Let L(x) := x − Γ(x+t) Γ(x+s) xs−t+1, where Γ(x) is Euler’s gamma function. We determine conditions for the numbers s, t so that the function Φ(x) := − Γ(x+t) xt−s−1 L′′(x) is strongly completely monotonic on (0, ∞). Through this result we obtain some inequalities involving the ratio of gamma functions and provide some applications in the context of trigonometric sum estimation. We also give se...

We consider the 1D nonlinear Schrodinger equation (NLS) with focusing point nonlinearity, \begin{document}$ \begin{equation} i\partial_t\psi + \partial_x^2\psi \delta|\psi|^{p-1}\psi = 0, \;\;\;\;\;\;(0.1)\end{equation} $\end{document} where {\delta} {\delta}(x) is delta function supported at origin. In L^2 supercritical setting p>3 , we construct self-similar blow-up solutions belonging to ene...

in this paper, we are interested to study the sine-gordon equation in generalized functions theory introduced by colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the colombeau algebra). then we study the association concept with the classical solution.

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

Photosystem I (PSI), a photoactive protein complex that participates in the light reactions of natural photosynthesis, can exhibit photocatalytic capabilities when incorporated to electrochemical systems. Here we present a simulation for the photoelectrochemical behavior of an electrode modified with a monolayer of Photosystem I complexes during photochronoamperometric experiments in which the ...

Schur functions are the common eigenfunctions of generalized cut-and-join operators which form a closed algebra. They can be expressed as differential in time-variables and also through eigenvalues auxiliary $N\times N$ matrices $X$, known Miwa variables. Relevant for cubic Kontsevich model spin Hurwitz theory is an alternative set Q-functions. appear representation Sergeev group, substitute sy...

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

We derive a generalized counting rule for hard exclusive processes involving parton orbital angular momentum and hadron helicity flip. We start with a systematic way to enumerate the Fock components of a hadronic light-cone wave function with n partons and orbital angular momentum projection l(z). We show that the wave-function amplitude psi(n)(x(i),k(i perpendicular ),l(zi)) has a leading beha...