Related papers: Exact lower and upper bounds on the incomplete gam…

In this paper we give the complete characterization of the boundedness of the generalized fractional maximal operator $$ M_{\phi,\Lambda^{\alpha}(b)}f(x) : = \sup_{Q \ni x} \frac{\|f \chi_Q\|_{\Lambda^{\alpha}(b)}}{\phi (|Q|)} \qquad (x \in…

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

A real valued function $f$ defined on a convex $K$ is anemconvex function iff it satisfies $$ f((x+y)/2) \le (f(x)+f(y))/2 + 1. $$ A thorough study of approximately convex functions is made. The principal results are a sharp universal upper…

We derive an upper bound on the number of models for exact satisfiability (XSAT) of arbitrary CNF formulas F. The bound can be calculated solely from the distribution of positive and negated literals in the formula. For certain subsets of…

In this paper, we develop Windschitl's approximation formula for the gamma function to two asymptotic expansions by using a little known power series. In particular, for $n\in \mathbb{N}$ with $n\geq 4$, we have \begin{equation*} \Gamma…

In this paper upper bounds are given for the successive differences $A_{n+1}-A_{n}$ and B$_{n}-B_{n-1}$ where $A_{n}=1/(n-1) \tsum_{r=1}^{n-1}f(r/n)$, $B_{n}=1/(n+1) \tsum_{r=0}^{n}f(r/n)$ and $f$ is superquadratic function. We obtain…

In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…

We study the BMO-type functional $\kappa_{\varepsilon}(f,\mathbb R^n)$, which can be used to characterize BV functions $f\in BV(\mathbb R^n)$. The $\Gamma$-limit of this functional, taken with respect to $L^1_{\mathrm{loc}}$-convergence, is…

We prove amongs others results that the harmonic mean of $\Gamma_q(x)$ and $\Gamma_q(1/x)$ is greater than or equal to $1$ for arbitrary $x > 0$ and $q\in J$ where $J$ is a subset of $[0,+\infty)$. Also, we prove that for there is…

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds…

When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions…

The angle gamma of the standard CKM unitarity triangle can be determined from B -> D K decays with a very small irreducible theoretical error, which is only due to second-order electroweak corrections. We study these contributions and…

In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

We establish completely log-free bounds for exponential sums over the primes and the M\"{o}bius function. Let $0<\eta \leq 1/10$, and suppose $\alpha = a/q + \delta/x$, with $(a,q)=1$ and $|\delta| \leq x^{1/5 + \eta}/q$, and set $\delta_0…

We calculate the leading order corrections to the anti-B --> X(s) gamma decay in the standard model with two large flat universal extra dimensions. We find that the contributions involving the exchange of Kaluza-Klein modes of the physical…

A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

From a comparison of the total gamma-spectra calculated for different functional dependencies of level density and radiative strength functions, there were obtained both their square root relative differences and analogous data for the used…

In this paper, we reconsider the large-$a$ asymptotic expansion of the Hurwitz zeta function $\zeta(s,a)$. New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds.…

We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…