A Deep Neural Network-Based Interference Mitigation for MIMO-FBMC/OQAM Systems

Offset quadrature amplitude modulation-based filter bank multicarrier (FBMC/OQAM) is among the promising waveforms for future wireless communication systems. This is due to its flexible spectrum usage and high spectral efficiency compared with the conventional multicarrier schemes. However, with OQAM modulation, the FBMC/OQAM signals are not orthogonal in the imaginary field. This causes a significant intrinsic interference, which is an obstacle to apply multiple input multiple output (MIMO) technology with FBMC/OQAM. In this paper, we propose a deep neural network (DNN)-based approach to deal with the imaginary interference, and enable the application of MIMO technique with FBMC/OQAM. We show, by simulations, that the proposed approach provides good performance in terms of bit error rate (BER).

Scaling of the Berry Phase in the Yang-Lee Edge Singularity

We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.

Development of Media Strike Zone for Pitching Learning Process on Softball

Softball games are one form of small ball games learned at school. In the softball game there is strike zone, which is an imaginary field between the elbow and the knee of a batter, and is above the home base. Students find it difficult to find the strike zone so that when throwing pitchers always “ball”. when the game takes place students have difficulty determining between “strike” and “ball”. The need for learning media that can provide a real form of strike zone for students. This research is a development research that uses the stages of development of Borg and Gall. Based on product testing, the target media strike zone is very suitable with the softball game and can effectively provide information about the real shape of the strike zone in the softball game, as well as helping students to set targets and throw accuracy.

Families of Picard modular forms and an application to the Bloch–Kato conjecture

In this article we construct a p-adic three-dimensional eigenvariety for the group $U$(2,1)($E$), where $E$ is a quadratic imaginary field and $p$ is inert in $E$. The eigenvariety parametrizes Hecke eigensystems on the space of overconvergent, locally analytic, cuspidal Picard modular forms of finite slope. The method generalized the one developed in Andreatta, Iovita and Stevens [$p$-adic families of Siegel modular cuspforms Ann. of Math. (2) 181, (2015), 623–697] by interpolating the coherent automorphic sheaves when the ordinary locus is empty. As an application of this construction, we reprove a particular case of the Bloch–Kato conjecture for some Galois characters of $E$, extending the results of Bellaiche and Chenevier to the case of a positive sign.

Foliations on unitary Shimura varieties in positive characteristic

When$p$is inert in the quadratic imaginary field$E$and$m<n$, unitary Shimura varieties of signature$(n,m)$and a hyperspecial level subgroup at$p$, carry a naturalfoliationof height 1 and rank$m^{2}$in the tangent bundle of their special fiber$S$. We study this foliation and show that it acquires singularities at deep Ekedahl–Oort strata, but that these singularities are resolved if we pass to a natural smooth moduli problem$S^{\sharp }$, a successive blow-up of$S$. Over the ($\unicode[STIX]{x1D707}$-)ordinary locus we relate the foliation to Moonen’s generalized Serre–Tate coordinates. We study the quotient of$S^{\sharp }$by the foliation, and identify it as the Zariski closure of the ordinary-étale locus in the special fiber$S_{0}(p)$of a certain Shimura variety with parahoric level structure at$p$. As a result, we get that this ‘horizontal component’ of$S_{0}(p)$, as well as its multiplicative counterpart, are non-singular (formerly they were only known to be normal and Cohen–Macaulay). We study two kinds of integral manifolds of the foliation: unitary Shimura subvarieties of signature$(m,m)$, and a certain Ekedahl–Oort stratum that we denote$S_{\text{fol}}$. We conjecture that these are the only integral submanifolds.

Fine Selmer groups, Heegner points and anticyclotomic ℤp-extensions

Let [Formula: see text] be an elliptic curve, [Formula: see text] a prime and [Formula: see text] the anticyclotomic [Formula: see text]-extension of a quadratic imaginary field [Formula: see text] satisfying the Heegner hypothesis. In this paper, we make a conjecture about the fine Selmer group over [Formula: see text]. We also make a conjecture about the structure of the module of Heegner points in [Formula: see text] where [Formula: see text] is the union of the completions of the fields [Formula: see text] at a prime of [Formula: see text] above [Formula: see text]. We prove that these conjectures are equivalent. When [Formula: see text] has supersingular reduction at [Formula: see text] we also show that these conjectures are equivalent to the conjecture in our earlier work. Assuming these conjectures when [Formula: see text] has supersingular reduction at [Formula: see text], we prove various results about the structure of the Selmer group over [Formula: see text].

Surface abéliennes à multiplication quaternionique munie d'une structure de niveau Γ0(N)

A theorem of Mazur gives the set of possible prime degrees for rational isogenies between elliptic curves. In this paper, we are working on a similar problem in the case of abelian surfaces of [Formula: see text]-type over [Formula: see text] with quaternionic multiplication (over [Formula: see text]) endowed with a [Formula: see text] level structure. We prove the following result: for a fixed indefinite quaternion algebra [Formula: see text] of discriminant [Formula: see text] and a fixed quadratic imaginary field [Formula: see text], there exists an effective bound [Formula: see text] such that for a prime number [Formula: see text], not dividing the conductor of the order [Formula: see text], there do not exist abelian surfaces [Formula: see text] such that [Formula: see text] is a maximal order of [Formula: see text] and [Formula: see text] is endowed with a [Formula: see text] level structure.

Wormhole in 5D Kaluza–Klein cosmology

We present wormhole as a solution of Euclidean field equations as well as the solution of the Wheeler–deWitt (WD) equation satisfying Hawking–Page wormhole boundary conditions in (4 + 1)-dimensional Kaluza–Klein cosmology. The wormholes are considered in the cases of pure gravity, minimally coupled scalar (imaginary) field and with a positive cosmological constant assuming dynamical extra-dimensional space. In above cases, wormholes are allowed both from Euclidean field equations and WD equation. The dimensional reduction is possible.

Selmer Groups and Anticyclotomic Zp-extensions

Let E/Q be an elliptic curve, p a prime and K∞/K the anticyclotomic Zp-extension of a quadratic imaginary field K satisfying the Heegner hypothesis. In this paper we give a new proof to a theorem of Bertolini which determines the value of the Λ-corank of Selp∞(E/K∞) in the case where E has ordinary reduction at p. In the case where E has supersingular reduction at p we make a conjecture about the structure of the module of Heegner points mod p. Assuming this conjecture we give a new proof to a theorem of Ciperiani which determines the value of the Λ-corank of Selp∞(E/K∞) in the case where E has supersingular reduction at p.