In this paper the authors give an efficient bounded distance decoding (BDD for short) algorithm for NTRU lattices under some conditions about the modulus number q and the public key h. They then use this algorithm to give plain-text recovery attack to NTRU Encrypt and forgery attack on NTRU Sign. In particular the authors figure out a weak domain of public keys such that the recent transcript secure version of NTRU signature scheme NTRUMLS with public keys in this domain can be forged.

The notion of normal elements for finite fields extension was generalized as k-normal elements by Huczynska et al. (2013). Several methods to construct k-normal elements were presented by Alizadah et al. (2016) and Huczynska et al. (2013), and the criteria on k-normal elements were given by Alizadah et al. (2016) and Antonio et al. (2018). In the paper by Huczynska, S., Mullen, G., Panario, D. and Thomson, D. (2013), the number of k-normal elements for a fixed finite field extension was calculated and estimated. In this paper the authors present a new criterion on k-normal elements by using idempotents and show some examples. Such criterion was given for usual normal elements before by Zhang et al. (2015).

A hypersurface x(M) in Lorentzian space R ₁ ⁴ is called conformal homogeneous, if for any two points p, q on M, there exists σ, a conformal transformation of R ₁ ⁴, such that σ(x(M)) = x(M), σ(x(p)) = x(q). In this paper, the authors give a complete classification for regular time-like conformal homogeneous hypersurfaces in R ₁ ⁴ with three distinct principal curvatures.

In this paper, the author constructs ghost symmetries of the extended Toda hierarchy with their spectral representations. After this, two kinds of Darboux transformations in different directions and their mixed Darboux transformations of this hierarchy are constructed. These symmetries and Darboux transformations might be useful in Gromov-Witten theory of ℂP ¹.

In this paper, the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere. As a consequence, many non-trivial examples of (semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.

The authors consider non-autonomous N-body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity. Using Ljusternik-Schnirelmann theory, the authors prove the existence of unbounded sequences of critical values for the Lagrangian action corresponding to non-collision periodic solutions.

Comparing to the construction of stringy cohomology ring of equivariant stable almost complex manifolds and its relation with the Chen-Ruan cohomology ring of the quotient almost complex orbifolds, the authors construct in this note a Chen-Ruan cohomology ring for a stable almost complex orbifold. The authors show that for a finite group G and a G-equivariant stable almost complex manifold X, the G-invariant part of the stringy cohomology ring of (X, G) is isomorphic to the Chen-Ruan cohomology ring of the global quotient stable almost complex orbifold [X/G]. Similar result holds when G is a torus and the action is locally free. Moreover, for a compact presentable stable almost complex orbifold, they study the stringy orbifold K-theory and its relation with Chen-Ruan cohomology ring.

Let R → S be a ring homomorphism and X be a complex of R-modules. Then the complex of S-modules S ⊗ _R ^L X in the derived category D(S) is constructed in the natural way. This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X (possibly unbounded) with those of the S-complex S ⊗ _R ^L X. It is shown that if R is a Noetherian ring of finite Krull dimension and ϕ: R → S is a faithfully flat ring homomorphism, then for any homologically degree-wise finite complex X, there is an equality Gpd _R X = Gpd _S(S ⊗ _R ^L X). Similar result is obtained for Ding projective dimension of the S-complex S ⊗ _R ^L X.

The aim of the paper is to deal with the algebraic dependence and uniqueness problem for meromorphic mappings by using the new second main theorem with different weights involved the truncated counting functions, and some interesting uniqueness results are obtained under more general and weak conditions where the moving hyperplanes in general position are partly shared by mappings from ℂ ⁿ into ℙ ^N (ℂ), which can be seen as the improvements of previous well-known results.

The author investigates the nonlinear parabolic variational inequality derived from the mixed stochastic control problem on finite horizon. Supposing that some sufficiently smooth conditions hold, by the dynamic programming principle, the author builds the Hamilton-Jacobi-Bellman (HJB for short) variational inequality for the value function. The author also proves that the value function is the unique viscosity solution of the HJB variational inequality and gives an application to the quasi-variational inequality.