We study log canonical thresholds (also called global canonicalthreshold or $\alpha$-invariant) of $\mathbb{R}$-linear systems. prove existence positive lower bounds in different settings, particular, proving a conjecture Ambro. then show that the Borisov-Alexeev-Borisov holds; is, given natural number $d$ and real $\epsilon$, set Fano varieties dimension with $\epsilon$-log singularities forms...

The goal of this study was to test the hypothesis that the relative amounts of the cardiac myosin heavy chain (MHC) isoforms MHC-alpha and MHC-beta change during development and transition to heart failure in the human myocardium. The relative amounts of MHC-alpha and MHC-beta in ventricular and atrial samples from fetal (gestational days 47--110) and nonfailing and failing adult hearts were de...

The aim of this paper is twofold. Firstly, we will investigate the link between condition for functions $\phi(s)$ from $(\alpha, \beta)$-metrics Douglas type to be self-concordant and k-self concordant, other objective continue recently new introduced \beta)$-metric ([17]): $$ F(\alpha,\beta)=\frac{\beta^{2}}{\alpha}+\beta+a \alpha where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ a Riemannian metric; $\b...

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

For a finite group scheme G, we continue our investigation of those finite dimensional kG-modules which are of constant Jordan type. We introduce a Quillen exact category structure C(kG) on these modules and investigate K0(C(kG)). We study which Jordan types can be realized as the Jordan types of (virtual) modules of constant Jordan type. We also briefly consider thickenings of C(kG) inside the...

Let T be a triangular ring. An additive map δ from T into itself is said to be Jordan derivable at an element Z ∈ T if δ(A)B +Aδ(B) + δ(B)A+Bδ(A) = δ(AB+BA) for any A,B ∈ T with AB + BA = Z. An element Z ∈ T is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable po...

The burden of smoking-related diseases in Jordan is increasingly evident. During 2006, chronic, noncommunicable diseases (NCDs) accounted for more than 50% of all deaths in Jordan. With this evidence in hand, we highlight the prevalence of smoking in Jordan among youth and adults and briefly review legislation that governs tobacco control in Jordan. The prevalence of smoking in Jordan remains u...

In this note, we prove weighted resolvent estimates for the semiclassical Schrodinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at infinity or obey a radial $\alpha$-Holder continuity condition, $0\leq \alpha \leq 1$, with sufficient of local $C^\alpha$ norm toward infinity. Note, however, t...

There are different inequivalent ways to define the R\'enyi capacity of a channel for fixed input distribution $P$. In 1995 paper Csisz\'ar has shown that classical discrete memoryless channels there is distinguished such quantity an operational interpretation as generalized cutoff rate constant composition coding. We show analogous notion capacity, defined in terms sandwiched quantum divergenc...