Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

Adaptive playfair cipher Crypto algorithm

A well known cryptographic techniques is Playfair Cryptography, it is considered one of the classical method. After the invention of different techniques, it is easy to break Playfair. This paper proposed some way for removal of the traditional Playfair drawbacks. The Adaptive playfair algorithm proposed in this paper, add more security and complexity to the classical playfair algorithm. In addition to the use of two keys in form of matrices to encrypt the message, the proposed method works depending on using the odd even positions for the every pairs of the letters. The odd pairs encrypt through the first matrix key and the even pairs encrypt by using the second matrix, then applying XOR function with the third key to the result. The resulting cipher text will be in binary form, the plain text obtained by run proposed step backwards.

Tight sets in finite classical polar spaces

We show that every i-tight set in the Hermitian variety H(2r + 1, q) is a union of pairwise disjoint (2r + 1)-dimensional Baer subgeometries $\text{PG}(2r+1,\,\sqrt{q})$ and generators of H(2r + 1, q), if q ≥ 81 is an odd square and i < (q2/3 − 1)/2. We also show that an i-tight set in the symplectic polar space W(2r + 1, q) is a union of pairwise disjoint generators of W(2r + 1, q), pairs of disjoint r-spaces {Δ, Δ⊥}, and (2r + 1)-dimensional Baer subgeometries. For W(2r + 1, q) with r even, pairs of disjoint r-spaces {Δ, Δ⊥} cannot occur. The (2r + 1)-dimensional Baer subgeometries in the i-tight set of W(2r + 1, q) are invariant under the symplectic polarity ⊥ of W(2r + 1, q) or they arise in pairs of disjoint Baer subgeometries corresponding to each other under ⊥. This improves previous results where $i \lt q^{5/8} / \sqrt{2} +1$ was assumed. Generalizing known techniques and using recent results on blocking sets and minihypers, we present an alternative proof of this result and consequently improve the upper bound on i to (q2/3 − 1)/2. We also apply our results on tight sets to improve a known result on maximal partial spreads in W(2r + 1, q).

DNA metabarcoding illuminates dietary niche partitioning by African large herbivores

Niche partitioning facilitates species coexistence in a world of limited resources, thereby enriching biodiversity. For decades, biologists have sought to understand how diverse assemblages of large mammalian herbivores (LMH) partition food resources. Several complementary mechanisms have been identified, including differential consumption of grasses versus nongrasses and spatiotemporal stratification in use of different parts of the same plant. However, the extent to which LMH partition food-plant species is largely unknown because comprehensive species-level identification is prohibitively difficult with traditional methods. We used DNA metabarcoding to quantify diet breadth, composition, and overlap for seven abundant LMH species (six wild, one domestic) in semiarid African savanna. These species ranged from almost-exclusive grazers to almost-exclusive browsers: Grass consumption inferred from mean sequence relative read abundance (RRA) ranged from >99% (plains zebra) to <1% (dik-dik). Grass RRA was highly correlated with isotopic estimates of % grass consumption, indicating that RRA conveys reliable quantitative information about consumption. Dietary overlap was greatest between species that were similar in body size and proportional grass consumption. Nonetheless, diet composition differed between all species—even pairs of grazers matched in size, digestive physiology, and location—and dietary similarity was sometimes greater across grazing and browsing guilds than within them. Such taxonomically fine-grained diet partitioning suggests that coarse trophic categorizations may generate misleading conclusions about competition and coexistence in LMH assemblages, and that LMH diversity may be more tightly linked to plant diversity than is currently recognized.