On finite complete rewriting systems and large subsemigroups

Let $S$ be a semigroup and $T$ be a subsemigroup of finite index in $S$ (that is, the set $S\setminus T$ is finite). The subsemigroup $T$ is also called a large subsemigroup of $S$. It is well known that if $T$ has a finite complete rewriting system then so does $S$. In this paper, we will prove the converse, that is, if $S$ has a finite complete rewriting system then so does $T$. Our proof is purely combinatorial and also constructive.Comment: We have made major changes to the paper and simplified most of the proof

Heat and work fluctuations for a harmonic oscillator

The formalism of Kundu et al. [J. Stat. Mech. (2011) P03007], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-t form of the moment generating function ~ g(s) exp[t m(s)], of the total heat flow Q from one of the baths to the particle in a given time interval t, is studied and exact explicit expressions are obtained for both m(s) and g(s). For a special case of the single particle problem that corresponds to the work done by an external stochastic force on a harmonic oscillator coupled to a thermal bath, the large-t form of the moment generating function is analyzed to obtain the exact large deviation function as well as the complete asymptotic forms of the probability density function of the work.Comment: 11 pages, 6 figure

Generalized inequalities on warped product submanifolds in nearly trans-Sasakian manifolds

In this paper, we study warped product submanifolds of nearly trans-Sasakian manifolds. The non-existence of the warped product semi-slant submanifolds of the type $N_\theta\times{_{f}N_T}$ is shown, whereas some characterization and new geometric obstructions are obtained for the warped products of the type $N_T\times{_{f}N_\theta}$. We establish two general inequalities for the squared norm of the second fundamental form. The first inequality generalizes derived inequalities for some contact metric manifolds [16, 18, 19, 24], while by a new technique, the second inequality is constructed to express the relation between extrinsic invariant (second fundamental form) and intrinsic invariant (scalar curvatures). The equality cases are also discussed.Comment: 16 page

New and emerging therapeutic options for malignant pleural mesothelioma: review of early clinical trials.

Malignant pleural mesothelioma (MPM) is a rare tumor that is challenging to control. Despite some benefit from using the multimodality-approach (surgery, combination chemotherapy and radiation), survival remains poor. However, current research produced a list of potential therapies. Here, we summarize significant new preclinical and early clinical developments in treatment of MPM, which include mesothelin specific antibody and toxin therapies, interleukin-4 (IL-4) receptor toxins, dendritic cell vaccines, immune checkpoint inhibitors, and gene-based therapies. In addition, several local modalities such as photodynamic therapy, postoperative lavage using betadine, and cryotherapy for local recurrence, have also shown to be effective for local control of disease