We review and formulate results concerning strong-log-concavity in both discrete and continuous settings. Although four different proofs of preservation of strong log-concavity are known in the discrete setting (where strong log-concavity is known as “ultra-log-concavity”), preservation of strong log-concavity under convolution has apparently not been investigated previously in the continuous c...

We consider the higher order Turán inequality and log-concavity for sequences {an}n≥0 such thatan−1an+1an2=1+∑i=1mri(log⁡n)nαi+o(1nβ), where m is a nonnegative integer, αi are real numbers, ri(x) rational functions of x and0<α1<α2<⋯<αm<β. will give sufficient condition on ℓ-log-concavity n sufficiently large. Many P-recursive fall in this frame. At last, we method to find N that any n>N, holds.

A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer add...

The 25-year old LCGD Conjecture is that the genus distribution of every graph is log-concave. We present herein a new topological conjecture, called the Local Log-Concavity Conjecture. We also present a purely combinatorial conjecture, which we prove to be equivalent to the Local Log-Concavity Conjecture. We use the equivalence to prove the Local Log-Concavity Conjecture for graphs of maximum d...

Background and objective We have explored whether assessing the degree of concavity in the descending limb of the maximum expiratory flow-volume curve enhanced spirometric detection of early small airway disease. Methods We used spirometry records from 890 individuals aged ≥40 years (mean 59 years), recruited for the Burden of Obstructive Lung Disease Australia study. Central and peripheral c...

BACKGROUND Current glenoid defect measurement techniques only quantify bone loss in terms of defect diameter or surface. However, the glenoid depth plays an important role in shoulder stabilization by means of concavity compression. CASE PRESENTATION We present a case of a professional wrestler who suffered from anterior shoulder instability after sustaining a bony Bankart lesion without loss...

Poor convergence to concave boundaries is a limitation in the use of snakes as a contour approximation technique. The external force for active contours, called gradient vector flow (GVF), has provided a remarkable improvement to this problem. However, the technique requires high computation time for reliable concavity performance. In this paper, we propose an efficient solution to overcome the...

In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q−functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum Q−function and its deformations is established with respect to each of the three parameters. Sinc...