A Recursive Definition of the Holographic Standard Signature

We provide a recursive description of the signatures realizable on the standard basis by a holographic algorithm. The description allows us to prove tight bounds on the size of planar matchgates and efficiently test for standard signatures. Over finite fields, it allows us to count the number of n-bit standard signatures and calculate their expected sparsity.Comment: Fixed small typo in Section 3.

Scientific publications and presentations relating to planetary quarantine. Volume 5: The 1975 supplement

Documents pertaining to planetary quarantine are listed. An author index is given along with a listing of books and journals containing related material

Scientific publications and presentations relating to planetary quarantine. Volume 5 - The 1970 supplement

Bibliography of scientific publications and presentations relating to planetary quarantine for year 1970 - Vol.

Conformational Control of Exciton-Polariton Physics in Metal - Poly(9,9-dioctylfluorene) - Metal Cavities

Control is exerted over the exciton-polariton physics in metal - Poly(9,9-dioctyl fluorene) - metal microcavities via conformational changes to the polymer backbone. Using thin-film samples containing increasing fractions of $\beta$-phase chain segments, a systematic study is reported for the mode characteristics and resulting light emission properties of cavities containing two distinct exciton sub-populations within the same semiconductor. Ultrastrong coupling for disordered glassy-phase excitons is observed from angle-resolved reflectivity measurements, with Rabi splitting energies in excess of 1.05 eV (more than 30% of the exciton transition energy) for both TE- and TM-polarized light. A splitting of the lower polariton branch is then induced via introduction of $\beta$-phase excitons and increases with their growing fraction. In all cases, the photoluminescence emanates from the lowermost polariton branch, allowing conformational control to be exerted over the emission energy and its angular variation. Dispersion-free cavities with highly saturated blue-violet emission are thus enabled. Experimental results are discussed in terms of the full Hopfield Hamiltonian generalized to the case of two exciton oscillators. The importance of taking account of the molecular characteristics of the semiconductor for an accurate description of its strong coupling behaviour is directly considered, in specific relation to the role of the vibronic structure

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Theoretical investigation of the magnetic structure in YBa_2Cu_3O_6

As experimentally well established, YBa_2Cu_3O_6 is an antiferromagnet with the magnetic moments lying on the Cu sites. Starting from this experimental result and the assumption, that nearest-neighbor Cu atoms within a layer have exactly antiparallel magnetic moments, the orientation of the magnetic moments has been determined within a nonadiabatic extension of the Heisenberg model of magnetism, called nonadiabatic Heisenberg model. Within this group-theoretical model there exist four stable magnetic structures in YBa_2Cu_3O_6, two of them are obviously identical with the high- and low-temperature structure established experimentally. However, not all the magnetic moments which appear to be antiparallel in neutron-scattering experiments are exactly antiparallel within this group-theoretical model. Furthermore, within this model the magnetic moments are not exactly perpendicular to the orthorhombic c axis

Tensile deformation damage in SiC reinforced Ti-15V-3Cr-3Al-3Sn

The damage mechanisms of a laminated, continuous SiC fiber reinforced Ti-15V-3Cr-3Al-3Sn (Ti-15-3) composite were investigated. Specimens consisting of unidirectional as well as cross-ply laminates were pulled in tension to failure at room temperature and 427 C and subsequently examined metallographically. Selected specimens were interrupted at various strain increments and examined to document the development of damage. When possible, a micromechanical stress analysis was performed to aid in the explanation of the observed damage. The analyses provide average constituent microstresses and laminate stresses and strains. It was found that the damage states were dependent upon the fiber architecture