidone, the other resin evaluated is a so-called hot melt solvent-less system. Commercial T300/3000 Graphite fabrics were used as reinforcement. The M 751 - Resin is a press grade material and laminates are therefore moulded in high pressure conditions (400 N/sq cm). The solvent-less resin system H 795 is an autoclave grade material and can be cured at 40 N/sq cm. The cure cycles for both the press grade and the autoclave grade material (Fiberite W 143 fabric prepregs) are provided and the mechanical properties of laminates at low (23 C) and high (232 C) temperatures were measured. For comparison, the neat resin flexural properties are also presented. The water absorption for the neat resins and the graphite fabric laminates after a 1000 hour period was evaluated

Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the detection operators associated with the two different conclusive outcomes does not exceed unity we obtain a general solution. As an application, we consider the discrimination of two mixed qubit states. Moreover, for the case of higher-rank detection operators we give a solution for particular states. The relation of the optimized measurement to other discrimination schemes is also discussed.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.

Optimum unambiguous discrimination of two mixed states and application to a class of similar states

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two conditions for the optimum measurement operators, and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by $\rho_2= U\rho_1 U^{\dag}$, and that belong to the class where the unitary operator U can be decomposed into multiple rotations in the d mutually orthogonal two-dimensional subspaces determined by the canonical representation.Comment: 8 pages, changes in title and presentatio

Four generated, squarefree, monomial ideals

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.Comment: to appear in "Bridging Algebra, Geometry, and Topology", Editors Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96, 201

Rapid Serial Sarcomere Loss Caused by Electrical Stimulation in Rabbit Triceps Surae Muscles

Muscle spasms, such as those observed in cerebral palsy patients, are involuntary muscle contractions that usually occur due to a lesion in the brain. These muscle spasms cause muscles to become hypoextensible, or very stiff. This hypoextensibility may be explained by a decrease in serial sarcomere number concomitant with a long stimulation period. In 1981, Tabary and Tardieu showed a 25% decrease in the number of serial sarcomeres in guinea pig Soleus muscles over a 12 hour stimulation period. As these results seem very extreme, it was necessary to try duplicating these results in our laboratory, as well as in a different animal model. The Medial Gastrocnemius, Plantaris, and Soleus muscles were stimulated via the tibial nerve in New Zealand White rabbits (n=3) for 10 hours in one of the legs (20 Hz at 3 times the α motoneuron threshold). The tibial nerve in the contralateral control leg was transected to ensure no cross- over training effects. After the stimulation period, the animals were sacrificed and the hind limbs were then placed in a 10% formalin solution at carefully controlled knee and ankle angles. Three to five samples were harvested from each muscle. After a digestion process, individual fascicles were teased out and mounted on prepared slides. These slides were then analyzed for fascicle length by using a camera system with specialized software and sarcomere lengths were determined using a laser diffraction method. Analysis showed that the serial sarcomere number decreased in the Medial Gastrocnemius by 23 ± 4.4%, in the Plantaris by 25 ± 2.9%, and the Soleus by 29 ± 7.0%. These numbers concur closely with the 25% loss of serial sarcomeres reported by Tabary and Tardieu in guinea pigs. These confirmed results will allow for more research to be done in this area

Programmable quantum state discriminators with simple programs

We describe a class of programmable devices that can discriminate between two quantum states. We consider two cases. In the first, both states are unknown. One copy of each of the unknown states is provided as input, or program, for the two program registers, and the data state, which is guaranteed to be prepared in one of the program states, is fed into the data register of the device. This device will then tell us, in an optimal way, which of the templates stored in the program registers the data state matches. In the second case, we know one of the states while the other is unknown. One copy of the unknown state is fed into the single program register, and the data state which is guaranteed to be prepared in either the program state or the known state, is fed into the data register. The device will then tell us, again optimally, whether the data state matches the template or is the known state. We determine two types of optimal devices. The first performs discrimination with minimum error, the second performs optimal unambiguous discrimination. In all cases we first treat the simpler problem of only one copy of the data state and then generalize the treatment to n copies. In comparison to other works we find that providing n > 1 copies of the data state yields higher success probabilities than providing n > 1 copies of the program states.Comment: 17 pages, 5 figure

Study of Giant Pairing Vibrations with neutron-rich nuclei

We investigate the possible signature of the presence of giant pairing states at excitation energy of about 10 MeV via two-particle transfer reactions induced by neutron-rich weakly-bound projectiles. Performing particle-particle RPA calculations on $^{208}$Pb and BCS+RPA calculations on $^{116}$Sn, we obtain the pairing strength distribution for two particles addition and removal modes. Estimates of two-particle transfer cross sections can be obtained in the framework of the 'macroscopic model'. The weak-binding nature of the projectile kinematically favours transitions to high-lying states. In the case of (~^6He, \~^4He) reaction we predict a population of the Giant Pairing Vibration with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.Comment: Talk presented in occasion of the VII School-Semina r on Heavy Ion Physics hosted by the Flerov Laboratory (FLNR/JINR) Dubna, Russia from May 27 to June 2, 200

Optimum measurement for unambiguously discriminating two mixed states: General considerations and special cases

Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A 71, 050301(R) (2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. Unambiguous discrimination of nonorthogonal states is possible in a probabilistic way, at the expense of a nonzero probability of inconclusive results, where the measurement fails. Along with a discussion of the general problem, we give an example illustrating our method of solution. We also provide general inequalities for the minimum achievable failure probability and discuss in more detail the necessary conditions that must be fulfilled when its absolute lower bound, proportional to the fidelity of the states, can be reached.Comment: Submitted to Journal of Physics:Conference Series (Proceedings of the 12th Central European Workshop on Quantum Optics, Ankara, June 2005