Results 51 to 60 of about 2,422,350 (276)

Notes on three conjectures involving the digamma and generalized digamma functions

Journal of Inequalities and Applications, 2018
In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function.
Ladislav Matejíčka
doaj   +1 more source

A conjecture concerning a completely monotonic function

Computers & Mathematics with Applications, 2010
Based on a sequence of numerical computations, a conjecture is presented regarding the class of functions $H(x;a)=\exp(a)-(1+a/x)^x$, and the open problem of determining the values of $a$ for which the functions are completely monotonic with respect to $x$.
Ekaterina Shemyakova, S. I. Khashin, D. J. Jeffrey   +2 more
openaire   +2 more sources

A Workflow to Accelerate Microstructure‐Sensitive Fatigue Life Predictions

Advanced Engineering Materials, EarlyView.
This study introduces a workflow to accelerate predictions of microstructure‐sensitive fatigue life. Results from frameworks with varying levels of simplification are benchmarked against published reference results. The analysis reveals a trade‐off between accuracy and model complexity, offering researchers a practical guide for selecting the optimal ...
Luca Loiodice, Krzysztof S. Stopka, Michael D. Sangid   +2 more
wiley   +1 more source

Certain Logarithmically N-Alternating Monotonic Functions Involving Gamma and q-Gamma Functions [PDF]

, 2005
In the paper, three basic properties of the logarithmically N-alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are obtained in [W. E. Clark and M. E.
Qi, Feng
core   +3 more sources

Monotonicity and inequalities for the gamma function

Journal of Inequalities and Applications, 2017
In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x ↦ 1 24 x ( ln Γ ( x + 1 / 2 ) − x ln x + x − ln 2 π ) + 1 − 120 7 x 2 $$ x\mapsto \frac{1}{24x ( \ln \Gamma ( x+1/2 ) -x\ln x+x- \ln \sqrt{
Zhen-Hang Yang, Jing-Feng Tian
doaj   +1 more source

Completely Monotonic and Related Functions

Journal of Mathematical Analysis and Applications, 1996
Let \(L^N\) denote the class of functions defined by \[ f\in L^N\Leftrightarrow (-1)^k f^{(k)}(t)\geq 0,\quad \forall t>0,\quad \forall k,\quad 0\leq k\leq N. \] For \(N\to \infty\) we write \(f\in L\); such functions are well known as completely monotonic on \((0,\infty)\). The implication \[ f\in L^N\Rightarrow [\forall \alpha> 1: f^\alpha\in L^N] \]
openaire   +1 more source

Flexural Behavior of 3D‐Printed Porous Bouligand‐Structured Polymers: Influence of Pitch Angle and Porosity

Advanced Engineering Materials, EarlyView.
This study examines how helicoidal architectures with different porosities respond to bending. Adjusting layer angle and spacing in 3D‐printed polymers reveals clear tradeoffs between stiffness, strength, and energy absorption. Experiments and simulations highlight designs that distribute stress effectively, offering pathways for optimizing lightweight
Praveenkumar Subhash Patil, Edward D. McCarthy, Parvez Alam   +2 more
wiley   +1 more source

Deciding monotonicity of simple drawings of the complete graph

Journal of Computational Geometry
A drawing of a graph is $x$-monotone if every vertical line intersects each edge of the graph at most once. We present an $O(n^5)$ time algorithm for deciding whether a simple drawing of the complete graph $K_n$ is weakly isomorphic to an $x$-monotone ...
Oswin Aichholzer, Gelasio Salazar, Birgit Vogtenhumber   +2 more
doaj   +1 more source

Note on Completely Monotone Densities

The Annals of Mathematical Statistics, 1969
In [2] it is proved that mixtures of exponential distributions are infinitely divisible (id). In [3] it is proved that the same holds for the discrete analogue, i.e. for mixtures of geometric distributions. In this note we show that these results imply that a density function $f(x)$ (or distribution $\{p_n\}$ on the integers) is id if the function $f(x)
openaire   +4 more sources

Distinct Microstructural Characteristic Lengths Defining Notch Fatigue Crack Initiation and Propagation, and Defect Tolerance in Advanced Steels

Advanced Engineering Materials, EarlyView.
Schematic representation of modes of microcrack nucleation, growth and temporary arrestment at different boundaries, with the criteria for crack propagation in three scenarios: (1) large notch, (2) defect/small sharp notch, and (3) long crack. This work revisits and integrates results on the fatigue behavior of advanced bainitic steels (in particular ...
Lucia Morales‐Rivas
wiley   +1 more source