in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

OBJECTIVES To compare Telfa with the Rapid Rhino Riemann nasal pack for use following endoscopic sinus surgery. DESIGN Prospective, randomized, double-blind, paired trial. SETTING Tertiary otolaryngology hospital. PARTICIPANTS Forty-five adult patients undergoing bilateral endoscopic sinus surgery for either chronic rhinosinusitis or nasal polyps. MAIN OUTCOME MEASURES A visual analogue...

1. Classical Topics 2 1.1. Complex numbers 2 1.2. Differentiability 2 1.3. Cauchy-Riemann Equations 3 1.4. The Riemann Sphere 4 1.5. Möbius transformations 5 1.6. Integration 6 1.7. Cauchy’s Theorems and Applications 7 1.8. Properties of Analytic Functions 9 1.9. The Winding Number 11 1.10. Singularities 12 1.11. Laurent Series 13 1.12. Residue Theory 15 1.13. Normal Families 18 1.14. The Riema...

We consider the Riemann Mapping Theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (i.e. bihilomorphic map) from the upper half plane to such a domain can be realized in a certain quasianalytic class used by Ilyashenko in his work on Hilbert’s 16 problem if the angle of the domain at the boundary point to which 0 is mapped, i...

a f(x, y) dy, it is often important to know when F is differentiable and when F (x) = ∫ b a f1(x, y) dy. A sufficient condition for differentiating under the integral sign is that ∫ b a f1(x, y) dy converges uniformly; see [6, p. 260]. When we have absolute convergence, the condition |f1(x, y)| ≤ g(y) with ∫ b a g(y) dy < ∞ suffices (Weierstrass M-test and Lebesgue Dominated Convergence). If we...

in this paper, the goursat problem of a third order equation on cases of explicit solvability isinvestigated, with the help of the riemann function. some results and one theorem are given concerning theexistence and uniqueness for the solution of the suggested problem.

Let R be the class of all functions that are properly Riemann-integrable on [0, 1], and let IR be the class of all functions that are properly Riemann-integrable on [a, 1 ] for all a > 0 and for which

In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.

In this paper we propose a quantum gauge system from which we construct generalized Wilson loops which will be as quantum knots. From quantum knots we give a classification table of knots where knots are one-to-one assigned with an integer such that prime knots are bijectively assigned with prime numbers and the prime number 2 corresponds to the trefoil knot. Then by considering the quantum kno...

In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem