Derivatives of tangent function and tangent numbers

In the paper, by induction, the Fa\`a di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the sine and cosine functions, obtains explicit formulas for two Bell polynomials of the second kind for successive derivatives of sine and cosine functions, presents curious identities for the sine function, discovers explicit formulas and recurrence relations for the tangent numbers, the Bernoulli numbers, the Genocchi numbers, special values of the Euler polynomials at zero, and special values of the Riemann zeta function at even numbers, and comments on five different forms of higher order derivatives for the tangent function and on derivative polynomials of the tangent, cotangent, secant, cosecant, hyperbolic tangent, and hyperbolic cotangent functions.Comment: 17 page

Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind

In the paper, the author establishes some identities which show that the functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients involving the combinatorial numbers and the Stirling numbers of the second kind, where $t\ne0$ and $i,k\in\mathbb{N}$.Comment: 9 page

Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Dynamic Uplink/Downlink Resource Management in Flexible Duplex-Enabled Wireless Networks

Flexible duplex is proposed to adapt to the channel and traffic asymmetry for future wireless networks. In this paper, we propose two novel algorithms within the flexible duplex framework for joint uplink and downlink resource allocation in multi-cell scenario, named SAFP and RMDI, based on the awareness of interference coupling among wireless links. Numerical results show significant performance gain over the baseline system with fixed uplink/downlink resource configuration, and over the dynamic TDD scheme that independently adapts the configuration to time-varying traffic volume in each cell. The proposed algorithms achieve two-fold increase when compared with the baseline scheme, measured by the worst-case quality of service satisfaction level, under a low level of traffic asymmetry. The gain is more significant when the traffic is highly asymmetric, as it achieves three-fold increase.Comment: 7 pages, 7 figures, ICC 2017 Worksho