Call a periodic map h on the closed orientable surface Σ _g extendable if h extends to a periodic map over the pair (S ³,Σ _g) for possible embeddings e: Σ _g → S ³. The authors determine the extendabilities for all periodical maps on Σ₂. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair (S ³,Σ _g). To do this the authors first list all periodic maps on Σ₂, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g, the maximum order periodic map on Σ _g is extendable, which contrasts sharply with the situation in the orientation preserving category.

This paper deals with the s-reflexive spaces introduced by Yang and Zhao. The authors prove that every s-reflexive Hausdorff space is zero-dimensional, and indicate a close relationship between the theory of s-reflexive spaces and that of continuous selections. Several examples relating to s-reflexivity are given.

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent: (1) P is hypercontinuous; (2) the dual of P is generalized completely continuous; (3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.

In this paper, the authors investigate the spectral inclusion properties of the quadratic numerical range for unbounded Hamiltonian operators. Moreover, some examples are presented to illustrate the main results.

This paper deals with injective and projective right Hom-H-modules for a Hom-algebra H. In particular, Baer Criterion of injective Hom-module is obtained, and it is shown that HomModH is an Abelian category. Next, the authors define Hom-path algebras and construct Hom-path algebras of some quivers.

The purpose of the paper is to study sharp weak-type bounds for functions of bounded mean oscillation. Let 0 < p < ∞ be a fixed number and let I be an interval contained in ℝ. The author shows that for any φ: I → ℝ and any subset E ⊂ I of positive measure, $\begin{array}{*{20}c} {\frac{{\left| I \right|^{ - \tfrac{1}{p}} }}{{\left| E \right|^{1 - \tfrac{1}{p}} }}\int_E {\left| {\phi - \frac{1}{{\left| I \right|}}\int_I {\phi dy} } \right|dx \leqslant \left\| \phi \right\|_{BMO(I)} , 0 < p \leqslant 2,} } \\ {\frac{{\left| I \right|^{ - \tfrac{1}{p}} }}{{\left| E \right|^{1 - \tfrac{1}{p}} }}\int_E {\left| {\phi - \frac{1}{{\left| I \right|}}\int_I {\phi dy} } \right|dx \leqslant \frac{p}{{2^{\tfrac{2}{p}} }}e^{\tfrac{2}{p} - 1} \left\| \phi \right\|_{BMO(I)} , p \geqslant 2.} } \\ \end{array}$ For each p, the constant on the right-hand side is the best possible. The proof rests on the explicit evaluation of the associated Bellman function. The result is a complement of the earlier works of Slavin, Vasyunin and Volberg concerning weak-type, L ^p and exponential bounds for the BMO class.

Let f(z) be a holomorphic cusp form of weight κ with respect to the full modular group SL ₂(ℤ). Let L(s, f) be the automorphic L-function associated with f(z) and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for $k = \tfrac{1}{n}$ with n ∈ ℕ, $M_k \left( {q,f} \right) = \sum\limits_{\begin{array}{*{20}c} {\chi (\bmod q)} \\ {\chi \ne \chi _0 } \\ \end{array} } {\left| {L\left( {\frac{1}{2},f \otimes \chi } \right)} \right|^{2k} < < _k \varphi \left( q \right)(\log q)^{k^2 } ,}$ and the result also holds for any real number 0 < k < 1 under the GRH for L(s, f ⊗ χ). The authors also prove that under the GRH for L(s, f ⊗ χ), $M_k \left( {q,f} \right) > > _k \varphi (q)(log q)^{k^2 }$ for any real number k > 0 and any large prime q.

The inverse spectral problem for the Dirac operators defined on the interval [0, π] with self-adjoint separated boundary conditions is considered. Some uniqueness results are obtained, which imply that the pair of potentials (p(x), r(x)) and a boundary condition are uniquely determined even if only partial information is given on (p(x), r(x)) together with partial information on the spectral data, consisting of either one full spectrum and a subset of norming constants, or a subset of pairs of eigenvalues and the corresponding norming constants. Moreover, the authors are also concerned with the situation where both p(x) and r(x) are C ⁿ-smoothness at some given point.

The author considers the perturbed Riemann problem for a scalar Chapman-Jouguet combustion model which comes from Majda’s model with a modified, bump-type ignition function proposed in the results of Lyng and Zumbrun in 2004. Under the entropy conditions, the unique solution in a neighborhood of the origin on the (x, t) plane (t > 0) is obtained. It is found that, for some cases, the perturbed Riemann solutions are essentially different from the corresponding Riemann solutions. The perturbation may transform a strong detonation into a weak deflagration in the neighborhood of the origin. Especially, it can be observed that burning happens although the corresponding Riemann solution does not contain combustion wave, which exhibits the instability for the unburnt state.

Let $\mathbb{F}$ be the underlying base field of characteristic p > 3 and denote by $\mathfrak{M}$ the even part of the finite-dimensional simple modular Lie superalgebra $\mathcal{M}$. In this paper, the generator sets of the Lie algebra $\mathfrak{M}$ which will be heavily used to consider the derivation algebra $Der\left( \mathfrak{M} \right)$ are given. Furthermore, the derivation algebra of $\mathfrak{M}$ is determined by reducing derivations and a torus of $\mathfrak{M}$, i.e., $Der(\mathfrak{M}) = ad(\mathfrak{M}) \oplus span_\mathbb{F} \left\{ {\prod\limits_l {ad(\xi _{r + 1} \xi _l )} } \right\} \oplus span_\mathbb{F} \left\{ {adx_{i'} ad\left( {x_i \xi ^v } \right)\prod\limits_l {ad(\xi _{r + 1} \xi _l )} } \right\}.$. As a result, the derivation algebra of the even part of M does not equal the even part of the derivation superalgebra of M.

Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D − 2i} _i=0 ^D, Suppose that ⊠ denotes the tetrahedron algebra. In this paper, the authors display an action of ⊠ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat _X(ℂ), called $A,A^* ,B,B^* ,K,K^* .$ Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ⊠ on V.

This paper presents a combination of the hybrid spectral collocation technique and the spectral homotopy analysis method (SHAM for short) for solving the nonlinear boundary value problem (BVP for short) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The accuracy of the present solution is found to be in excellent agreement with the previously published solution. The authors use an averaged residual error to find the optimal convergence-control parameters. Comparisons are made between SHAM generated results, results from literature and Matlab ode45 generated results, and good agreement is observed.