Let Mg be the coarse moduli space of stable curves of genus g. Eisenbud, Harris and Mumford proved a relation between certain divisors on Mg (the Brill-Noether divisors, to be described below). Calculating their classes in PicMg⊗Q, they succeeded in proving that Mg is of general type for g > 23, g+1 composite. In subsequent work, the restriction that g + 1 be composite was removed. In this pape...

One of the most important prediction problems in finite population is the prediction of a linear function of characteristic values of a finite population. In this paper the admissibility of linear predictors of an arbitrary linear function of characteristic values in a finite population under reflected normal loss function is considered. Under the super-population model, we obtain the condition...

In this paper, at first, we introduce $alpha_{mu}$-admissible, $Z_mu$-contraction and  $N_{mu}$-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions   via $alpha$-admissible simulation mappings, as well. Our results  can be viewed as extension of the corresponding results in this area.  Moreover, some examples and an application to funct...

In this paper, we study the null controllability of Mullins equation with control acting on periodic boundary. Firstly, using duality relation between and observability, express condition in terms solution backward adjoint system. After showing existence uniqueness system, determine admissible initial data class since system is not always controllable under these boundary conditions. Finally, s...

If Visser’s rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of Visser’s rules are admissible is not known. Here we study the situation for specific intermediate logics. We provide natural examples of logics for which Visser’s rule are derivable, admissible b...

We establish a Harder–Narasimhan formalism for modifications of $G$ -bundles on the Fargues–Fontaine curve. The semi-stable stratum associated stratification ${B^+_{{\rm dR}}}$ -Grassmannian coincides with variant weakly admissible locus defined by Viehmann, and its classical points agree those basic Newton stratum. When restricted to minuscule affine Schubert cells, corresponds Dat, Orlik Rapo...

We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for general admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes. 1.Introduction. In our paper Delbaen and Schacherma...