The present paper is aimed to a brief ecological study on three species (S1, S2, S3) neutralism with mortality rates. Here all the three species posses limited resources. Neutralism is an absence of any interaction between members of a mixed population. i.e, The species may be living side by side but are unaware of each other and also cause no harm or nor beneficial to each other. A real life example is certain plant species, bacteria, animal species which do not affect each other. The model equations of the system constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight critical points are established. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex.
Traditional Ankle Foot Orthoses (AFOs) are designed to work for a range of patients. They could not tend to the needs of comfort and orthotic functions arising due to individual differences. This can be solved by custom fit AFO’s but the current methods involve a lot of manual labor. Rapid Prototyping and reverse engineering can be used on 3-D parts or models designed in CAD software. Through 3-D scanning, we design an AFO’s customized to an individual foot’s anatomy. The scanned data was used to design an AFO structure. The designed structure was virtually tested for different materials and an analysis of the same was done.
Among the different energy dissipation mechanisms, thermoelastic damping plays a vital role and need to be alleviated in resonators inorder to enhance its performance parameters by improving its thermoelastic damping limited qualityfactor, QTED. The maximum energy dissipation is also interrelated with critical length (L_c) of the plates and by optimizing the dimensions the peaking of energy dissipation can be diminished. As the size of the devices is scaled down, classical continuum theories are not able to explain the size effect related mechanical behavior at micron or submicron levels and as a result non-classical continuum theories are pioneered with the inception of internal length scale parameters. In this paper, analysis of isotropic rectangular micro-plates based on Kirchhoff model applying Modified Coupled Stress Theory is used toanalyzethe size-dependent thermoelastic damping and its impact on quality factor and critical dimensions.Hamilton principle is adapted to derive the governing equations of motion and the coupled heat conduction equation is employed to formulate the thermoelastic damping limited quality factor of the plates. Five different structural materials (PolySi, Diamond,Si, GaAs and SiC)are used for optimizing QTED which depends on the materialperformance index parameters. Thermoelastic Damping Index [TDI] and thermal diffusion length, lT. According to this work, the maximum QTED is attained for PolySi with the lowest TDI and Lcmax is obtained for SiC which is having the lowest lT. The impact of lengthscale parameters (l), vibration modes, boundary conditions (Clamped–Clamped and Simply Supported), and operating temperatures on QTED and Lcare also investigated. It is concluded that QTED is further maximized by selecting low temperatures and higher internal length scale parameters (l).The prior knowledge of QTED and Lchelp the designers to come out with high performance low loss resonators.
Biomorphological features of bones of hip joint and muscles which act on it of some species of the order Gruiformes were stated on the basis of comparative anatomical analysis. It was established that biomorphological features of the bones of hip joint of birds are caused by a specific bipedalism that lies in the location of the body’s axis relatively to the pelvic limbs. It provides the body’s confinement between two limbs in the gravitational field of the Earth. It was defined that the bones which form the hip joint of the studied species of birds are differ in shape and size. Among the investigated Gruiformes the internal structure of the proximal part of the thigh bone and the area of glenoid cavity is different, as well as location of trabecules of compact and spongy substances. The development of muscles and muscle groups that act on the hip joint depends on the load during staticolocomotion.
In this paper we define and study another interesting generalization of Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for k=2 Fibonacci quaternions, for k=3 Tribonacci quaternions and for k=4 Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also, we identify and prove the matrix representation for k-order Fibonacci quaternions. The Q_{k} matrix given for k-order Fibonacci numbers is defined for k-order Fibonacci quaternions and after the matrices with the k-order Fibonacci quaternions is obtained with help of auxiliary matrices, important relationships and identities were established.