A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Barbour’s model. The model consists of four delay differential equations. Stability of the disease free equilibrium and the existence of an endemic equilibrium for this model are stated in terms of a key threshold parameter. The study of dynamics for the model shows that the endemic equilibrium is globally stable in an open region if it exists and there is no delays, and for some nonzero delays the endemic equilibrium undergoes Hopf bifurcation and a periodic orbit emerges. Some numerical results are provided to support the theoretic results in this paper. These results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy on schistosomiasis control to lengthen in prepatent period on infected definitive hosts by drug treatment (or lengthen in prepatent period on infected intermediate snails by lower water temperature).

The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.

The authors show that the Cauchy integral operator is bounded from H _ω ^p(R ¹) to h _w ^p(R ¹) (the weighted local Hardy space). To prove the results, a kind of generalized atoms is introduced and a variant of weighted “Tb theorem” is considered.

This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.

Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in [1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in mod(R). As an application, it is proved that the “Minimal Horseshoe Lemma” is true in the category of quasi-d-Koszul modules under certain conditions.

The author constructs a sequence of cubes in the infinitely dimensional hyperbolic space ℍ^∞ which is equi-coarsely equivalent to ℤ₂ ⁿ. As a corollary, it is proved that the infinitely dimensional hyperbolic space ℍ^∞ does not have property A.

In this paper, groups of order p ⁿ in which the number of subgroups of possible order is less than or equal to p ³ are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order p ⁿ in which the number of subgroups of possible order is less than or equal to p ³ and the classification of groups of order p ⁿ with a cyclic subgroup of index p ² are the same.

One-dimensional local Dirichlet spaces associated with linear diffusions are studied. The first result is to give a representation for any 1-dim local, irreducible and regular Dirichlet space. The second result is a necessary and sufficient condition for a Dirichlet space to be regular subspace of another Dirichlet space.

The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {X _i} _i=1 ^∞, if {C _u ^*(X _i)} _i=1 ^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C _u ^*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear.

In this paper, for any given observation time and suitable moving observation domains, the author establishes a sharp observability inequality for the Kirchhoff-Rayleigh plate like equation with a suitable potential in any space dimension. The approach is based on a delicate energy estimate. Moreover, the observability constant is estimated by means of an explicit function of the norm of the coefficient involved in the equation.

Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a 1-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N and the special case A = k(X) of function algebra on a finite set X are considered.

The authors prove Carleman estimates for the Schrödinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining L ^p-potentials. An L ²-level observability inequality and unique continuation results for the Schrödinger equation are also obtained.