Functional analytic analysis of the pursuit problem of Kelendzeridze

Functional analysis of pursuit problems based on theory of moment

Character of Locally Inequivalent Classes of States and Entropy of Entanglement

In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite number of deterministically locally inequivalent classes of pure bipartite states in the same Schmidt rank (starting from three) having same amount of entanglement. Further, if there exists incomparable states with same entanglement in higher Schmidt ranks (greater than three), then they should differ in at least three Schmidt coefficients.Comment: 4 pages, revtex4, no figure, accepted in Physical Review A (rapid communications

Design of high speed proprotors using multiobjective optimization techniques

An integrated, multiobjective optimization procedure is developed for the design of high speed proprotors with the coupling of aerodynamic, dynamic, aeroelastic, and structural criteria. The objectives are to maximize propulsive efficiency in high speed cruise and rotor figure of merit in hover. Constraints are imposed on rotor blade aeroelastic stability in cruise and on total blade weight. Two different multiobjective formulation procedures, the Min summation of beta and the K-S function approaches are used to formulate the two-objective optimization problems

Quadratic non-residues and non-primitive roots satisfying a coprimality condition

Let $q\geq 1$ be any integer and let $\epsilon \in [\frac{1}{11}, \frac{1}{2})$ be a given real number. In this short note, we prove that for all primes $p$ satisfying p\equiv 1\pmod{q}, \quad \log\log p > \frac{\log 6.83}{\frac{1}{2}-\epsilon} \mbox{ and } \frac{\phi(p-1)}{p-1} \leq \frac{1}{2} - \epsilon, there exists a quadratic non-residue $g$ which is not a primitive root modulo $p$ such that $gcd\left(g, \frac{p-1}{q}\right) = 1$.Comment: to appear in Bulletin of the Australian Mathematical Societ

Improved mild steel for structural purposes

THE majority of structures is usually constructed from steels with yield points not more than 17 t.s.i. but the recent developments in this field have led to structural steels with yield points between 20 t.s.i. and 40 t.s.i. Additions of about 2% allo- ying elements can produce appreciably higher yield strength. These low alloy steels show good impact properties and render them suitable for use at temp-eratures down to -50°C or even lower.The improvement in yield, tensile and impact properties are not achi- eved at the expense of weldability because carbon, the principal cause of welding trouble, is maintain- ed at a very low level. The type of steels to be dis-cussed has a low carbon I'5 Mn base with very small quantity of alloying elements, and it would not be improper to term them as improved mild steel. By making use of strengthening mechanisms in mild steel containing residual alloying addition, it would be possible to use a cheaper steel in structures needing a more highly alloyed steel, and a significant reduction in cost can be achieved. Also, by replacing mild steel with this improved variety, thinner sections can be used in structures and this would increase the payload of vehicle and a consequent reduction in freight cost

Streamer evolution arrest governed amplified AC breakdown strength of graphene and CNT colloids

The present article experimentally explores the concept of large improving the AC dielectric breakdown strength of insulating mineral oils by the addition of trace amounts of graphene or CNTs to form stable dispersions. The nano-oils infused with these nanostructures of high electronic conductance indicate superior AC dielectric behaviour in terms of augmented breakdown strength compared to the base oils. Experimental observations of two grades of synthesized graphene and CNT nano-oils show that the nanomaterials not only improve the average breakdown voltage but also significantly improve the reliability and survival probabilities of the oils under AC high voltage stressing. Improvement of the tune of ~ 70-80 % in the AC breakdown voltage of the oils has been obtained via the present concept. The present study examines the reliability of such nano-colloids with the help of two parameter Weibull distribution and the oils show greatly augmented electric field bearing capacity at both standard survival probability values of 5 % and 63.3 %. The fundamental mechanism responsible for such observed outcomes is reasoned to be delayed streamer development and reduced streamer growth rates due to effective electron scavenging by the nanostructures from the ionized liquid insulator. A mathematical model based on the principles of electron scavenging is proposed to quantify the amount of electrons scavenged by the nanostructures. The same is then employed to predict the enhanced AC breakdown voltage and the experimental values are found to match well with the model predictions. The present study can have strong implications in efficient, reliable and safer operation of real life AC power systems

Optimum design of high speed prop rotors including the coupling of performance, aeroelastic stability and structures

An optimization procedure is developed for the design of high speed prop-rotors to be used in civil tiltrotor applications. The goal is to couple aerodynamic performance, aeroelastic stability, and structural design requirements inside a closed-loop optimization procedure. The objective is to minimize the gross weight and maximize the propulsive efficiency in high speed cruise. Constraints are imposed on the rotor aeroelastic stability in both hover and cruise and rotor figure of merit in hover. Both structural and aerodynamic design variables are used