In its additive version, Bohr–Mollerup’s remarkable theorem states that the unique (up to an constant) convex solution f(x) equation $$\Delta f(x)=\ln x$$ on open half-line $$(0,\infty )$$ is log-gamma function $$f(x)=\ln \Gamma (x)$$ , where $$ denotes classical difference operator and $$\Gamma Euler gamma function. a recently published access book, authors provided illustrated far-reaching ge...

The usefulness of thallium-201 myocardial imaging in assessing right ventricular (RV) overloading was evaluated and compared with the electrocardiographic and hemodynamic measurements. Multiple unprocessed photoscans were obtained using a gamma camera in 47 patients who had chronic RV overload, including 28 subjects with pressure overload, 14 with volume overload and five with pressure and volu...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

This article studies the pointwise convergence for fractional Schr\"odinger operator $P^{t}_{a,\gamma}$ with complex time in one spatial dimension. Through establishing $L^2$-maximal estimates initial datum $H^{s}(\mathbb{R})$, we see that solution converges to data almost everywhere $s>\frac14 a(1-\frac1\gamma)_+$ when $0\frac{1}{2}(1-\frac{1}{\gamma})_{+}$ $a=1$. By constructing ...

We prove the global existence of non-negative unique mild solution for Cauchy problem cutoff Boltzmann equation soft potential model $$-1\le \gamma < 0$$ with small initial data in three dimensional space. Thus our result fixes gap case $$\gamma =-1$$ space authors’ previous work (He and Jiang J Stat Phys 168(2):470–481, 2017) where estimate loss term was improperly used. The other He (2017) =0...

Radiation-shielding glass is utilized in a few applications such as nuclear medicine, (PET) scans, x-rays, or treatment use. Nuclear reactors additionally require shielding from radiation types gamma, and neutron emissions. the exploration industry fields, for example, cyclotron support testing of non-destructive materials, improvement airport x-ray machines. Notwithstanding, radiation-shieldin...

Abstract In this article, we study the observability (or equivalently, controllability) of some subelliptic evolution equations depending on their step. This sheds light speed propagation these equations, notably in ‘degenerated directions’ structure. First, for any $\gamma \geq 1$ , establish a resolvent estimate Baouendi–Grushin-type operator $\Delta _{\gamma }=\partial _x^2+\left \lvert x\ri...