Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic g...

Previous studies have shown alterations of eyeblink reflex in patients with various psychiatric disorders. It has previously been demonstrated by our group that EEG measures of the reactivity to eye opening could effectively predict patient-reported startle response in patients with acute stress reaction. In our present study, EEG spectral power analysis and eyeblink electrical startle response...

We classify all integrable triples in simple Lie algebras, up to equivalence. The importance of this problem stems from the fact that for each such equivalence class one can construct corresponding hierarchy bi-Hamiltonian PDE. simplest triple $(f,0,e)$ $\mathfrak{sl}_2$ corresponds KdV hierarchy, and $(f,0,e_\theta)$, where $f$ is sum negative root vectors $e_\theta$ highest vector a algebra, ...

A graph is color-critical if it contains an edge whose removal reduces its chromatic number. Let T n , k ${T}_{n,k}$ be the Turán with $n$ vertices and $k$ parts. Given a H $H$ let e x ( ) $ex(n,H)$ number of . Simonovits' critical theorem states that χ = + 1 $\chi (H)=k+1$ then there exists 0 ${n}_{0}(H)$ such | E $ex(n,H)=|E({T}_{n,k})|$ only extremal provided ≥ $n\ge {n}_{0}(H)$ Nikiforov pr...

We study the first-order formalism of pure four-dimensional SU(2) Yang–Mills theory with theta-term. We describe the Green functions associated to electric and magnetic flux operators à la ’t Hooft by means of gauge-invariant non-local operators. These Green functions are related to Witten’s invariants of four-manifolds. E-mail: [email protected] 2 E-mail: [email protected] E-mail:...

Motivated by an open problem and a conjecture, this work studies the of single server private information retrieval with coded side (PIR-PCSI) that was recently introduced Heidarzadeh et al. The goal PIR-PCSI is to allow user efficiently retrieve desired message ...

The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains quantum physics. Mathematically, the split between open and closed systems can be characterized by respective triviality non-triviality an auxiliary inner-product metric $\Theta=\Theta(H)$. With our attention restricted to latter, mathematically more ...

Let $E/\mathbb{Q}$ be an elliptic curve that has complex multiplication (CM) by imaginary quadratic field $K$. For a prime $p$, there exists $\theta_p \in [0, \pi]$ such $p+1-\#E(\mathbb{F}_p) = 2\sqrt{p} \cos \theta_p$. $x>0$ large, and let $I\subseteq[0,\pi]$ subinterval. We prove if $\delta>0$ $\theta>0$ are fixed numbers $\delta+\theta<\frac{5}{24}$, $x^{1-\delta}\leq h\leq x$, $|I|\geq x^{...

The aim of this paper is to introduce and obtain some characterizations of weakly $e$-irresolute functions by means of $e$-open sets defined by Ekici [6]. Also, we look into further properties relationships between weak $e$-irresoluteness and separation axioms and completely $e$-closed graphs.

It is proved that the theta series of an even lattice whose level is a power of a prime l is congruent modulo l to an elliptic modular form of level 1. The proof uses arithmetic and algebraic properties of lattices rather than methods from the theory of modular forms. The methods presented here may therefore be especially pleasing to those working in the theory of quadratic forms, and they admi...