Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement

Difference control schemes for controlling unstable fixed points become important if the exact position of the fixed point is unavailable or moving due to drifting parameters. We propose a memory difference control method for stabilization of a priori unknown unstable fixed points by introducing a memory term. If the amplitude of the control applied in the previous time step is added to the present control signal, fixed points with arbitrary Lyapunov numbers can be controlled. This method is also extended to compensate arbitrary time steps of measurement delay. We show that our method stabilizes orbits of the Chua circuit where ordinary difference control fails.Comment: 5 pages, 8 figures. See also chao-dyn/9810029 (Phys. Rev. E 70, 056225) and nlin.CD/0204031 (Phys. Rev. E 70, 046205

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Minimal Work Principle and its Limits for Classical Systems

The minimal work principle asserts that work done on a thermally isolated equilibrium system, is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well-defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For non-ergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte

Phenomenological Consequences of Right-handed Down Squark Mixings

The mixings of $d_R$ quarks, hidden from view in Standard Model (SM), are naturally the largest if one has an Abelian flavor symmetry. With supersymmetry (SUSY) their effects can surface via $\tilde d_R$ squark loops. Squark and gluino masses are at TeV scale, but they can still induce effects comparable to SM in $B_d$ (or $B_s$) mixings, while $D^0$ mixing could be close to recent hints from data. In general, CP phases would be different from SM, as may be indicated by recent B Factory data. Presence of non-standard soft SUSY breakings with large $\tan\beta$ could enhance $b\to d\gamma$ (or $s\gamma$) transitions.Comment: Version to appear in Phys. Rev. Let

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.Comment: LaTeX v2.09, 14 pages with 4 PNG figure

The Fourth Element: Characteristics, Modelling, and Electromagnetic Theory of the Memristor

In 2008, researchers at HP Labs published a paper in {\it Nature} reporting the realisation of a new basic circuit element that completes the missing link between charge and flux-linkage, which was postulated by Leon Chua in 1971. The HP memristor is based on a nanometer scale TiO$_2$ thin-film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and nonvolatile RAM (NVRAM), they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application specific integrated circuits (ASICs) and field programmable gate arrays (FPGAs). A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for Integrated Circuits (ICs). This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.Comment: 28 pages, 14 figures, Accepted as a regular paper - the Proceedings of Royal Society

SU(3) and Nonet Breaking Effects in KL→γγK_L \to \gamma \gamma Induced by s→d+2gluons \to d + 2{gluon} due to Anomaly

In this paper we study the effects of $s\to d + 2{gluon}$ on $K_L \to \gamma\gamma$ in the Standard Model. We find that this interaction can induce new sizeable SU(3) and U(3) nonet breaking effects in $K_L - \eta, \eta'$ transitions and therefore in $K_L\to \gamma\gamma$ due to large matrix elements of $$ from QCD anomaly. These new effects play an important role in explaining the observed value. We also study the effects of this interaction on the contribution to $\Delta m_{K_L-K_S}$.Comment: RevTex, 12 Pages, no figures. Version to be published in PR

Nutritional and Biological Evaluation of Leaves of Mangifera indica from Mauritius

Mango trees are evergreen plants that are present all around Mauritius. In this study, mango leaves, Mangifera indica grown in Mauritius were investigated for their nutritional values involving proximate composition, total flavonoid (TFC), total phenolic (TPC), and mineral content, and phytochemicals as well as its antioxidant and antibacterial properties. The ash, crude fat, neutral detergent fiber (NDF), acid detergent fiber (ADF), and acid detergent lignin (ADL) of the mango leaves were found to be 12.61, 3.92, 35.32, 34.98, and 12.86%, respectively. The calcium content (2.15%) was above the normal required range, while the phosphorus content (0.12%) and crude protein content (13.60%) were within the normal required range of common fodders. The phytochemical results showed the presence of saponins, alkaloids, phenols, tannins, and flavonoids in the crude, EtOAC, and MeOH extracts. The values of TPC and TFC were higher for the EtOAC extract compared to the MeOH extract. Several secondary metabolites were identified from the leaves of the Mangifera indica which include 11 phenols, 4 xanthones, 9 flavanols, 10 benzophenones, 7 terpenoids, and 4 derivatives of gallotannins using UPLC-MS/MS. The presence of these metabolites is responsible for good antioxidant and antibacterial properties. Hence, mango leaves can be exploited for its potential use as a supplementary fodder for ruminants

Non-invertible transformations and spatiotemporal randomness

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems can generate random dynamics. For instance, the chaotic Chua's circuit coupled to a circuit with a non-invertible I-V characteristic can generate unpredictable dynamics. In general, a nonperiodic time-series with truncated exponential behavior can be converted into unpredictable dynamics using non-invertible transformations. Using a new theoretical framework for chaos and randomness, we investigate some classes of coupled map lattices. We show that, in some cases, these systems can produce completely unpredictable dynamics. In a similar fashion, we explain why some wellknown spatiotemporal systems have been found to produce very complex dynamics in numerical simulations. We discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao