Two-loop superstring five-point amplitudes. Part III. Construction via the RNS formulation: even spin structures

The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers [29] and [33].

Constant cycle and co-isotropic subvarieties in a Mukai system

Combining theorems of Voisin and Marian, Shen, Yin and Zhao, we compute the dimensions of the orbits under rational equivalence in the Mukai system of rank two and genus two. We produce several examples of algebraically coisotropic and constant cycle subvarieties.

studu species of mosquitoes in c study classification of mosquitoes

The current study included the collection and classification of mosquitoes and the identification of some species because of their medical and veterinary importance in terms of their harmful effect on health and their transmission of diseases. Three species of mosquitoes were diagnosed in the different study sites, namely Anopheles, Culex and Aedes, where five types of Anopheles and four types of Culex were recorded. As for the third genus, two types of it were recorded, and the proportions of the types collected from the study sites varied among themselves, as the percentages varied according to the day and night and the different seasons of the year, and the temperature had a role in this disparity of adults mosquitoes .

Non-negativity of BMN two-point functions with three string modes

Recently, we proposed a novel entry of the pp-wave holographic dictionary, which equated the Berenstein-Maldacena-Nastase (BMN) two-point functions in free $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory with the norm squares of the quantum unitary transition amplitudes between the corresponding tensionless strings in the infinite curvature limit, for the cases with no more than three string modes in different transverse directions. A seemingly highly non-trivial conjectural consequence, particularly in the case of three string modes, is the non-negativity of the BMN two-point functions at any higher genus for any mode numbers. In this paper, we further perform the detailed calculations of the BMN two-point functions with three string modes at genus two, and explicitly verify that they are always non-negative through mostly extensive numerical tests.

Classification of periodic transformations of an orientable surface of genus two

In this paper, we find all admissible topological conjugacy classes of periodic transformations of a two-dimensional surface of genus two. It is proved that there are exactly seventeen pairwise topologically non-conjugate orientation-preserving periodic pretzel transformations. The implementation of all classes by lifting the full characteristics of mappings from a modular surface to a surface of genus two is also presented. The classification results are based on Nielsen’s theory of periodic surface transformations, according to which the topological conjugacy class of any such homeomorphism is completely determined by its characteristic. The complete characteristic carries information about the genus of the modular surface, the ramified bearing surface, the periods of the ramification points and the turns around them. The necessary and sufficient conditions for the admissibility of the complete characteristic are described by Nielsen and for any surface they give a finite number of admissible collections. For surfaces of a small genus, one can compile a complete list of admissible characteristics, which was done by the authors of the work for a surface of genus 2.

Another new exotic bark beetle in Florida: Ernoporus parvulus (Eggers, 1943) (Coleoptera: Curculionidae: Scolytinae), with additional taxonomic changes

The bark beetle, Ernoporus parvulus (Eggers, 1943) was collected from Pinellas County, Florida, USA representing the first North American record of the genus. Two species previously described from the Caribbean were examined and are synonymous: Ernoporus minutus (Bright & Torres, 2006) syn. nov. and E. exquisitus (Bright, 2019) syn. nov. This beetle is likely an overlooked exotic from Africa, known only from sea hibiscus, Talipariti tiliaceum (L.) Fryxell (Malvaceae). There is no evidence that this is a threat to commercial or ornamental Hibiscus and related species.