Representation of Finite Abelian Group Elements by Subsequence Sums

Let $G\cong C_{n_1}\oplus ... \oplus C_{n_r}$ be a finite and nontrivial abelian group with $n_1|n_2|...|n_r$. A conjecture of Hamidoune says that if $W=w_1... w_n$ is a sequence of integers, all but at most one relatively prime to $|G|$, and $S$ is a sequence over $G$ with $|S|\geq |W|+|G|-1\geq |G|+1$, the maximum multiplicity of $S$ at most $|W|$, and $\sigma(W)\equiv 0\mod |G|$, then there exists a nontrivial subgroup $H$ such that every element $g\in H$ can be represented as a weighted subsequence sum of the form $g=\sum_{i=1}^{n}w_is_i$, with $s_1... s_n$ a subsequence of $S$. We give two examples showing this does not hold in general, and characterize the counterexamples for large $|W|\geq {1/2}|G|$. A theorem of Gao, generalizing an older result of Olson, says that if $G$ is a finite abelian group, and $S$ is a sequence over $G$ with $|S|\geq |G|+D(G)-1$, then either every element of $G$ can be represented as a $|G|$-term subsequence sum from $S$, or there exists a coset $g+H$ such that all but at most $|G/H|-2$ terms of $S$ are from $g+H$. We establish some very special cases in a weighted analog of this theorem conjectured by Ordaz and Quiroz, and some partial conclusions in the remaining cases, which imply a recent result of Ordaz and Quiroz. This is done, in part, by extending a weighted setpartition theorem of Grynkiewicz, which we then use to also improve the previously mentioned result of Gao by showing that the hypothesis $|S|\geq |G|+D(G)-1$ can be relaxed to $|S|\geq |G|+d^*(G)$, where d^*(G)=\Sum_{i=1}^{r}(n_i-1). We also use this method to derive a variation on Hamidoune's conjecture valid when at least $d^*(G)$ of the $w_i$ are relatively prime to $|G|$

Transformations to additivity for binary data

Imperial Users onl

Experimental Analysis of Unsteady Aerodynamic Covert Feather Behavior

The interest in man-made flying vehicles has existed for over 100 years. Bird flight has been the major inspiration for the creation of such vehicles. More recently, UAVs (unmanned aerial vehicles) have become more popular and their use in more applications has developed the need for improved maneuverability. UAVs are also decreasing in size which has allowed them to operate within similar flight conditions as birds. Studying bird feather behavior may open doors and shed some light as to how the bird achieves such agility and control, which may then be adapted to UAV flight. In this research, the motion of the freely moving covert feathers on a live trained American kestrel and a preserved pre-existing Red-tailed hawk wing were studied. High-speed and GoPro video footage was taken of an American kestrel while landing on a perch inside of the WVU Emissions and Free Flight Wind Tunnel. The distance between the perches varied. The GoPro and high-speed cameras were setup in different locations capturing movement from a variety of perspectives. Video analysis was performed on this footage to obtain flight data, including velocity and covert feather frequency as the bird approached the landing perch. The pre-existing Red-tailed hawk wing was tested in the WVU Closed Loop Wind Tunnel. A high-speed camera was used to capture feather movements. The test regime included static and dynamic angles of attack. The dynamic motion was achieved using a motor and link system. Frequencies recorded during static angle testing were compared to frequencies found during dynamic motion. Both sets of frequencies were found to be within the same range. These recorded feather frequencies were then compared to the frequencies obtained in the free flight experiment. Frequencies observed during the free flight experiment were slightly higher than those found while testing the preserved wing

Características mecánicas del mármol de Gualba (Barcelona) bajo comprensión uniaxial

The mechanical strength of Gualba marble (Barcelona, Spain), under compressive stresses is determined. Experimen- tal results appear to be very low, mean value 391 kg/cma (5.560 psi), compared with those shown by some other mar- bles : 500-700 kg/cma, (7.000-10.000 psi). The nature of the experimental failure of this rock is ana- lized

Adjoint-Based Design of a Distributed Propulsion Concept with a Power Objective

The adjoint-based design capability in FUN3D is extended to allow efficient gradient-based optimization and design of concepts with highly integrated and distributed aero-propulsive systems. Calculations of propulsive power, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. The design capability is demonstrated by the shape optimization and propulsor sizing of NASAs PEGASUS aircraft concept. The optimization objective is the minimization of flow power at the aerodynamic interface planes for the wing-mounted propulsors, as well as the tail-cone boundary layer ingestion propulsor, subject to vehicle performance and propulsive constraints

Tissue biochemical diversity of 20 gooseberry cultivars and the effect of ethylene supplementation on postharvest life

The European gooseberry (Ribes uva-crispa) is still an understudied crop with limited data available on its biochemical profile and postharvest life. A variety of polyphenols were detected in the skin and flesh of 20 gooseberry cvs, representing mainly flavonol glycosides, anthocyanins and flavan-3-ols. In contrast, gooseberry seeds were for the first time characterised by the presence of considerable amounts of hydroxycinnamic acid glycosides tentatively identified by UPLC-QToF/MS. All cvs examined represented a good source of vitamin C while being low in sugar. Furthermore, the postharvest stability of bioactives was explored by supplementation of exogenous ethylene in air at 5 °C. Results suggest a low sensitivity of gooseberries to ethylene. The overall quality of gooseberries remained stable over two weeks, showing potential for extended bioactive life